# Zero-Shot Question Generation from Knowledge Graphs for Unseen Predicates
and Entity Types

Hady Elsahar, Christophe Gravier, Frederique Laforest
Université de Lyon
Laboratoire Hubert Curien
Saint-Étienne, France
{hady.elsahar, christophe.gravier<EMAIL_ADDRESS>

###### Abstract

We present a neural model for question generation from knowledge base triples
in a “Zero-Shot” setup, that is generating questions for triples containing
predicates, subject types or object types that were not seen at training time.
Our model leverages triples occurrences in the natural language corpus in an
encoder-decoder architecture, paired with an original part-of-speech copy
action mechanism to generate questions. Benchmark and human evaluation show
that our model sets a new state-of-the-art for zero-shot QG.

##  1 Introduction

Questions Generation (QG) from Knowledge Graphs is the task consisting in
generating natural language questions given an input knowledge base (KB)
triple Serban et al. (2016). QG from knowledge graphs has shown to improve the
performance of existing factoid question answering (QA) systems either by dual
training or by augmenting existing training datasets Dong et al. (2017);
Khapra et al. (2017). Those methods rely on large-scale annotated datasets
such as SimpleQuestions Bordes et al. (2015). In practice many of the
predicates and entity types in KB are not covered by those annotated datasets.
For example $75\%$ of Freebase predicates are not covered by SimpleQuestions.
So, one challenge for QG from knowledge graphs is to adapt to predicates and
entity types that were not seen at training time (aka Zero-Shot QG).
Ultimately, generating questions to predicates and entity types unseen at
training time will allow QA systems to cover predicates and entity types that
would not have been used for QA otherwise.

Intuitively, a human who is given the task to write a question on a fact
offered by a KB, would read natural language sentences where the entity or the
predicate of the fact occur, and build up questions that are aligned with what
he reads from both a lexical and grammatical standpoint. In this paper, we
propose a model for Zero-Shot Question Generation that follows this intuitive
process. In addition to the input KB fact, we feed our model with a set of
textual contexts paired with the input KB triple through distant supervision.
Our model derives an encoder-decoder architecture, in which the encoder
encodes the input KB triple, along with a set of textual contexts into hidden
representations. Those hidden representations are fed to a decoder equipped
with an attention mechanism to generate an output question.
In the Zero-Shot setup, the emergence of new predicates and new class types
during test time requires new lexicalizations to express these predicates and
classes in the output question. These lexicalizations might not be encountered
by the model during training time and hence do not exist in the model
vocabulary, or have been seen only few times not enough to learn a good
representation for them by the model. Recent works on Text Generation tackle
the rare words/unknown words problem using copy actions Luong et al. (2015);
Gülçehre et al. (2016): words with a specific position are copied from the
source text to the output text – although this process is blind to the role
and nature of the word in the source text. Inspired by research in open
information extraction Fader et al. (2011) and structure-content neural
language models Kiros et al. (2014), in which part-of-speech tags represent a
distinctive feature when representing relations in text, we extend these
positional copy actions. Instead of copying a word in a specific position in
the source text, our model copies a word with a specific part-of-speech tag
from the input text – we refer to those as part-of-speech copy actions.
Experiments show that our model using contexts through distant supervision
significantly outperforms the strongest baseline among six ($+2.04$ BLEU-4
score). Adding our copy action mechanism further increases this improvement
($+2.39$). Additionally, a human evaluation complements the comprehension of
our model for edge cases; it supports the claim that the improvement brought
by our copy action mechanism is even more significant than what the BLEU score
suggests.

##  2 Related Work

QG became an essential component in many applications such as education
Heilman and Smith (2010), tutoring Graesser et al. (2004); Evens and Michael
(2006) and dialogue systems Shang et al. (2015). In our paper we focus on the
problem of QG from structured KB and how we can generalize it to unseen
predicates and entity types. Seyler et al. (2015) generate quiz questions from
KB triples. Verbalization of entities and predicates relies on their existing
labels in the KB and a dictionary. Serban et al. (2016) use an encoder-decoder
architecture with attention mechanism trained on the SimpleQuestions dataset
Bordes et al. (2015). Dong et al. (2017) generate paraphrases of given
questions to increases the performance of QA systems; paraphrases are
generated relying on paraphrase datasets, neural machine translation and rule
mining. Khapra et al. (2017) generate a set of QA pairs given a KB entity.
They model the problem of QG as a sequence to sequence problem by converting
all the KB entities to a set of keywords. None of the previous work in QG from
KB address the question of generalizing to unseen predicates and entity types.
Textual information has been used before in the Zero-Shot learning. Socher et
al. (2013) use information in pretrained word vectors for Zero-Shot visual
object recognition. Levy et al. (2017) incorporates a natural language
question to the relation query to tackle Zero-Shot relation extraction
problem.

Previous work in machine translation dealt with rare or unseen word problem
problem for translating names and numbers in text. Luong et al. (2015) propose
a model that generates positional placeholders pointing to some words in
source sentence and copy it to target sentence (copy actions). Gülçehre et al.
(2016); Gu et al. (2016) introduce separate trainable modules for copy actions
to adapt to highly variable input sequences, for text summarization. For text
generation from tables, Lebret et al. (2016) extend positional copy actions to
copy values from fields in the given table. For QG, Serban et al. (2016) use a
placeholder for the subject entity in the question to generalize to unseen
entities. Their work is limited to unseen entities and does not study how they
can generalize to unseen predicates and entity types.

Figure 1: The proposed model for Question Generation. The model consists of a
single fact encoder and $n$ textual context encoders, each consists of a
separate GRU. At each time step $t$, two attention vectors generated from the
two attention modules are fed to the decoder to generate the next word in the
output question.

##  3 Model

Let $F=\\{s,p,o\\}$ be the input fact provided to our model consisting of a
subject $s$, a predicate $p$ and an object $o$, and $C$ be the set of textual
contexts associated to this fact. Our goal is to learn a model that generates
a sequence of $T$ tokens $Y=y_{1},y_{2},\ldots,y_{T}$ representing a question
about the subject $s$, where the object $o$ is the correct answer. Our model
approximates the conditional probability of the output question given an input
fact $p(Y|F)$, to be the probability of the output question, given an input
fact and the additional textual context $C$, modelled as follows:

$\displaystyle p(Y|F)$ $\displaystyle=\prod_{t=1}^{T}p(y_{t}|y_{<t},F,C)$ (1)

where $y_{<t}$ represents all previously generated tokens until time step $t$.
Additional textual contexts are natural language representation of the triples
that can be drawn from a corpus – our model is generic to any textual contexts
that can be additionally provided, though we describe in Section 4.1 how to
create such texts from Wikipedia.

Our model derives the encoder-decoder architecture of Sutskever et al. (2014);
Bahdanau et al. (2014) with two encoding modules: a feed forward architecture
encodes the input triple (sec. 3.1) and a set of recurrent neural network
(RNN) to encode each textual context (sec. 3.2). Our model has two attention
modules Bahdanau et al. (2014): one acts over the input triple and another
acts over the input textual contexts (sec. 3.4). The decoder (sec. 3.3) is
another RNN that generates the output question. At each time step, the decoder
chooses to output either a word from the vocabulary or a special token
indicating a copy action (sec. 3.5) from any of the textual contexts.

###  3.1 Fact Encoder

Given an input fact $F=\\{s,p,o\\}$, let each of $e_{s}$, $e_{p}$ and $e_{o}$
be a 1-hot vectors of size $K$. The fact encoder encodes each 1-hot vector
into a fixed size vector $h_{s}=\mathbf{E_{f}}\,e_{s}$,
$h_{p}=\mathbf{E_{f}}\,e_{p}$ and $h_{o}=\mathbf{E_{f}}\,e_{o}$, where
$\mathbf{E_{f}}\in\mathbb{R}^{H_{k}\times K}$ is the KB embedding matrix,
$H_{k}$ is the size of the KB embedding and $K$ is the size of the KB
vocabulary. The _encoded fact_ $h_{f}\in\mathbb{R}^{3H_{k}}$ represents the
concatenation of those three vectors and we use it to initialize the decoder.

$\displaystyle h_{f}=[h_{s};\enspace h_{p};\enspace h_{o}]$ (2)

Following Serban et al. (2016), we learn $\mathbf{E_{f}}$ using TransE Bordes
et al. (2015). We fix its weights and do not allow their update during
training time.

###  3.2 Textual Context Encoder

Given a set of $n$ textual contexts $C=\\{c_{1},c_{2},\ldots,c_{n}\
:c_{j}=(x_{1}^{j},x_{2}^{j},\ldots,x^{j}_{|c_{j}|})\\}$, where $x_{i}^{j}$
represents the 1-hot vector of the $i^{th}$ token in the $j^{th}$ textual
context $c_{j}$, and $|c_{j}|$ is the length of the $j^{th}$ context. We use a
set of $n$ Gated Recurrent Neural Networks (GRU) Cho et al. (2014) to encode
each of the textual concepts separately:

$\displaystyle h_{i}^{c_{j}}=GRU_{j}\left(\mathbf{E_{c}}\,x_{i}^{j},\enspace
h_{i-1}^{c_{j}}\right)$ (3)

where $h_{i}^{c_{j}}\in\mathbb{R}^{H_{c}}$ is the hidden state of the GRU that
is equivalent to $x_{i}^{j}$ and of size $H_{c}$ . $\mathbf{E_{c}}$ is the
input word embedding matrix. The _encoded context_ represents the encoding of
all the textual contexts; it is calculated as the concatenation of all the
final states of all the encoded contexts:

$\displaystyle h_{c}$
$\displaystyle=[h^{c_{1}}_{|c_{1}|};h^{c_{2}}_{|c_{2}|};\ldots;h^{c_{n}}_{|c_{n}|}].$
(4)

###  3.3 Decoder

For the decoder we use another GRU with an attention mechanism Bahdanau et al.
(2014), in which the decoder hidden state $s_{t}\in\mathbb{R}^{H_{d}}$ at each
time step $t$ is calculated as:

$\displaystyle s_{t}$ $\displaystyle=z_{t}\circ
s_{t-1}+(1-z_{t})\circ\tilde{s}_{t}\enspace,$ (5)

Where:

$\displaystyle\tilde{s}_{t}$
$\displaystyle=tanh\left(WE_{w}y_{t-1}+U[r_{t}\circ
s_{t-1}]+A\,[a^{f}_{t};a^{c}_{t}]\right)$ (6) $\displaystyle z_{t}$
$\displaystyle=\sigma\left(W_{z}\,E_{w}\,y_{t-1}+U_{z}\,s_{t-1}+A_{z}\,[a^{f}_{t};a^{c}_{t}]\right)$
(7) $\displaystyle r_{t}$
$\displaystyle=\sigma\left(W_{r}\,E_{w}\,y_{t-1}+U_{r}\,s_{t-1}+A_{r}\,[a^{f}_{t};a^{c}_{t}]\right)$
(8)

$W,W_{z},W_{r}\in\mathbb{R}^{m\times H_{d}}$,
$U,U_{z},U_{r},A,A_{z},A_{r}\in\mathbb{R}^{H_{d}\times H_{d}}$ are learnable
parameters of the GRU. $E_{w}\in\mathbf{R}^{m\times V}$ is the word embedding
matrix, $m$ is the word embedding size and $H_{d}$ is the size of the decoder
hidden state. $a^{f}_{t}$, $a^{c}_{t}$ are the outputs of the fact attention
and the context attention modules respectively, detailed in the following
subsection.
In order to enforce the model to pair output words with words from the textual
inputs, we couple the word embedding matrices of both the decoder $E_{w}$ and
the textual context encoder $E_{c}$ (eq.(3)). We initialize them with GloVe
embeddings Pennington et al. (2014) and allow the network to tune them.
The first hidden state of the decoder $s_{0}=[h_{f};\,h_{c}]$ is initialized
using a concatenation of the encoded fact (eq.(2)) and the encoded context
(eq.(4)) .
At each time step $t$, after calculating the hidden state of the decoder, the
conditional probability distribution over each token $y_{t}$ of the generated
question is computed as the $softmax(W_{o}\,s_{t})$ over all the entries in
the output vocabulary, $W_{o}\in\mathbb{R}^{H_{d}\times V}$ is the weight
matrix of the output layer of the decoder.

###  3.4 Attention

Our model has two attention modules:
Triple attention over the input triple to determine at each time step $t$ an
attention-based encoding of the input fact $a^{f}_{t}\in\mathbb{R}^{H_{k}}$:

$\displaystyle
a^{f}_{t}=\alpha_{s,t}\,h_{s}+\alpha_{p,t}\,h_{p}+\alpha_{s,t}\,h_{o}\enspace,$
(9)

$\alpha_{s,t},\alpha_{p,t},\alpha_{o,t}$ are scalar values calculated by the
attention mechanism to determine at each time step which of the encoded
subject, predicate, or object the decoder should attend to.
Textual contexts attention over all the hidden states of all the textual
contexts $a^{c}_{t}\in\mathbb{R}^{H_{c}}$:

$\displaystyle
a^{c}_{t}=\sum_{i=1}^{|C|}\sum_{j=1}^{|c_{i}|}\alpha_{t,j}^{c_{i}}\,h_{j}^{c_{i}}\enspace,$
(10)

$\alpha_{t,j}^{c_{i}}$ is a scalar value determining the weight of the
$j^{th}$ word in the $i^{th}$ context $c^{i}$ at time step $t$.

Given a set of encoded input vectors $I=\\{h_{1},h_{2},...h_{k}\\}$ and the
decoder previous hidden state $s_{t-1}$, the attention mechanism calculates
$\alpha_{t}=\alpha_{i,t},\ldots,\alpha_{k,t}$ as a vector of scalar weights,
each $\alpha_{i,t}$ determines the weight of its corresponding encoded input
vector $h_{i}$.

$\displaystyle e_{i,t}$ $\displaystyle=\mathbf{v_{a}}^{\top}\enspace
tanh(\mathbf{W_{a}\,s_{t-1}+U_{a}\,h_{i}})$ (11) $\displaystyle\alpha_{i,t}$
$\displaystyle=\frac{exp\left(e_{i,t}\right)}{\sum_{j=1}^{k}exp\left(e_{j,t}\right)}\enspace,$
(12)

where $\mathbf{v_{a}},\mathbf{W_{a}},\mathbf{U_{a}}$ are trainable weight
matrices of the attention modules. It is important to notice here that we
encode each textual context separately using a different GRU, but we calculate
an overall attention over all tokens in all textual contexts: at each time
step the decoder should ideally attend to only one word from all the input
contexts.

What caused the [C1_NOUN] of the [C3_NOUN] [S] ?
---
C1 | [S] death by [O]
[S] [C1_NOUN] [C1_ADP] [O]
C2 | Disease
[C2_NOUN]
C3 | Musical artist
[C3_ADJ] [C3_NOUN]
Table 1: An annotated example of part-of-speech copy actions from several
input textual contexts (C1, C2, C3), the words or placeholders in bold are
copied in the generated question

###  3.5 Part-Of-Speech Copy Actions

We use the method of Luong et al. (2015) by modeling all the copy actions on
the data level through an annotation scheme. This method treats the model as a
black box, which makes it adaptable to any text generation model. Instead of
using positional copy actions, we use the part-of-speech information to decide
the alignment process between the input and output texts to the model. Each
word in every input textual context is replaced by a special token containing
a combination of its context id (e.g. C1) and its POS tag (e.g. NOUN). Then,
if a word in the output question matches a word in a textual context, it is
replaced with its corresponding tag as shown in Table 1.
Unlike Serban et al. (2016); Lebret et al. (2016) we model the copy actions in
the input and the output levels. Our model does not have the drawback of
losing the semantic information when replacing words with generic
placeholders, since we provide the model with the input triple through the
fact encoder. During inference the model chooses to either output words from
the vocabulary or special tokens to copy from the textual contexts. In a post-
processing step those special tokens are replaced with their original words
from the textual contexts.

##  4 Textual contexts dataset

As a source of question paired with KB triples we use the SimpleQuestions
dataset Bordes et al. (2015). It consists of 100K questions with their
corresponding triples from Freebase, and was created manually through
crowdsourcing. When asked to form a question from an input triple, human
annotators usually tend to mainly focus on expressing the predicate of the
input triple. For example, given a triple with the predicate
fb:spacecraft/manufacturer the user may ask ”What is the manufacturer of [S]
?”. Annotators may specify the entity type of the subject or the object of the
triple: ”What is the manufacturer of the spacecraft [S]?” or ”Which company
manufactures [S]?”. Motivated by this example we chose to associate each input
triple with three textual contexts of three different types. The first is a
phrase containing lexicalization of the predicate of the triple. The second
and the third are two phrases containing the entity type of the subject and
the object of the triple. In what follows we show the process of collection
and preprocessing of those textual contexts.

###  4.1 Collection of Textual Contexts

We extend the set of triples given in the SimpleQuestions dataset by using the
FB5M Bordes et al. (2015) subset of Freebase. As a source of text documents,
we rely on Wikipedia articles.

#### Predicate textual contexts:

In order to collect textual contexts associated with the SimpleQuestions
triples, we follow the distant supervision setup for relation extraction Mintz
et al. (2009). The distant supervision assumption has been effective in
creating training data for relation extraction and shown to be 87% correct
Riedel et al. (2010) on Wikipedia text.
First, we align each triple in the FB5M KB to sentences in Wikipedia if the
subject and the object of this triple co-occur in the same sentence. We use a
simple string matching heuristic to find entity mentions in text111 We map
Freebase entities to Wikidata through the Wikidata property P646, then we
extract their labels and aliases. We use the Wikidata truthy dump:
https://dumps.wikimedia.org/wikidatawiki/entities/. Afterwards we reduce the
sentence to the set of words that appear on the dependency path between the
subject and the object mentions in the sentence. We replace the positions of
the subject and the object mentions with [S] and [O] to the keep track of the
information about the direction of the relation. The top occurring pattern for
each predicate is associated to this predicate as its textual context. Table 2
shows examples of predicates and their corresponding textual context.

#### Sub-Type and Obj-Type textual contexts:

We use the labels of the entity types as the sub-type and obj-type textual
contexts. We collect the list of entity types of each entity in the FB5M
through the predicate fb:type/instance. If an entity has multiple entity types
we pick the entity type that is mentioned the most in the first sentence of
each Wikipedia article. Thus the textual contexts will opt for entity types
that is more natural to appear in free text and therefore questions.

Freebase Relation | Predicate Textual Context
---|---
person/place_of_birth | [O] is birthplace of [S]
currency/former_countries | [S] was currency of [O]
airline_accident/operator | [S] was accident for [O]
genre/artists | [S] became a genre of [O]
risk_factor/diseases | [S] increases likelihood of [O]
book/illustrations_by | [S] illustrated by [O]
religious_text/religion | [S] contains principles of [O]
spacecraft/manufacturer | [S] was spacecraft developed by [O]
Table 2: Table showing an example of textual contexts extracted for freebase
predicates

###  4.2 Generation of Special tokens

To generate the special tokens for copy actions (sec. 3.5) we run POS tagging
on each of the input textual contexts222For the predicate textual contexts we
run pos tagging on the original text not the lexicalized dependency path. We
replace every word in each textual context with a combination of its context
id (e.g. C1) and its POS tag (e.g. NOUN). If the same POS tag appears multiple
times in the textual context, it is given an additional id (e.g. C1_NOUN_2).
If a word in the output question overlaps with a word in the input textual
context, this word is replaced by its corresponding tag.
For sentence and word tokenization we use the Regex tokenizer from the NLTK
toolkit Bird (2006), and for POS tagging and dependency parsing we use the
Spacy333https://spacy.io/ implementation.

##  5 Experiments

###  5.1 Zero-Shot Setups

We develop three setups that follow the same procedure as Levy et al. (2017)
for Zero-Shot relation extraction to evaluate how our model generalizes to: 1)
unseen predicates, 2) unseen sub-types and 3) unseen obj-types.
For the unseen predicates setup we group all the samples in SimpleQuestions by
the predicate of the input triple, and keep groups that contain at least 50
samples. Afterwards we randomly split those groups to 70% train, 10% valid and
20% test mutual exclusive sets respectively. This guarantees that if the
predicate fb:person/place_of_birth for example shows during test time, the
training and validation set will not contain any input triples having this
predicate. We repeat this process to create 10 cross validation folds, in our
evaluation we report the mean and standard deviation results across those 10
folds. While doing this we make sure that the number of samples in each fold –
not only unique predicates – follow the same 70%, 30%, 10% distribution. We
repeat the same process for the subject entity types and object entity types
(answer types) individually. Similarly, for example in the unseen object-type
setup, the question ”Which artist was born in Berlin?” appearing in the test
set means that, there is no question in the training set having an entity of
type artist. Table 3 shows the mean number of samples, predicates, sub-types
and obj-types across the 10 folds for each experiment setup.

|  | Train | Valid | Test
---|---|---|---|---
pred | # pred | 169.4 | 24.2 | 48.4
| # samples | 55566.7 | 7938.1 | 15876.2
| % samples | 70.0 $\pm$ 2.77 | 10.0 $\pm$ 1.236 | 20.0 $\pm$ 2.12
sub-types | # types | 112.7 | 16.1 | 32.2
| # samples | 60002.6 | 8571.8 | 17143.6
| % samples | 70.0 $\pm$ 7.9 | 10.0 $\pm$ 3.6 | 20.0 $\pm$ 6.2
obj-types | # types | 521.6 | 189.9 | 282.2
| # samples | 57878.1 | 8268.3 | 16536.6
| % samples | 70.0 $\pm$ 4.7 | 10.0 $\pm$ 2.5 | 20.0 $\pm$ 3.8
Table 3: Dataset statistics across 10 folds for each experiment

###  5.2 Baselines

#### SELECT

is a baseline built from Serban et al. (2016) and adapted for the zero shot
setup. During test time given a fact $F$, this baseline picks a fact $F_{c}$
from the training set and outputs the question that corresponds to it. For
evaluating unseen predicates, $F_{c}$ has the same answer type (obj-type) as
$F$. And while evaluating unseen sub-types or obj-types, $F_{c}$ and $F$ have
the same predicate.

#### R-TRANSE

is an extension that we propose for SELECT. The input triple is encoded using
the concatenation of the TransE embeddings of the subject, predicate and
object. At test time, R-TRANSE picks a fact from the training set that is the
closest to the input fact using cosine similarity and outputs the question
that corresponds to it. We provide two versions of this baseline: R-TRANSE
which indexes and retrieves raw questions with only a single placeholder for
the subject label, such as in Serban et al. (2016). And R-TRANSEcopy which
indexes and retrieves questions using our copy actions mechanism (sec. 3.5).

#### IR

is an information retrieval baseline. Information retrieval has been used
before as baseline for QG from text input Rush et al. (2015); Du et al.
(2017). We rely on the textual context of each input triple as the search
keyword for retrieval. First, the IR baseline encodes each question in the
training set as a vector of TF-IDF weights Joachims (1997) and then does
dimensionality reduction through LSA Halko et al. (2011). At test time the
textual context of the input triple is converted into a dense vector using the
same process and then the question with the closest cosine distance to the
input is retrieved. We provide two versions of this baseline: IR on raw text
and IRcopy on text with our placeholders for copy actions.

#### Encoder-Decoder.

Finally, we compare our model to the Encoder-Decoder model with a single
placeholder, the best performing model from Serban et al. (2016). We
initialize the encoder with TransE embeddings and the decoder with GloVe word
embeddings. Although this model was not originally built to generalize to
unseen predicates and entity types, it has some generalization abilities
represented in the encoded information in the pre-trained embeddings.
Pretrained KB terms and word embeddings encode relations between entities or
between words as translations in the vector space. Thus the model might be
able to map new classes or predicates in the input fact to new words in the
output question.

| Model | BLEU-1 | BLEU-2 | BLEU-3 | BLEU-4 | ROUGEL | METEOR
---|---|---|---|---|---|---|---
Unseen Predicates | SELECT | 46.81 $\pm$ 2.12 | 38.62 $\pm$ 1.78 | 31.26 $\pm$ 1.9 | 23.66 $\pm$ 2.22 | 52.04 $\pm$ 1.43 | 27.11 $\pm$ 0.74
IR | 48.43 $\pm$ 1.64 | 39.13 $\pm$ 1.34 | 31.4 $\pm$ 1.66 | 23.59 $\pm$ 2.36 | 52.88 $\pm$ 1.24 | 27.34 $\pm$ 0.55
IRCOPY | 48.22 $\pm$ 1.84 | 38.82 $\pm$ 1.5 | 31.01 $\pm$ 1.72 | 23.12 $\pm$ 2.24 | 52.72 $\pm$ 1.26 | 27.24 $\pm$ 0.57
R-TRANSE | 49.09 $\pm$ 1.69 | 40.75 $\pm$ 1.42 | 33.4 $\pm$ 1.7 | 25.97 $\pm$ 2.22 | 54.07 $\pm$ 1.31 | 28.13 $\pm$ 0.54
| R-TRANSECOPY | 49.0 $\pm$ 1.76 | 40.63 $\pm$ 1.48 | 33.28 $\pm$ 1.74 | 25.87 $\pm$ 2.23 | 54.09 $\pm$ 1.35 | 28.12 $\pm$ 0.57
| Encoder-Decoder | 58.92 $\pm$ 2.05 | 47.7 $\pm$ 1.62 | 38.18 $\pm$ 1.86 | 28.71 $\pm$ 2.35 | 59.12 $\pm$ 1.16 | 34.28 $\pm$ 0.54
| Our-Model | 60.8 $\pm$ 1.52 | 49.8 $\pm$ 1.37 | 40.32 $\pm$ 1.92 | 30.76 $\pm$ 2.7 | 60.07 $\pm$ 0.9 | 35.34 $\pm$ 0.43
| Our-Modelcopy |  62.44 $\pm$ 1.85 |  50.62 $\pm$ 1.46 |  40.82 $\pm$ 1.77 |  31.1 $\pm$ 2.46 |  61.23 $\pm$ 1.2 |  36.24 $\pm$ 0.65
Table 4: Evaluation results of our model and all other baselines for the unseen predicate evaluation setup | Model | BLEU-4 | ROUGEL
---|---|---|---
Sub-Types | R-TRANSE | 32.41 $\pm$ 1.74 | 59.27 $\pm$ 0.92
Encoder-Decoder | 42.14 $\pm$ 2.05 | 68.95 $\pm$ 0.86
Our-Model | 42.13 $\pm$ 1.88 | 69.35 $\pm$ 0.9
Our-Modelcopy |  42.2 $\pm$ 2.0 |  69.37 $\pm$ 1.0
Obj-Types | R-TRANSE | 30.59 $\pm$ 1.3 | 57.37 $\pm$ 1.17
Encoder-Decoder | 37.79 $\pm$ 2.65 | 65.69 $\pm$ 2.25
Our-Model | 37.78 $\pm$ 2.02 | 65.51 $\pm$ 1.56
Our-Modelcopy |  38.02 $\pm$ 1.9 |  66.24 $\pm$ 1.38
Table 5: Automatic evaluation of our model against selected baselines for
unseen sub-types and obj-types

###  5.3 Training & Implementation Details

To train the neural network models we optimize the negative log-likelihood of
the training data with respect to all the model parameters. For that we use
the RMSProp optimization algorithm with a decreasing learning rate of $0.001$,
mini-batch size $=200$, and clipping gradients with norms larger than $0.1$.
We use the same vocabulary for both the textual context encoders and the
decoder outputs. We limit our vocabulary to the top $30,000$ words including
the special tokens. For the word embeddings we chose GloVe Pennington et al.
(2014) pretrained embeddings of size $100$. We train TransE embeddings of size
$H_{k}=200$, on the FB5M dataset Bordes et al. (2015) using the TransE model
implementation from Lin et al. (2015). We set GRU hidden size of the decoder
to $H_{d}=500$, and textual encoder to $H_{c}=200$. The networks
hyperparameters are set with respect to the final BLEU-4 score over the
validation set. All neural networks are implemented using Tensorflow Abadi et
al. (2015). All experiments and models source code are publicly
available444https://github.com/NAACL2018Anonymous/submission for the sake of
reproducibility.

###  5.4 Automatic Evaluation Metrics

To evaluate the quality of the generated question, we compare the original
labeled questions by human annotators to the ones generated by each variation
of our model and the baselines. We rely on a set of well established
evaluation metrics for text generation: BLEU-1, BLEU-2, BLEU-3, BLEU-4
Papineni et al. (2002), METEOR Denkowski and Lavie (2014) and ROUGEL Lin
(2004).

###  5.5 Human Evaluation

Metrics for evaluating text generation such as BLEU and METEOR give an measure
of how close the generated questions are to the target correct labels.
However, they might not be able to evaluate directly whether the predicate in
the question was expressed in the text or not. Thus we run two further human
evaluations to directly measure the following.
Predicate identification: annotators were asked to indicate whether the
generated question contains the given predicate in the fact or not, either
directly or implicitly.
Naturalness: following Ngomo et al. (2013), we measure the comprehensibility
and readability of the generated questions. Each annotator was asked to rate
each generated question using a scale from $1$ to $5$, where: (5) perfectly
clear and natural, (3) artificial but understandable, and (1) completely not
understandable. We run our studies on $100$ randomly sampled input facts
alongside with their corresponding generated questions by each of the systems
using the help of $4$ annotators.

##  6 Results & Discussion

#### Automatic Evaluation

Table 4 shows results of our model compared to all other baselines across all
evaluation metrics. Our that encodes the KB fact and textual contexts achieves
a significant enhancement over all the baselines in all evaluation metrics,
with $\mathbf{+2.04}$ BLEU-4 score than the Encoder-Decoder baseline.
Incorporating the part-of-speech copy actions further improves this
enhancement to reach $\mathbf{+2.39}$ BLEU-4 points.
Among all baselines, the Encoder-Decoder baseline and the R-TRANSE baseline
performed the best. This shows that TransE embeddings encode intra-predicates
information and intra-class-types information to a great extent, and can
generalize to some extent to unseen predicates and class types.

Similar patterns can be seen in the evaluation on unseen sub-types and obj-
types (Table 5). Our model with copy actions was able to outperform all the
other systems. Majority of systems have reported a significantly higher BLEU-4
scores in these two tasks than when generalizing to unseen predicates ($+12$
and $+8$ BLEU-4 points respectively). This indicates that these tasks are
relatively easier and hence our models achieve relatively smaller enhancements
over the baselines.

Model |  $\%$ Pred. Identified | Natural.
---|---|---
Encoder-Decoder | $6$ | $3.14$
Our-Model (No Copy) | $6$ | $2.72$
Our-Modelcopy (Types context) | $\mathbf{37}$ | $\mathbf{3.21}$
Our-Modelcopy (All contexts) | $\mathbf{46}$ | $2.61$
Table 6: results of Human evaluation on % of predicates identified and naturalness 0-5 1 | Reference |  what language is spoken in the tv show three sheets?
---|---|---
| Enc-Dec. |  in what language is three sheets in?
| Our-Model |  what the the player is the three sheets?
| Our-ModelCopy |  what is the language of three sheets?
2 | Reference |  how is roosevelt in Africa classified?
| Enc-Dec. |  what is the name of a roosevelt in Africa?
| Our-Model |  what is the name of the movie roosevelt in Africa?
| Our-ModelCopy |  what is a genre of roosevelt in Africa?
3 | Reference |  where can 5260 philvéron be found?
| Enc-Dec. |  what is a release some that 5260 philvéron wrote?
| Our-Model |  what is the name of an artist 5260 philvéron?
| Our-ModelCopy |  which star system contains the star system body 5260 philvéron?
4 | Reference |  which university did ezra cornell create?
| Enc-Dec. |  which films are part of ezra cornell?
| Our-Model |  what is a position of ezra cornell?
| Our-ModelCopy |  what founded the name of a university that ezra cornell founded?
Table 7: Examples of generated questions from different systems in comparison

#### Human Evaluation

Table 6 shows how different variations of our system can express the unseen
predicate in the target question with comparison to the Encoder-Decoder
baseline.
Our proposed copy actions have scored a significant enhancement in the
identification of unseen predicates with up to $\mathbf{+40\%}$ more than best
performing baseline and our model version without the copy actions.
By examining some of the generated questions (Table 7) we see that models
without copy actions can generalize to unseen predicates that only have a very
similar freebase predicate in the training set. For example
fb:tv_program/language and fb:film/language, if one of those predicates exists
in the training set the model can use the same questions for the other during
test time.
Copy actions from the sub-type and the obj-type textual contexts can
generalize to a great extent to unseen predicates because of the overlap
between the predicate and the object type in many questions (Example 2 Table
7). Adding the predicate context to our model has enhanced model performance
for expressing unseen predicates by $+9\%$ (Table 6). However we can see that
it has affected the naturalness of the question. The post processing step does
not take into consideration that some verbs and prepositions do not fit in the
sentence structure, or that some words are already existing in the question
words (Example 4 Table 7). This does not happen as much when having copy
actions from the sub-type and the obj-type contexts because they are mainly
formed of nouns which are more interchangeable than verbs or prepositions. A
post-processing step to reform the question instead of direct copying from the
input source is considered in our future work.

##  7 Conclusion

In this paper we presented a new neural model for question generation from
knowledge bases, with a main focus on predicates, subject types or object
types that were not seen at the training phase (Zero-Shot Question
Generation). Our model is based on an encoder-decoder architecture that
leverages textual contexts of triples, two attention layers for triples and
textual contexts and finally a part-of-speech copy action mechanism. Our
method exhibits significantly better results for Zero-Shot QG than a set of
strong baselines including the state-of-the-art question generation from KB.
Additionally, a complimentary human evaluation, helps in showing that the
improvement brought by our part-of-speech copy action mechanism is even more
significant than what the automatic evaluation suggests. The source code and
the collected textual contexts are provided for the community:
https://github.com/NAACL2018Anonymous/submission

## References

  * Abadi et al. (2015) Martín Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Ian Goodfellow, Andrew Harp, Geoffrey Irving, Michael Isard, Yangqing Jia, Rafal Jozefowicz, Lukasz Kaiser, Manjunath Kudlur, Josh Levenberg, Dan Mané, Rajat Monga, Sherry Moore, Derek Murray, Chris Olah, Mike Schuster, Jonathon Shlens, Benoit Steiner, Ilya Sutskever, Kunal Talwar, Paul Tucker, Vincent Vanhoucke, Vijay Vasudevan, Fernanda Viégas, Oriol Vinyals, Pete Warden, Martin Wattenberg, Martin Wicke, Yuan Yu, and Xiaoqiang Zheng. 2015.  TensorFlow: Large-scale machine learning on heterogeneous systems.  Software available from tensorflow.org.  https://www.tensorflow.org/.
  * Bahdanau et al. (2014) Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. 2014.  Neural machine translation by jointly learning to align and translate.  CoRR abs/1409.0473.  http://arxiv.org/abs/1409.0473.
  * Bird (2006) Steven Bird. 2006.  NLTK: the natural language toolkit.  In ACL 2006, 21st International Conference on Computational Linguistics and 44th Annual Meeting of the Association for Computational Linguistics, Proceedings of the Conference, Sydney, Australia, 17-21 July 2006.  http://aclweb.org/anthology/P06-4018.
  * Bordes et al. (2015) Antoine Bordes, Nicolas Usunier, Sumit Chopra, and Jason Weston. 2015.  Large-scale simple question answering with memory networks.  CoRR abs/1506.02075.  http://arxiv.org/abs/1506.02075.
  * Cho et al. (2014) Kyunghyun Cho, Bart van Merrienboer, Çaglar Gülçehre, Fethi Bougares, Holger Schwenk, and Yoshua Bengio. 2014.  Learning phrase representations using RNN encoder-decoder for statistical machine translation.  CoRR abs/1406.1078.
  * Denkowski and Lavie (2014) Michael J. Denkowski and Alon Lavie. 2014.  Meteor universal: Language specific translation evaluation for any target language.  In Proceedings of the Ninth Workshop on Statistical Machine Translation, WMT@ACL 2014, June 26-27, 2014, Baltimore, Maryland, USA. pages 376–380.  http://aclweb.org/anthology/W/W14/W14-3348.pdf.
  * Dong et al. (2017) Li Dong, Jonathan Mallinson, Siva Reddy, and Mirella Lapata. 2017.  Learning to paraphrase for question answering.  In Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, EMNLP 2017, Copenhagen, Denmark, September 9-11, 2017. pages 875–886.  https://aclanthology.info/papers/D17-1091/d17-1091.
  * Du et al. (2017) Xinya Du, Junru Shao, and Claire Cardie. 2017.  Learning to ask: Neural question generation for reading comprehension.  In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics, ACL 2017, Vancouver, Canada, July 30 - August 4, Volume 1: Long Papers. pages 1342–1352.  https://doi.org/10.18653/v1/P17-1123.
  * Evens and Michael (2006) Martha Evens and Joel Michael. 2006.  One-on-one tutoring by humans and machines.  Computer Science Department, Illinois Institute of Technology .
  * Fader et al. (2011) Anthony Fader, Stephen Soderland, and Oren Etzioni. 2011.  Identifying relations for open information extraction.  In Proceedings of the 2011 Conference on Empirical Methods in Natural Language Processing, EMNLP 2011, 27-31 July 2011, John McIntyre Conference Centre, Edinburgh, UK, A meeting of SIGDAT, a Special Interest Group of the ACL. pages 1535–1545.  http://www.aclweb.org/anthology/D11-1142.
  * Graesser et al. (2004) Arthur C Graesser, Shulan Lu, George Tanner Jackson, Heather Hite Mitchell, Mathew Ventura, Andrew Olney, and Max M Louwerse. 2004.  Autotutor: A tutor with dialogue in natural language.  Behavior Research Methods 36(2):180–192.
  * Gu et al. (2016) Jiatao Gu, Zhengdong Lu, Hang Li, and Victor O. K. Li. 2016.  Incorporating copying mechanism in sequence-to-sequence learning.  In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics, ACL 2016, August 7-12, 2016, Berlin, Germany, Volume 1: Long Papers.  http://aclweb.org/anthology/P/P16/P16-1154.pdf.
  * Gülçehre et al. (2016) Çaglar Gülçehre, Sungjin Ahn, Ramesh Nallapati, Bowen Zhou, and Yoshua Bengio. 2016.  Pointing the unknown words.  In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics, ACL 2016, August 7-12, 2016, Berlin, Germany, Volume 1: Long Papers.  http://aclweb.org/anthology/P/P16/P16-1014.pdf.
  * Halko et al. (2011) Nathan Halko, Per-Gunnar Martinsson, and Joel A. Tropp. 2011.  Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions.  SIAM Review 53(2):217–288.  https://doi.org/10.1137/090771806.
  * Heilman and Smith (2010) Michael Heilman and Noah A. Smith. 2010.  Good question! statistical ranking for question generation.  In Human Language Technologies: Conference of the North American Chapter of the Association of Computational Linguistics, Proceedings, June 2-4, 2010, Los Angeles, California, USA. pages 609–617.  http://www.aclweb.org/anthology/N10-1086.
  * Joachims (1997) Thorsten Joachims. 1997.  A probabilistic analysis of the rocchio algorithm with TFIDF for text categorization.  In Proceedings of the Fourteenth International Conference on Machine Learning (ICML 1997), Nashville, Tennessee, USA, July 8-12, 1997. pages 143–151.
  * Khapra et al. (2017) Mitesh M. Khapra, Dinesh Raghu, Sachindra Joshi, and Sathish Reddy. 2017.  Generating natural language question-answer pairs from a knowledge graph using a RNN based question generation model.  In Proceedings of the 15th Conference of the European Chapter of the Association for Computational Linguistics, EACL 2017, Valencia, Spain, April 3-7, 2017, Volume 1: Long Papers. pages 376–385.  https://aclanthology.info/pdf/E/E17/E17-1036.pdf.
  * Kiros et al. (2014) Ryan Kiros, Ruslan Salakhutdinov, and Richard S. Zemel. 2014.  Unifying visual-semantic embeddings with multimodal neural language models.  CoRR abs/1411.2539.  http://arxiv.org/abs/1411.2539.
  * Lebret et al. (2016) Rémi Lebret, David Grangier, and Michael Auli. 2016.  Neural text generation from structured data with application to the biography domain.  In Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing, EMNLP 2016, Austin, Texas, USA, November 1-4, 2016. pages 1203–1213.  http://aclweb.org/anthology/D/D16/D16-1128.pdf.
  * Levy et al. (2017) Omer Levy, Minjoon Seo, Eunsol Choi, and Luke Zettlemoyer. 2017.  Zero-shot relation extraction via reading comprehension.  In Proceedings of the 21st Conference on Computational Natural Language Learning (CoNLL 2017), Vancouver, Canada, August 3-4, 2017. pages 333–342.  https://doi.org/10.18653/v1/K17-1034.
  * Lin (2004) Chin-Yew Lin. 2004.  Rouge: A package for automatic evaluation of summaries.  In Text summarization branches out: Proceedings of the ACL-04 workshop. Barcelona, Spain, volume 8.
  * Lin et al. (2015) Yankai Lin, Zhiyuan Liu, Maosong Sun, Yang Liu, and Xuan Zhu. 2015.  Learning entity and relation embeddings for knowledge graph completion.  In Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, January 25-30, 2015, Austin, Texas, USA.. pages 2181–2187.  http://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/view/9571.
  * Luong et al. (2015) Thang Luong, Ilya Sutskever, Quoc V. Le, Oriol Vinyals, and Wojciech Zaremba. 2015\.  Addressing the rare word problem in neural machine translation.  In Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing of the Asian Federation of Natural Language Processing, ACL 2015, July 26-31, 2015, Beijing, China, Volume 1: Long Papers. pages 11–19.  http://aclweb.org/anthology/P/P15/P15-1002.pdf.
  * Mintz et al. (2009) Mike Mintz, Steven Bills, Rion Snow, and Daniel Jurafsky. 2009.  Distant supervision for relation extraction without labeled data.  In ACL 2009, Proceedings of the 47th Annual Meeting of the Association for Computational Linguistics and the 4th International Joint Conference on Natural Language Processing of the AFNLP, 2-7 August 2009, Singapore. pages 1003–1011.  http://www.aclweb.org/anthology/P09-1113.
  * Ngomo et al. (2013) Axel-Cyrille Ngonga Ngomo, Lorenz Bühmann, Christina Unger, Jens Lehmann, and Daniel Gerber. 2013.  Sorry, i don’t speak SPARQL: translating SPARQL queries into natural language.  In 22nd International World Wide Web Conference, WWW ’13, Rio de Janeiro, Brazil, May 13-17, 2013. pages 977–988.  http://dl.acm.org/citation.cfm?id=2488473.
  * Papineni et al. (2002) Kishore Papineni, Salim Roukos, Todd Ward, and Wei-Jing Zhu. 2002.  Bleu: a method for automatic evaluation of machine translation.  In Proceedings of the 40th Annual Meeting of the Association for Computational Linguistics, July 6-12, 2002, Philadelphia, PA, USA.. pages 311–318.  http://www.aclweb.org/anthology/P02-1040.pdf.
  * Pennington et al. (2014) Jeffrey Pennington, Richard Socher, and Christopher D. Manning. 2014.  Glove: Global vectors for word representation.  In Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing, EMNLP 2014, October 25-29, 2014, Doha, Qatar, A meeting of SIGDAT, a Special Interest Group of the ACL. pages 1532–1543.  http://aclweb.org/anthology/D/D14/D14-1162.pdf.
  * Riedel et al. (2010) Sebastian Riedel, Limin Yao, and Andrew McCallum. 2010.  Modeling relations and their mentions without labeled text.  In Machine Learning and Knowledge Discovery in Databases, European Conference, ECML PKDD 2010, Barcelona, Spain, September 20-24, 2010, Proceedings, Part III. pages 148–163.  https://doi.org/10.1007/978-3-642-15939-8_10.
  * Rush et al. (2015) Alexander M. Rush, Sumit Chopra, and Jason Weston. 2015.  A neural attention model for abstractive sentence summarization.  In Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, EMNLP 2015, Lisbon, Portugal, September 17-21, 2015. pages 379–389.  http://aclweb.org/anthology/D/D15/D15-1044.pdf.
  * Serban et al. (2016) Iulian Vlad Serban, Alberto García-Durán, Çaglar Gülçehre, Sungjin Ahn, Sarath Chandar, Aaron C. Courville, and Yoshua Bengio. 2016.  Generating factoid questions with recurrent neural networks: The 30m factoid question-answer corpus.  In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics, ACL 2016, August 7-12, 2016, Berlin, Germany, Volume 1: Long Papers.  http://aclweb.org/anthology/P/P16/P16-1056.pdf.
  * Seyler et al. (2015) Dominic Seyler, Mohamed Yahya, and Klaus Berberich. 2015.  Generating quiz questions from knowledge graphs.  In Proceedings of the 24th International Conference on World Wide Web Companion, WWW 2015, Florence, Italy, May 18-22, 2015 - Companion Volume. pages 113–114.  https://doi.org/10.1145/2740908.2742722.
  * Shang et al. (2015) Lifeng Shang, Zhengdong Lu, and Hang Li. 2015.  Neural responding machine for short-text conversation.  In Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing of the Asian Federation of Natural Language Processing, ACL 2015, July 26-31, 2015, Beijing, China, Volume 1: Long Papers. pages 1577–1586.  http://aclweb.org/anthology/P/P15/P15-1152.pdf.
  * Socher et al. (2013) Richard Socher, Milind Ganjoo, Christopher D. Manning, and Andrew Y. Ng. 2013.  Zero-shot learning through cross-modal transfer.  In Advances in Neural Information Processing Systems 26: 27th Annual Conference on Neural Information Processing Systems 2013. Proceedings of a meeting held December 5-8, 2013, Lake Tahoe, Nevada, United States.. pages 935–943.
  * Sutskever et al. (2014) Ilya Sutskever, Oriol Vinyals, and Quoc V. Le. 2014.  Sequence to sequence learning with neural networks.  In Advances in Neural Information Processing Systems 27: Annual Conference on Neural Information Processing Systems 2014, December 8-13 2014, Montreal, Quebec, Canada. pages 3104–3112.


# Learning disentangled representations for explainable chest X-ray
classification using Dirichlet VAEs

Rachael Harkness  CISTIB Centre for Computational Imaging and Simulation
Technologies in Biomedicine, School of Computing  University of Leeds, Leeds,
United Kingdom  Alejandro F Frangi  CISTIB Centre for Computational Imaging
and Simulation Technologies in Biomedicine, School of Computing  University of
Leeds, Leeds, United Kingdom  Kieran Zucker  University of Leeds, Leeds,
United Kingdom  LIMR Leeds Institute of Medical Research  Nishant Ravikumar
CISTIB Centre for Computational Imaging and Simulation Technologies in
Biomedicine, School of Computing  University of Leeds, Leeds, United Kingdom

##  1 ABSTRACT

This study explores the use of the Dirichlet Variational Autoencoder (DirVAE)
for learning disentangled latent representations of chest X-ray (CXR) images.
Our working hypothesis is that distributional sparsity, as facilitated by the
Dirichlet prior, will encourage disentangled feature learning for the complex
task of multi-label classification of CXR images. The DirVAE is trained using
CXR images from the CheXpert database, and the predictive capacity of multi-
modal latent representations learned by DirVAE models is investigated through
implementation of an auxiliary multi-label classification task, with a view to
enforce separation of latent factors according to class-specific features. The
predictive performance and explainability of the latent space learned using
the DirVAE were quantitatively and qualitatively assessed, respectively, and
compared with a standard Gaussian prior-VAE (GVAE). We introduce a new
approach for explainable multi-label classification in which we conduct
gradient-guided latent traversals for each class of interest. Study findings
indicate that the DirVAE is able to disentangle latent factors into class-
specific visual features, a property not afforded by the GVAE, and achieve a
marginal increase in predictive performance relative to GVAE. We generate
visual examples to show that our explainability method, when applied to the
trained DirVAE, is able to highlight regions in CXR images that are clinically
relevant to the class(es) of interest and additionally, can identify cases
where classification relies on spurious feature correlations.

Keywords: Multi-label classification, chest X-ray images, variational
autoencoders, Dirichlet distribution, disentanglement, explainability

Copyright notice: Copyright 2023 Society of PhotoOptical Instrumentation
Engineers. One print or electronic copy may be made for personal use only.
Systematic reproduction and distribution, duplication of any material in this
paper for a fee or for commercial purposes, or modification of the content of
the paper are prohibited.

##  2 INTRODUCTION

Medical image interpretation is a complex and challenging task requiring in-
depth understanding of anatomy and physiology, and years of education and
experience. In particular, the interpretation of chest X-rays (CXRs), a 2D
projection of 3D thoracic organs/structures, can be especially challenging.
The resulting ‘overlapping’ tissue features makes identification of object
boundaries challenging due to insufficient tissue contrast, impeding detection
of abnormalities. Additionally, pre-existing conditions and comorbidities are
common in patients that require acute chest X-ray exams, or are frequently
invited to screenings (e.g. chronic obstructive pulmonary disorder and lung
cancer screenings). Consequently, in practice multiple pathologies are often
observed in a single exam. Co-occurring disease features can appear similarly
and can often create diagnostic uncertainty for both expert radiologists and
deep learning systems. The learning of explainable representations of
clinically complex medical images, where anatomical and extrinsic image
acquisition-related features are disentangled from relevant disease features,
is a crucial step in overcoming these challenges.

In this study, we propose to use variational autoencoders (VAEs) to learn
disentangled multi-modal latent representations of CXRs for explainable
classification of multiple co-occurring labels/class (i.e. multi-label
classification) [1]. VAEs are able to learn compressed representations of
data, in which observed variations of salient visual features are captured by
a number of latent factors. Disentanglement is achieved when each factor
corresponds uniquely to some meaningful composite part of the data.
Disentangled representations offer a more explainable latent space, unlike
their entangled counterparts. The matching of latent factors to interpretable
variations in the data manifold, afforded by disentangled representations,
makes them advantageous to downstream predictive tasks that utilise the
learned latent space (e.g. classification, regression, clustering) [2].
Popular approaches to learning disentangled representations with VAEs,
includes, $\beta$-VAE [3], Factor-VAE[4] and $\beta$-TCVAE [5].

While these approaches improve disentanglement in Gaussian-prior VAEs, success
is limited due to the dense and unimodal nature of a multivariate Gaussian
prior. With this in mind, we propose to use a VAE with a Dirichlet prior,
referred to as Dirichlet VAE (DirVAE). We hypothesise that a DirVAE will allow
a multi-modal latent representation of CXRs to be learned through multi-peak
sampling and will encourage latent disentanglement due to the sparse nature of
the Dirichlet prior [6].

To evaluate the potential benefits of DirVAE over a conventional VAE with a
Gaussian prior (GVAE), we use the CheXpert dataset to tackle a complex multi-
label classification problem [7]. We convert the multi-label task to a series
of binary classification problems. Logistic regression classifiers are trained
jointly within a representation learning-centered framework, to predict each
class of interest, with all binary classification tasks tackled
simultaneously. Specifically, we jointly train the class-specific logistic
regression classifiers with the DirVAE, to encourage disentanglement of class-
specific latent factors, and evaluate model capacity for learning
diagnostically separable representations of CXRs. Model evaluations
investigate classifier performance, latent factorisation and its
explainability. We train and evaluate the GVAE identically to the DirVAE for
fair comparison, and highlight the benefits of the latter in terms of
predictive performance and explainability.

##  3 METHODOLOGY

###  3.1 Data

The CheXpert data set, one of the largest publicly available CXR datasets with
multi-label outcomes, is used throughout this study. To overcome issues of
severe class imbalance in the data, and simplify training of the logistic
regression classifiers, we sample 17,000 images of each of the four most
represented classes featured in the CheXpert dataset, namely, ‘No Finding’,
‘Lung Opacity’, ‘Pleural Effusion’, and ‘Support Devices’. Figure 1 presents
the frequency of classes of interest as well as their frequency of co-
occurrence. We split the CheXpert dataset into train $(n=52,943)$, validation
$(n=5057)$ and test $(n=10,000)$ sets.

Figure 1: Label co-occurrence matrix of multi-label CheXpert data (training
data)

###  3.2 Dirichlet VAE

The goal of this study is to explore the benefits of using the DirVAE to learn
a multi-modal latent representation of CXR images, comprised of explainable
latent factors. To accomplish this we model the Dirichlet prior explicitly as
in Gawlikowski, J. et al. (2022). [8]. Alternative approaches frequently
utilize a softmax-Laplace approximation [9]. However, such approaches to
modelling the Dirichlet prior prevents true approximation of multi-modal
representations as shown in Joo, W. et al. (2020) [10]. The Dirichlet
distribution is a continuous multivariate probability distribution defined
over a set of discrete distributions. It is parameterised by a $K$-dimensional
vector typically referred to as the concentration, where, $K$ corresponds to
the set of discrete distributions. Here, the set of discrete distributions
represent the latent space in a DirVAE.

We define the Dirichlet probability density function as,

$\text{Dir}(x;\alpha)=\frac{\Gamma(\sum\alpha_{k})}{\prod\Gamma(\alpha_{k})}\prod
x_{k}^{\alpha_{k}-1},\hskip 28.45274pt\left(x_{k}\geq 0;\hskip
5.69046pt\sum\limits_{k}x_{k}=1\right)$ (1)

where, $\alpha_{k}>0$ and $\Gamma(\cdot)$ denotes the gamma function. The
Dirichlet distribution can expressed with a composition of gamma random
variables with the Gamma distribution defined as,

$\text{Gamma}(x;\alpha,\beta)=\frac{\beta^{\alpha}}{\Gamma(\alpha)}x^{\alpha-1}e^{-\beta
x},\hskip 28.45274pt\left(\alpha>0;\hskip 5.69046pt\beta>0\right)$ (2)

where $\beta$ is a constant, if $X_{k}\sim$ Gamma $(\alpha_{k})$ are
independently distributed, then $(X_{1}/X_{0},\dots,X_{n}/X_{0})$ follows a
Dirichlet distribution parameterised by a vector of
$\alpha_{1},\dots,\alpha_{n}$, with $X_{0}=\sum X_{k}$. Alternatively, we can
say where $K$ independent random variables are sampled from the multivariate
Gamma distribution $X\sim$ MultiGamma$(\alpha,\beta\cdot\mathbf{1}_{K})$, then
we get $\mathbf{Y}\sim$ Dir$(\alpha)$, where $Y_{k}=X_{k}/X_{0}$ [10].

The Dirichlet concentration governs the shape of distribution on the
probability simplex and is selected according to an acceptable trade-off
between distributional sparsity and distributional smoothness. This can be
observed in Figure 2. For enhancing explainability and to capture multi-modal
latent distributions a Dirichlet concentration that enforces sparsity is
essential. For these reasons we apply a Dirichlet prior parameterised with a
concentration of $0.5\cdot\mathbf{1}_{1024}$, where $\mathbf{1}_{1024}$
represents the $K$-dimensional latent space with $K=1024$. This latent
dimension was used throughout this study for both the DirVAE and the GVAE.

Figure 2: 3-dimensional probability density functions from the Dirichlet
distribution, each with different $\alpha$ values. The values of $\alpha$ are
set to (0.5, 0.5, 0.5), (0.9, 0.9, 0.9) and (2, 5, 15).

###  3.3 Experimental Settings

Both the DirVAE and GVAE were trained in four stages categorised as follows:
(1) reconstruction, (2) reconstruction and regularisation, (3) classifier
initialisation, and (4) joint training. During the first stage, the model is
trained using just the reconstruction loss (L1 loss), defined as
$L_{1}=\sum_{i=1}^{n}|x_{i}-f(x_{i})|$, where $f$ denotes the encoder-decoder
functions. In the second stage, the Kullback-Leibler (KL) divergence term is
used to regularise model training by minimising the divergence between the
approximated posterior distribution of the latent factors and the assumed
prior distribution (i.e. Dirichlet for DirVAE and centered multivariate
Gaussian for GVAE). KL divergence is defined as
$L_{KL}=D_{KL}(q_{\phi}(z|x)\parallel p_{\theta}(z|x))$, and for DirVAE is
derived as in below,

$KL(Q\parallel P)=\sum log\Gamma(\alpha_{k})-\sum
log\Gamma(\hat{\alpha}_{k})+\sum(\hat{\alpha}_{k}-\alpha_{k})\psi(\hat{\alpha}_{k})$
(3)

where $P$ is the prior distribution, equal to MultiGamma$(\alpha,\beta\cdot
1_{k})$, $Q$ represents the learned posterior, $Q=$
MultiGamma$(\hat{\alpha},\beta\cdot 1_{k})$ and $\psi$ is a digamma function
[10].

In the next stage, the weights of the pre-trained VAE are frozen and each of
the four class-specific logistic regression classifiers are independently
optimised for their respective binary classification tasks with binary cross
entropy loss, using CXR latent representations as inputs. Once each classifier
is fully optimised, the ensemble of logistic regression models are trained
together, this objective takes the form,

$L_{BCE}=\frac{1}{4}\sum_{c=1}^{4}-\frac{1}{n}\sum_{i=1}^{n}(y_{c,i}\cdot
log(p_{c,i})+1-y_{c,i}\cdot log(1-p_{c,i})),$ (4)

where $y$ represents the class labels, $p$ is the predicted probabilities and
$c$ represents the different classes.

In the final stage of training, the VAEs and logistic regression classifiers
are trained jointly, where, the reconstruction loss, KL divergence loss and
all four classifier losses are combined into a single training objective and
minimised. Based on preliminary experiments, we found that training the multi-
label GVAE and DirVAE models in this stage-wise manner helped stabilise the
training process, relative to training the models end-to-end from the
beginning. Optimising the latent space with the multi-label classification
task encourages latent factors to explain class-specific visual features and
allows the classifiers to predict target classes from the learned latent
space. This enhances explainability of the learned latent space as latent
factors with higher importance/discriminative power for predicting a given
class correctly, should correspondingly encode visual features in the CXR
image that are representative of that class.

Our working hypothesis was that this method of training combined with the
properties of a DirVAE should yield a disentangled latent space resulting in
improved explainability over the GVAE. Both the DirVAE and GVAE were optimized
using the Adam algorithm. Logistic regression models were optimized under SGD.

Figure 3: Dirichlet VAE encoder with a (a) decoder which generates image
reconstructions from the latent space $z$ and (b) an ensemble of logistic
regression classifiers $C$, each predicting independent class probabilities
$p$ from latent space $z$. Classification thresholds are applied to the
probabilities to produce class predictions $\hat{y}$.

###  3.4 Evaluations

The goal of this study is to evaluate the capacity of the DirVAE to learn
explainable, disentangled latent representations of CXR images, for multi-
label classification. Accordingly, we assess the performance of the DirVAE by
evaluating the performance of their logistic regression classifiers on the
multi-label classification problem, and qualitatively assessing the
explainability of their respective learned latent spaces. Classifier
performance is evaluated through ROC curves and standard classification
metrics (evaluated per-class). All results are compared directly with GVAE
performance. We perform a qualitative assessment of the explainability of the
latent space through a series of ‘latent factor traversals’. Once the GVAE and
DirVAE models were trained, given a CXR image from the test set as input, we
first identify a single latent factor with the largest gradient activation
from a positive classifier (i.e. where the positive class of interest to a
classifier was predicted correctly for the input image). The identified latent
factor is adjusted incrementally or ‘traversed’, while all other factors are
preserved. We visualise the influence of changing the single factor of
interest on the decoder reconstructions. Intuitively, if changing only a
single latent factor results in class-specific structural changes in the CXR
reconstructions, we can assume that the latent space has been successfully
disentangled into visual features relating to the class of interest. Pixel-
wise variance is created to summarise changes across a traversal and identify
features controlled by a specific latent factor. In these evaluations, cases
with co-occurring labels are not considered, to simplify interpretation (as
co-occurring labels would require exploring multiple relevant latent factors).

##  4 RESULTS

Table 1 summarises the classification performance of the logistic regression
models, for both the DirVAE and the GVAE. The DirVAE classifiers marginally
outperform GVAE classifiers with higher values across most classification
metrics (see tab. 1) and higher AUC scores as shown in Figure 4. While
individual label prediction metrics are good, multi-label metrics show that
the DirVAE classifiers offer only modest performance in the prediction of all
four labels, achieving an exact match rate (EMR) of 0.38 $\pm$ 0.01 and
Hamming loss of 0.25 $\pm$ 0.02. GVAE achieved an EMR of only 0.37 $\pm$ 0.01
and Hamming loss of 0.26 $\pm$ 0.01.

|  | Dirichlet VAE | Gaussian VAE
---|---|---|---
Accuracy | No Finding | 0.82 $\pm$ 0.01 | 0.82 $\pm$ 0.01
Lung Opacity | 0.72 $\pm$ 0.01 | 0.72 $\pm$ 0.01
Pleural Effusion | 0.70 $\pm$ 0.01 | 0.70 $\pm$ 0.01
Support Devices | 0.74 $\pm$ 0.02 | 0.72 $\pm$ 0.01
Precision | No Finding | 0.61 $\pm$ 0.06 | 0.62 $\pm$ 0.03
Lung Opacity | 0.82 $\pm$ 0.06 | 0.82 $\pm$ 0.02
Pleural Effusion | 0.81 $\pm$ 0.01 | 0.82 $\pm$ 0.02
Support Devices | 0.87 $\pm$ 0.01 | 0.89 $\pm$ 0.01
Recall | No Finding | 0.74 $\pm$ 0.01 | 0.72 $\pm$ 0.01
Lung Opacity | 0.69 $\pm$ 0.02 | 0.68 $\pm$ 0.02
Pleural Effusion | 0.72 $\pm$ 0.01 | 0.72 $\pm$ 0.01
Support Devices | 0.76 $\pm$ 0.02 | 0.74 $\pm$ 0.01
AUC | No Finding | 0.87 $\pm$ 0.02 | 0.87 $\pm$ 0.01
Lung Opacity | 0.78 $\pm$ 0.02 | 0.77 $\pm$ 0.01
Pleural Effusion | 0.75 $\pm$ 0.01 | 0.74 $\pm$ 0.01
Support Devices | 0.78 $\pm$ 0.03 | 0.76 $\pm$ 0.02
Table 1: Label-wise table of logistic regression classification performance
results Figure 4: Label-wise ROC curves for GVAE and DirVAE logistic
regression classifier performance.

Figure 6 presents the results of traversing the latent spaces in the direction
of the most predictive latent dimension. For the DirVAE, clear structural
changes are observed for each class. Typically, latent traversals will
gradually remove or intensify disease-related features, in a manner specific
to the input CXR image. We consider both types of change as evidence of
disease-/class-specific and image-specific disentanglement and generate pixel
intensity variance maps (presented along side each traversal, bottom right
corner of each panel) in order to capture both types of feature change. We
find that the features highlighted by DirVAE traversals are not only disease-
and image-specific, but also clinically relevant. The feature changes observed
during latent traversals for the ‘Pleural Effusion’ class are largely isolated
to the lower regions of the lungs, typically affecting the appearance of the
costophrenic angles and hemidiaphragm region, two keys areas of diagnostic
relevance for pleural effusion (fig. 6(a)) [11].

For lung opacity cases, DirVAE traversals consistently highlight areas of
suspected consolidation. Clinically, the radiographic presentation of lung
opacities can vary greatly, this is reflected in the diversity of feature
changes observed during DirVAE traversals. Traversals capture features of
consolidation that vary in shape, size and position, matching the appearance
of diagnostic features in the example CXRs (fig. 5(b)). Similarly, in
evaluating traversals of the ‘Support Devices’ class, we observe a diverse set
of well-defined structural changes in all areas of the CXR, with significant
changes mirroring the location and shape of support devices in the evaluated
CXR (see fig. 5(a) and fig. 10). These results indicate that the DirVAE has
the capacity to learn disease/class-specific latent factors that are
representative of all modes within the class of interest.

With successful isolation of salient features in the latent space, potential
reliance on ‘spurious’ features for class prediction can be observed in some
cases (indicated by red boxes overlaid on CXR images in fig. 6). Here, we see
that latent traversal causes feature changes relating to radiology annotation,
co-occurring classes (particularly support devices) and shoulder position.
This indicates that the disentangled latent space learned by the DirVAE could
also be used to identify spurious features resulting from biases in the data,
which is a requisite for mitigating the same.

Crucially, no such class-specific changes are observed during evaluation of
GVAE latent traversals, for any class (fig. 8). Traversal variance appears
diffuse across the reconstructed image, showing only subtle changes in
anatomical areas and little to no change in areas of diagnostic relevance.
Where disease-related feature changes are observed they are not localised to
regions relevant to the class of interest, but are accompanied by changes to
other features across the images. Changes in clavicle, shoulder position,
mediastinum and lung width are often observed together, causing non-specific
changes in the size or shape of the lung airspace. With non-specific changes
GVAE traversals appear similar for all examples and localisation of CXR
features of significance is near impossible. This is especially apparent in
Figure 9 and 10, which present direct comparisons between DirVAE and GVAE
traversals (for the same input CXR images), with ‘Support Devices’ as the
class of interest.

(a) Examples of DirVAE latent traversal results of the ‘Support Devices’ CXR
class

(b) Examples of DirVAE latent traversal results of the ‘Lung Opacity’ CXR
class

(a) Examples of DirVAE latent traversal results of the ‘Pleural Effusion’
class Figure 6: DirVAE latent traversals, with examples from each CXR class.
Each grid presents a different example, the top left image in the grid is the
original reconstruction, the entire traversal is presented sequentially in the
grid. The bottom right image presents a pixel-wise variance map summarising
the entire traversal. Green arrows () in the variance map point to disease-
related feature changes while red arrows () point to likely confounding
features. Similarly, red and green boxes are used to highlight key features
changes in the final reconstruction. (a) Examples of GVAE latent traversal
results of the ‘Support Devices’ class

(a) Examples of GVAE latent traversal results of the ‘Lung Opacity’ class

(b) Examples of GVAE latent traversal results of the ‘Pleural Effusion’ class

Figure 8: GVAE latent traversals, with examples from each CXR class. Each grid
presents a different example, the top left image in the grid is the input CXR,
the next image is the original reconstruction, the entire traversal is then
presented sequentially in the grid. The bottom right image presents a pixel-
wise variance map summarising the entire traversal. Figure 9: A direct
comparison of GVAE and DirVAE traversals, with examples from the ‘Support
Devices’ class. Each row presents a different example, the top left image in
the grid is the input CXR, the next image is the original reconstruction, the
entire traversal is then presented sequentially in the grid. The bottom right
image presents a pixel-wise variance map summarising the entire traversal.
Green arrows () in the variance map point to class-related feature changes.
Similarly, green boxes are used to highlight key features changes in the final
reconstruction. Figure 10: Saliency maps representing variance over all
reconstructions in a latent traversal series, performed for the ‘Support
Devices’ class, with comparison between GVAE and DirVAE. We include arrows in
DirVAE examples to show areas of class-related feature changes.

##  5 DISCUSSION

Analysis of latent traversals suggests that the DirVAE learns a more
disentangled representation (than its GVAE counterpart), despite the
challenges presented by a multi-label task, where the co-occurrence of disease
features complicates representation learning. In addition to its superiority
in terms of disentanglement and therefore, explainability, DirVAE classifiers
perform marginally better than GVAE. The improvement in disentanglement
afforded by the DirVAE, relative to the GVAE, is attributed to the sparsity
and multi-modal characteristics of the latent space learned by the former.
Specifically, the sparsity of our Dirichlet prior is enforced by setting its
concentration parameter $\alpha=0.5$ across all experiments. This pushes areas
of the posterior distribution towards zero, i.e. the inner areas of the
simplex, and creates a narrower information bottleneck.

In order to generate quality reconstructions under strict sparsity constraints
the latent factors have to capture more global features [12]. Our approach to
encouraging disentanglement follows a similar principle to $\beta$-VAE, but
with a different strategy for narrowing the information bottleneck [13]. If we
consider this with our classification objective, which influences the model to
prioritise learning of disease-related features, we could say that our
strategy encourages the learned latent variables to capture ‘global disease
features’ and explain away noise. We can observe this principle in latent
traversal evaluations, by traversing latent dimensions important for lung
opacity classification, we do not observe diffuse changes in unrelated CXR
features, but clear changes in homologous features of the image. Moreover, we
observe the capacity of the DirVAE to disentangle global patterns of disease
features, with localised regions of consolidation changing across both lungs
and in upper and lower lung regions. Similarly, global features are observed
in ‘Support Device’ classification, where all support structures, including
connecting wiring (distributed spatially across the image) are altered during
traversal; during traversal coordinated feature changes can be observed across
the entire image, for all images classes.

Our proposed use of latent embedding manipulation for identification of the
salient visual features underlying classifier predictions facilitates improved
model explainability. Within our explainability approach, superior
disentanglement in DirVAE latent representations allow us to more clearly
observe the appearance of ‘spurious correlations’ alongside disease features,
across traversals. Examples of observed ‘spurious correlation’ includes, sex
changes, the appearance of various support devices, as well as changing body
position (relating to switches from AP to PA projection) [14].

Highlighting the influence of confounders and biases in predictions made by
learning-based systems is essential for building safer and fairer predictive
models. This is especially relevant for translating learning-based computer-
aided diagnostic/screening systems to routine clinical care [15].
Particularly, multi-label classification tasks, where the co-occurrence of
disease makes deep learning models more vulnerable to reliance on confounding
factors. Typical approaches to multi-label image classification
explainability, including GradCAM [16], have been criticised for their
inability to highlight smaller pathologies or structures with complex shapes,
for example, mechanical wiring [17]. Our work opens doors to a novel approach
for this task. By interrogating the direct influence of important/identified
latent factors on the generated images and the classification of independent
outcomes (or indeed the fluctuation in the predicted class-specific
probabilities) for the generated images, our approach provides a systematic
framework to identify relevant class-specific features and confounders and/or
biases in image data. Interrogating the effects of the most predictive latent
factor demonstrates that this approach is able to clearly highlight small and
complex features as well as important correlations with, potentially,
confounding image features [17]. This is well-illustrated by an example of
confounding highlighted in a ‘Lung Opacity’ traversal (fig. 5(b) (iv)), where
the classifier appears to mistake the gas in the digestive system for
opacities in the lower lung regions (highlighted by red box and arrows).

Strong classification results alongside unclear traversals suggest that GVAE
classifiers rely on latent factors that combine to explain shared variation
and describe the CXR image (and its corresponding class(es)) as a whole,
rather than rely on a sparse set of disentangled latent factors that describe
the presence/absence of disease-/class-specific features (as with the DirVAE).
While some disease-/class-specific features are visible in the latent
traversals visualised for GVAE, these are attributed to the effects of multi-
task representation learning, i.e. to the joint training of the GVAE with the
logistic regression classifiers for the multi-label classification problem.
Due to the dense and unimodal nature of Gaussian distributions, the learned
latent space appears unable to separate disease-/class-specific features other
image-specific features. This is particularly evident in the latent traversals
presented for CXR images from the ‘Support Devices’ class (see fig. 9 and fig.
10). From this, we can conclude that GVAE has limited functionality as a
method for prediction explainability.

##  6 CONCLUSION

In this work we demonstrate that disentanglement of class-/disease-specific
(and potentially, clinically-relevant) features can be achieved using our
DirVAE model and that its capacity for class-/disease-specific disentanglement
is superior to a GVAE. We introduce a promising new approach for explainable
multi-label classification, where we apply an ensemble of simple logistic
regression classifiers and explore latent dimensions of significance to class
predictions through so-called ‘latent traversals’. With this we provide visual
examples of how our explainability method can highlight regions in CXR images
clinically relevant to the class(es) of interest and additionally, identify
cases where classification is biased and relies on spurious feature
correlations.

##  7 FUTURE WORK

Future work will explore the use of metrics to quantify disentanglement in
order to formalise our qualitative assessment. We will improve image
reconstruction/generation quality, with a view to improve the clarity of
feature changes during latent traversals. We will explore latent space
interpolations between CXR images of different classes and observe
corresponding changes to classifier predictions during the transitions between
disease representations, for further explainability. With improved
reconstruction quality the developed approach would have applications in both
explainable medical AI and synthetic data.

## ACKNOWLEDGEMENTS

This study was partially supported by cloud computing credits awarded by
Amazon Web Services through the Diagnostic Development Initiative. Kieran
Zucker is funded by the NIHR for this research project. The views expressed in
this publication are those of the author(s) and not necessarily those of the
NIHR, NHS or the UK Department of Health and Social Care.

## References

  * [1] Kingma, D. P. and Welling, M., “Auto-encoding variational bayes,” CoRR abs/1312.6114 (2013).
  * [2] Tschannen, M., Bachem, O., and Lucic, M., “Recent advances in autoencoder-based representation learning,” (2018).
  * [3] Higgins, I., Matthey, L., Pal, A., Burgess, C. P., Glorot, X., Botvinick, M. M., Mohamed, S., and Lerchner, A., “beta-vae: Learning basic visual concepts with a constrained variational framework,” in [5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings ], OpenReview.net (2017).
  * [4] Kim, H. and Mnih, A., “Disentangling by factorising,” in [International Conference on Machine Learning (ICML) ], (2018).
  * [5] Chen, R. T. Q., Li, X., Grosse, R. B., and Duvenaud, D. K., “Isolating sources of disentanglement in variational autoencoders,” in [Advances in Neural Information Processing Systems ], Bengio, S., Wallach, H., Larochelle, H., Grauman, K., Cesa-Bianchi, N., and Garnett, R., eds., 31, Curran Associates, Inc. (2018).
  * [6] Tonolini, F., Jensen, B. S., and Murray-Smith, R., “Variational sparse coding,” in [Proceedings of The 35th Uncertainty in Artificial Intelligence Conference ], Adams, R. P. and Gogate, V., eds., Proceedings of Machine Learning Research 115, 690–700, PMLR (22–25 Jul 2020).
  * [7] Irvin, J., Rajpurkar, P., Ko, M., Yu, Y., Ciurea-Ilcus, S., Chute, C., Marklund, H., Haghgoo, B., Ball, R. L., Shpanskaya, K. S., Seekins, J., Mong, D. A., Halabi, S. S., Sandberg, J. K., Jones, R., Larson, D. B., Langlotz, C. P., Patel, B. N., Lungren, M. P., and Ng, A. Y., “Chexpert: A large chest radiograph dataset with uncertainty labels and expert comparison,” CoRR abs/1901.07031 (2019).
  * [8] Gawlikowski, J., Saha, S., Kruspe, A., and Zhu, X. X., “An advanced dirichlet prior network for out-of-distribution detection in remote sensing,” IEEE Transactions on Geoscience and Remote Sensing 60, 1–19 (2022).
  * [9] Srivastava, A. and Sutton, C., “Autoencoding variational inference for topic models,” in [Proceedings for the 5th International Conference on Learning Representations ], (Apr. 2017).  5th International Conference on Learning Representations, ICLR 2017 ; Conference date: 24-04-2017 Through 26-04-2017.
  * [10] Joo, W., Lee, W., Park, S., and Moon, I.-C., “Dirichlet variational autoencoder,” Pattern Recognition 107, 107514 (2020).
  * [11] Ruskin, J., Gurney, J., Thorsen, M., and Goodman, L., “Detection of pleural effusions on supine chest radiographs,” American Journal of Roentgenology 148(4), 681–683 (1987).  PMID: 3493648.
  * [12] Makhzani, A. and Frey, B. J., “k-sparse autoencoders,” in [2nd International Conference on Learning Representations, ICLR 2014, Banff, AB, Canada, April 14-16, 2014, Conference Track Proceedings ], Bengio, Y. and LeCun, Y., eds. (2014).
  * [13] Burgess, C. P., Higgins, I., Pal, A., Matthey, L., Watters, N., Desjardins, G., and Lerchner, A., “Understanding disentangling in $\beta$-vae,” CoRR abs/1804.03599 (2018).
  * [14] Jabbour, S., Fouhey, D., Kazerooni, E., Sjoding, M. W., and Wiens, J., “Deep learning applied to chest x-rays: Exploiting and preventing shortcuts,” in [Proceedings of the 5th Machine Learning for Healthcare Conference ], Doshi-Velez, F., Fackler, J., Jung, K., Kale, D., Ranganath, R., Wallace, B., and Wiens, J., eds., Proceedings of Machine Learning Research 126, 750–782, PMLR (07–08 Aug 2020).
  * [15] Gaube, S., Suresh, H., Raue, M., Lermer, E., Koch, T., Hudecek, M., Ackery, A., Grover, S., Coughlin, J., Frey, D., Kitamura, F., Ghassemi, M., and Colak, E., “Non-task expert physicians benefit from correct explainable ai advice when reviewing x-rays,” Sci Rep 13(1), 1383 (2023).
  * [16] Selvaraju, R. R., Cogswell, M., Das, A., Vedantam, R., Parikh, D., and Batra, D., “Grad-cam: Visual explanations from deep networks via gradient-based localization,” in [2017 IEEE International Conference on Computer Vision (ICCV) ], 618–626 (2017).
  * [17] Saporta, A., Gui, X., Agrawal, A., et al., “Benchmarking saliency methods for chest x-ray interpretation,” Nature Machine Intelligence 4, 867–878 (2022).