# Diverse Preference Augmentation with Multiple Domains for Cold-start
Recommendations

Yan Zhang†‡♮, Changyu Li†, Ivor W. Tsang♯‡, Hui Xu†, Lixin Duan†, Hongzhi
Yin§, Wen Li†, Jie Shao† †University of Electronic Science and Technology of
China, Chengdu 611731, China
‡Australian Artificial Intelligence Institute, University of Technology
Sydney, Sydeny 2007, Australia
♮Intelligent Terminal Key Laboratory of Sichuan Province, Yibin 644000, China
♯Center for Frontier AI Research, Research Agency for Science, Technology and
Research (A⋆STAR), Singapore
§The University of Queensland, Brisbane 4067, Australia
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
<EMAIL_ADDRESS><EMAIL_ADDRESS>{liwen<EMAIL_ADDRESS>
###### Abstract

Cold-start issues have been more and more challenging for providing accurate
recommendations with the fast increase of users and items. Most existing
approaches attempt to solve the intractable problems via content-aware
recommendations based on auxiliary information and/or cross-domain
recommendations with transfer learning. Their performances are often
constrained by the extremely sparse user-item interactions, unavailable side
information, or very limited domain-shared users. Recently, meta-learners with
meta-augmentation by adding noises to labels have been proven to be effective
to avoid overfitting and shown good performance on new tasks. Motivated by the
idea of meta-augmentation, in this paper, by treating a user’s preference over
items as a task, we propose a so-called Diverse Preference Augmentation
framework with multiple source domains based on meta-learning (referred to as
MetaDPA) to i) generate diverse ratings in a new domain of interest (known as
target domain) to handle overfitting on the case of sparse interactions, and
to ii) learn a preference model in the target domain via a meta-learning
scheme to alleviate cold-start issues. Specifically, we first conduct multi-
source domain adaptation by dual conditional variational autoencoders and
impose a Multi-domain InfoMax (MDI) constraint on the latent representations
to learn domain-shared and domain-specific preference properties. To avoid
overfitting, we add a Mutually-Exclusive (ME) constraint on the output of
decoders to generate diverse ratings given content data. Finally, these
generated diverse ratings and the original ratings are introduced into the
meta-training procedure to learn a preference meta-learner, which produces
good generalization ability on cold-start recommendation tasks. Experiments on
real-world datasets show our proposed MetaDPA clearly outperforms the current
state-of-the-art baselines.

###### Index Terms:

Recommender system, preference augmentation, meta leaning, cold-start

##  I Introduction

Recommender systems have shown great success in both academia and industries,
and so become indispensable in our life by helping us filter millions of
possible choices. Recommender systems provide a small set of items from the
underlying pool of items based on users’ historical interactions and their
side information. One of the well known recommendation frameworks is
Collaborative Filtering (CF)[1, 2], where the only available data is user-item
historical interactive information. A key challenge in CF-based methods is to
provide accurate recommendations from a large number of items with extremely
sparse interactions[3]. Such recommender systems suffer from poor performance
due to sparse interactive data or ratings and cannot even handle user cold-
start and item cold-start issues brought by new users and new items [4]. So as
a very critical problem in recommender systems, how to make accurate
recommendation under sparse and cold-start scenarios attracts rising attention
from a wide range of stakeholders in recent years.

Existing approaches for solving cold-start and sparse issues are proposed from
the following three directions: (1) content-aware recommender systems[5, 6, 7,
8, 9] that integrate auxiliary side information and interactive data to
enhance representations of users and items, and then feed them into the
preference model to improve the performance of recommender systems, where
user’s and item’s content information (user’s profile, item’s description,
user’s review, etc.) is taken as auxiliary side information for strengthening
representations of users and items. (2) Cross-domain recommender systems
transfer preference knowledge from source domains to its similar target
domain, and then improve the performance of recommendations in the target
domain. These methods can be categorized into single source[10, 11, 12, 13,
14, 15, 16, 17] and multiple source[18, 19, 20, 21, 22, 23, 24] cross-domain
recommendations based on the number of source domains applied for transferring
preference knowledge. (3) Meta-learning based recommender systems[25, 26, 27,
25] learn the prior preference distribution of users over items by taking
users’ preferences as meta-learning tasks. They can improve the performance of
recommendations under sparse and cold-start settings by fine-tuning the
preference model with only a few ratings.

Content-aware recommender systems have been widely studied for solving the
cold-start and sparse issues with the help of auxiliary side information. One
of the most commonly used side information is content[5, 6, 7, 8, 9, 2, 28,
29, 30]. By learning with content data, the features of users or items with
just a few ratings or even no ratings can be then effectively represented,
making those content-aware recommender systems be able to improve the
performance under sparse and cold-start scenarios. However, there exist
inconsistencies between item content and user preferences. That is to say,
users under the same profile (e.g., age, occupation, gender, place of
residence, etc.) often have different preferences over the same item; and
items having similar content (e.g., description, category, users’ reviews,
etc.) are often rated with different scores by the same user. As a result, the
performance improvement of content-aware recommender systems are limited by
the gap between content and preferences.

Cross-domain recommendations based on transfer learning are another type of
solutions for solving cold-start and sparse challenges. Existing methods
transfer knowledge from source domains with rich preference information to a
target domain with very sparse historical data[31, 12, 13, 14]. Moreover,
those methods transfer preference information by domain adaptation with
domain-shared users in order to strengthen the representations of users and
items. Thus, the cross-domain model can learn effective representations of
users and items than only using preference information of a single domain.
However, the limit number of shared users affects the capability of preference
transferring, which restricts the performance improvement in the target
domain. For example, on Amazon datasets, Books and Electronics subsets only
share 5% users, which limits the transferable preference patterns from the
source domain to the target domain, and thus the performance of cross-domain
recommendations is also constrained.

To acquire more preference patterns, some scholars study multi-domain
recommendations of transferring preference patterns from multiple source
domains to a target domain[18, 19, 20, 21, 22, 23, 24]. These methods extract
correlations between source domains and the target domain and tie factors from
different source domains together. Such correlation enrich rating patterns of
the target domain with multiple related source domains. Thus, these methods
can achieve better performance than single source domain. The transferable
preference patterns are also limited because the correlation is dependent on
shared users. The performance is still limited by the ratio of shared users
among all users. In addition, some of these multi-source cross-domain methods
can only provide recommendation for shared users and do not work for providing
recommendations for unshared users. Besides, the augmentation method is
another way to acquire more preference patterns, such as AugCF[32]. It is
designed based on Conditional Generative Adversarial Nets by considering the
class (like or dislike) as a feature to generate new interaction data, which
is evaluated to be a sufficiently real augmentation to the original dataset in
their work.

Meta-learning has been validated as a promising approach for mitigating cold-
start issues of recommendations[4, 33, 34, 27, 25], which treats user’s
preferences as meta-learning tasks and learns a preference prior distribution
of all users over items. Meta-learning based methods can fast adapt to new
users’ or new items’ recommendations with the learned meta-learner of the
preference prediction model. However, the meta-learner easily overfits to the
sparse preference (rating) data, which makes it difficult to provide accurate
recommendations under new users or new items settings.

To avoid overfitting on meta-training tasks, meta-augmentation[35] adds noise
to labels $y$ without changing inputs $x$. It is capable of handling two forms
of overfitting: (1) memorization overfitting, in which the model is able to
overfit to the training set without relying on the meta-learner, and (2) meta-
learner overfitting, in which the learner overfits to the training set and
does not generalize to the test set. Yin et al.[36] identify the memorization
overfitting can happen when the set of tasks are non-mutually-exclusive. The
meta-augmentation is proven to avoid memorization overfitting effectively by
transforming the task setting from non-mutually-exclusive to mutually-
exclusive and proven to avoid the learner overfitting effectively[36]. Tasks
are said to be mutually-exclusive[35] if a single model cannot solve them all
at once. For example, if the task $\mathcal{T}_{1}$ is ‘output 0 if the input
image is a dog’, and task $\mathcal{T}_{2}$ is ‘output 1 if the image is a
dog’, then we call tasks $\\{\mathcal{T}_{1},\mathcal{T}_{2}\\}$ are mutually-
exclusive.

Generally, we define ‘Mutual Exclusivity’ as: Training samples
$(x,y_{1}),(x,y_{2}),\cdots,(x,y_{k})$ are called mutually-exclusive samples,
if all continuous labels $y_{1},y_{2},\cdots,y_{k}$ are different from each
other with the same input $x$. For example, training samples
$(x,0.1),(x,0.2),(x,0.3)$ with the same input $x$ are mutually-exclusive
samples because all labels are different from each other. However, in
practice, it is difficult to obtain training samples that meet such a strict
assumption (i.e., all labels are required to be different with the same
input). By relaxing the assumption, we define ‘Diversity’ as: Training samples
$(x,y_{1}),(x,y_{2}),\cdots,(x,y_{k})$ are called diverse samples, if not all
continuous labels $y_{1},y_{2},\cdots,y_{k}$ are different from each other
with the same input $x$. For example, training samples
$(x,0.1),(x,0.1),(x,0.3)$ are diverse samples because not all labels are
different (the first and the second samples are with the same label $0.1$).
It’s worth noting that labels in the above two definitions are continuous
values. Particularly, continuous labels are within the interval $[0,1]$,
because we train our model on real interactive data(‘0’ or ‘1’) and augmented
interactive data within the interval $[0,1]$. It is also worth mention that
all labels are required to be different from each other in mutually-exclusive
samples; while in diverse samples, some labels from
$\\{y_{1},y_{2},\cdots,y_{k}\\}$ may be the same, so mutually-exclusive
samples are diverse samples, but not vice versa.

To avoid overfitting, our initial goal is to construct mutually-exclusive
samples (tasks) in the target domain for training our model. Specifically, we
develop a multi-source domain adaptation module that transfers the preference
patterns from multiple source domains ($k$ source domains) to a target domain
by $k$ dual conditional variational autoencoders (Dual-CVAEs) shown in Fig. 1.
By enforcing Mutually-Exclusive (ME) constraints on decoders of those $k$
Dual-CVAEs, we hope to generate mutually-exclusive ratings by $k$ encoder-
decoder frameworks (highlighted with red line in Fig. 1) given the input
$\mathbf{x}_{t}$. However, it is computationally intractable to obtain an
optimal solution due to the strict assumption (i.e., all generated ratings
from different source domains are required to be different from each other),
because it needs $\mathcal{O}(k^{2})$ operations to assert the assumption in
each iteration of training those $k$ Dual-CVAEs. Accordingly, we relax the ME
constraint by adding it to the objective with a weight (hyper-parameter
$\beta_{2}$ in Eq. (8)). Hence, these generated ratings may not be all
different from each other, but they increase the rating diversity[35].
Consequently, we generate diverse ratings
$\mathbf{\hat{r}}_{t1},\mathbf{\hat{r}}_{t2},\cdots,\mathbf{\hat{r}}_{tk}$ by
the learned $k$ encoder-decoder frameworks with the same content
$\mathbf{x}_{t}$ in the target domain, which is different from the work[35]
where it augments diverse samples by adding noises to the ground-truth label
$y$.

We call our proposed method as Diverse Preference Augmentation based on meta-
learning (MetaDPA). To learn domain-shared and domain-specific information by
these $k$ Dual-CVAEs, we add Multi-domain InfoMax (MDI) constraints imposed on
the latent representations of source and target domains[37], which maximizes
the mutual information between representations of source and target domains.
To augment diverse ratings, we impose ME constraints on the decoders of $k$
Dual-CVAEs. Then we adopt the learned $k$ encoder-decoders (red line in Fig.
1) to generate diverse ratings by the content data $\mathbf{x}_{u}$ of target
domain. Finally we combine the augmented diverse ratings and true ratings to
learn a prior preference distribution via a meta-learning framework in the
target domain, which is expected to quickly adapt to new users’ or new items’
recommendations via only a few fine-tuning steps. The main contributions are
summarized as follows:

  * •

We propose a multi-source cross-domain recommender system, coined as Diverse
Preference Augmentation based meta-learning (MetaDPA), for solving cold-start
and sparse issues in recommendations. MetaDPA consists of three blocks: multi-
source domain adaptation, diverse preference augmentation, and preference
meta-learning.

  * •

For multi-source domain adaptation, MetaDPA augments diverse ratings with
content data via the ME constraint imposed on the multi-source domain
adaptation.

  * •

We develop the MDI constraint to learn domain-shared and domain-specific
preference information, where the domain-shared information makes it possible
to transfer preference patterns from the source domain to the target domain,
and the domain-specific preference information contributes to generate diverse
ratings in the preference augmentation step.

  * •

In experiments, we demonstrate the effectiveness of MetaDPA to relieve the
sparse issue (‘Warm-start’) and three types of cold-start issues (‘C-U’,
‘C-I’, ‘C-UI’) by comparing with existing competitive baselines. Besides, we
conduct ablation studies to evaluate the effectiveness of ME and MDI
constraints.

The rest of this paper is organized as follows. Section II introduces three
types of closely related work, content-aware recommender systems in Section
II-A, cross-domain recommendations in Section II-B and meta-learning based
recommender systems in Section II-C. In Section III, we introduce the problem
formulation and notations in Section III-A, and briefly state the recommender
systems equipped with the meta-learning framework in Section III-B. Next, we
give a detailed introduction of the proposed three-block MetaDPA in Section
IV. Specifically, we firstly introduce the multi-source cross-domain
adaptation in Section IV-A including MDI and ME constraints added on the
domain adaption; we then introduce the diverse preference augmentation in
Section IV-B after multi-source domain adaptation; finally we introduce the
preference meta-learning framework in Section IV-C. Then we demonstrate the
experiments of the proposed MetaDPA together with the competing baselines in
Section V, which includes introductions of the experimental settings in
Section V-A, the overall experimental results compared with baselines in
Section V-B, the ablation studies to evaluate the effectiveness of MDI and ME
constraints in Section V-E, and the impact of hyper-parameters $\beta_{1}$,
$\beta_{2}$ the above two constraints in Section V-F. Finally, we conclude
this paper in Section VI.

Figure 1: The framework of cross-domain adaptation with Dual-CVAE. The MDI
constraint is imposed on latent representations $\mathbf{z}_{s}$ and
$\mathbf{z}_{t}$. The ME constraint is enforced on the outputs of two decoders
$D_{s}$ and $D_{t}$. Given ratings $\mathbf{r}_{s}$, $\mathbf{r}_{t}$ and
content data $\mathbf{x}_{s}$, $\mathbf{x}_{t}$, the goal of Dual-CVAE is to
learn domain-shared and domain-specific preference information, and then
generate diverse ratings by decoders of $k$ Dual-CVAEs.

##  II Related Work

In this section, we focus on closely related work to our method: content-aware
recommender systems, cross-domain recommender systems, and mete-learning based
recommender systems. The proposed MetaDPA is a kind of cross-domain
recommendation that transfers preference patterns from multiple source domains
to a target domain based on a meta-learning optimization framework with
content information.

###  II-A Content-aware Recommender Systems

Content-aware recommender system, as a representative content-aware method, is
widely studied by scholars recently. Such as the state-of-the-art
collaborative deep learning (CDL) [6] was proposed as a probabilistic model by
jointly learning a probabilistic stacked denoising auto-encoder (SDAE) [38]
and CF. CDL exploits the interaction and content data to alleviate cold start
and data sparsity problems. However, unlike CTR, CDL takes advantage of deep
learning framework to learn effective real latent representations. Thus, it
can also be applied in the cold-start and sparse settings. CDL is also a
tightly coupled method for recommender systems by developing a hierarchical
Bayesian model.

Another classic content-aware method is deep cooperative neural networks
(CoNN)[39], which consists of two parallel neural networks: one learns user
behaviors exploiting users’ reviews, and the other one learns item properties
from the items’ reviews. A shared layer is introduced on the top to couple
these two networks together. Then, dual attention mutual learning (DAML)[40]
integrates ratings and reviews into a joint neural network with a local and
mutual attention mechanism to strengthen the interpretability. In addition,
higher-order nonlinear interaction of features are extracted by the neural
factorization machines to predict ratings.

###  II-B Cross-domain Recommender Systems

Cross-domain recommender systems, as a type of methods for solving cold-start
and sparse challenges, transfer preference information from source domains to
its related target domain and then improve the performance of recommendations
in the target domain. These methods can be categorized into single source and
multiple source cross-domain recommendations based on the number of source
domains applied for transferring.

Cross-domain recommendations with single source domain, such as cross-domain
triadic factorization (CDTF)[41], deep domain adaptation model (DARec)[42] ,
and equivalent transformation learner (ETL)[43] were proposed to transfer
user-item preference relations from a single source domain to a target domain
without relying on any auxiliary information. By combining content
information, a transfer meeting content-aware method (TMH)[44] is formulated
with unstructured text in an end-to-end manner. Then, Cross-domain
recommendation framework via aspect transfer network (CATN)[45] is developed
via an aspect transfer network for cold-start users. Another related study is
text-enhanced domain adaptation recommendation (TDAR)[46] that extracts the
textual features in word semantic space for each user and item and feeds them
into a domain classifier with the embeddings of users and items for better
domain adaptation.

For multi-source cross-domain recommendations, one pioneer work is Collective
Matrix Factorization (CMF)[18] that extends linear models to arbitrary
relational domains. Then, multi-domain collaborative filtering (MCF)[47] is
proposed by considering multiple collaborative filtering tasks in different
domains simultaneously and exploiting the relationships between domains. MCF
also introduces the link function for different domains to correct their
biases. Recently, MINDTL[14] exploits transfer learning and compresses the
knowledge from the source domain into a cluster-level rating matrix to model
user’s rating pattern. The rating patterns in the low level matrix are
transferred to the target domain by enriching rating patterns by relaxing the
full rating restriction on source domains.

###  II-C Meta-learning Based Recommender Systems

Recently, many scholars focus on formulating recommendation frameworks with
meta-learning[4, 48, 26] for solving cold-start and sparse issues. Current
meta-learning-based recommender systems adopt optimization-based meta-learning
methods, such as model-agnostic meta-learning (MAML)[49], to improve the
performance of new tasks. One representative work is MeLU[4] that utilizes
MAML to rapidly adapts to new tasks with a few ratings. Another
straightforward application of MAML on the recommender system is MetaCS[50],
which formulates each user’s rating pattern as a task in MAML and designs a
recommendation framework based on this. Then, Memory-augmented meta-
optimization (MAMO)[26] designs two memory matrices to store task-specific
memories for parameter initialization and feature-specific memories for fast
predicting users’ preferences, respectively. By integrating heterogeneous
information, MetaHIN[27] exploits meta-learning to alleviate the cold-start
problem at both the data and model levels, which leverages multifaceted
semantic contexts and a co-adaptation meta-learner to learn finer grained
semantic priors for new tasks in both semantic and task-wise manners. By
dynamic subgraph sampling to construct representative training tasks,
MetaCF[51] dynamically samples subgraph centered at a user in the training
phase to account for the effect of limited interactions under cold-start
settings, and extends the historical interactions by incorporating potential
interactions to avoid the overfitting problem. It can achieve good performance
under cold-start settings. However, the drawback is obvious due to the
introduction of potential interaction leading to low efficiency of training
the model.

As a promising approach, meta-learning frameworks can fast adapt to new users’
or new items’ recommendations. However, existing meta-learning based methods
suffer poor performance caused by meta-overfitting on sparse interactive data.
So in this paper we aim to solve the meta-overfitting problems in meta-
learning based recommendations by the proposed diverse preference augmentation
technique as introduced in Section I.

##  III Preliminaries

In this section, we first describe the basic notations used in this paper and
the problem formulation in Section III-A. Then we briefly introduce a general
framework of meta-learning based recommender systems in Section III-B.

###  III-A Problem Formulation

In this paper, we aim to provide recommendations in the target domain by
transferring preference knowledge from source domains. We suppose there are
$n$ users and $m$ items in the target domain, and their index sets are denoted
as $U=\\{1,\cdots,n\\}$ and $I=\\{1,\cdots,m\\}$, respectively. The available
data includes user-item interactive matrix $\mathbf{R}=\\{r_{ui}\geq 0:u\in
U,i\in I\\}$, the user content data $\mathbf{C}^{U}$, and the item content
data $\mathbf{C}^{I}$. If user $u$ has an interaction with item $i$, then
$r_{ui}=1$; otherwise, $r_{ui}=0$. For each user $u$, the content data
$\mathbf{c}_{u}\in\mathbf{C}^{U}$ is composed of bag-of-vectors generated from
her/his rated items’ review data. Similarly, the content data of each item
$\mathbf{c}_{i}\in\mathbf{C}^{I}$ is extracted from all obtained reviews.

In this work, we divide users’ set $U$ as $U_{e}$ and $U_{n}$, where we define
$U_{e}$ as ‘existing users’, and each $u\in U_{e}$ represents the user who
rates no less than 5 items, i.e., $|\\{r_{ui}:u\in U_{e}\\}|\geq 5$. The
remaining users $u\in U_{n}$ are defined as ‘new users’ (or cold-start users).
Similarly, we divide items’ set $I$ as $I_{e}$ and $I_{n}$, where we define
$I_{e}$ as ‘existing items’, and each $i\in I_{e}$ denotes the item of
receiving no less than 5 ratings, i.e., $|\\{r_{ui}:i\in I_{e}\\}|\geq 5$, and
the remaining items $i\in I_{n}$ are defined as ‘new items’ (or cold-start
items). Then, we define the following four recommendation problems including
the sparse issue (‘Warm-start’) and three kinds of cold-start issues solved in
this paper:

  * (1)

Warm-start: how to improve the accuracy of recommending existing items to
existing users with sparse interactions available? Given sparse ratings
$R_{w}$ of users $U_{e}$ to items $I_{e}$, i.e., $R_{w}=\\{r_{ui}>0,u\in
U_{e},i\in I_{e}\\}$, then we train our model $f(\theta):U_{e}\times
I_{e}\rightarrow R_{w}$ on $R_{w}$. The goal of ‘Warm-start’ is to predict
unknown ratings $\hat{r}_{ui}\notin R_{w}$ of existing users $U_{e}$ to
existing items $I_{e}$ with the trained model $f(\theta)$ and recommend $k$
existing items with top-$k$ ratings to each user in $U_{e}$.

  * (2)

C-U: how to improve the accuracy of recommending existing items to new users?
After training our model $f(\theta)$ with $R_{w}$, we finetune $f(\theta)$
with only a few ratings $R_{cu}$ of new users $u\in U_{n}$ to existing items
$i\in I_{e}$. The goal of ‘C-U’ is to predict unknown ratings
$\hat{r}_{ui}\notin R_{cu}$ of new users $U_{n}$ to existing items $I_{e}$ by
the finetuned model $f(\theta)$ and recommend $k$ existing items with top-$k$
ratings to new users.

  * (3)

C-I: how to improve the accuracy of recommending new items to existing users?
Similar to C-U, we finetune $f(\theta)$ with only a few ratings $R_{ci}$ of
existing users $U_{e}$ to new items $I_{n}$. The goal of ‘C-I’ is to predict
unknown ratings $\hat{r}_{ui}\notin R_{ci}$ of existing users $U_{e}$ to new
items $I_{n}$ by the finetuned model $f(\theta)$ and recommend $k$ new items
with top-$k$ ratings to existing users.

  * (4)

C-UI: how to improve the accuracy of recommending new items to new users? We
finetune $f(\theta)$ with a few ratings $R_{cui}$ of new users $U_{n}$ to new
items $I_{n}$. The goal of ‘C-UI’ is to predict unknown ratings
$\hat{r}_{ui}\notin R_{cui}$ of new users $U_{n}$ to new items $I_{n}$ with
the finetuned model and recommend $k$ new items with top-$k$ ratings to new
users.

Figure 2: The framework of diverse preference augmentation with multiple
source domains based on meta-learning (MetaDPA) consists of three blocks:
Multi-source Domain Adaptation, Diverse Preference Augmentation, and
Preference Meta-learning. We first train the framework of multi-source domain
adaptation; and then we generate diverse ratings for the target domain given
the content data; and finally we learn the preference model formulated as a
multi-layer architecture based on the meta-learning optimization framework
MAML.

###  III-B Meta-learning for Recommendations

The objective of meta-learning is to learn good initial weights for a model
that can fast adapt to previously unseen tasks with a few samples[25]. In
meta-learning based recommendations[4, 52], a user’s preference prediction
over all items is treated as a meta-learning task $\mathcal{T}_{u}$, which is
denoted as the dataset used for the task. To be specific,
$\mathcal{T}_{u}=(\mathbf{c}_{u},\mathbf{r}_{u})$, where $\mathbf{c}_{u}$ is
the input of all items for a specific user $u$ and $\mathbf{r}_{u}$ is the
ratings of a user to all items. The input identifies a user, and it could be
her/his identity, profile, historical preference information, or the review
comments written by the user. In this paper, we user the review comments as
the input. In particular, according to the setting of meta-learning, we divide
into a support set $\mathcal{S}_{u}$ and a query set $\mathcal{Q}_{u}$. Tasks
from all users’ preferences are randomly splited into two disjoint partitions:
one for meta-training tasks denoted as $\mathbb{T}_{tr}$, and another one for
meta-testing tasks denoted as $\mathbb{T}_{te}$. The meta-learning based
recommendations aim to learn a good preference prior distribution on meta-
training tasks, and then can fast adapt to new tasks in meta-testing tasks.

Suppose a supervised learning problem considers training on a dataset for a
single task $\mathcal{T}$. In contrast, meta-learning considers to learn a set
of tasks ${\mathcal{T}_{u}}\in\mathbb{T}_{tr}$, which are sampled from the
task distribution $p(\mathcal{T})$. The objective of meta-training for
recommendations is formulated as follows:

$\displaystyle\mathop{min}_{\theta}\sum_{\mathcal{T}_{u}\sim\mathbb{T}_{tr}}\mathcal{L}_{\mathcal{T}_{u}}(\mathcal{\theta}-\alpha\nabla_{\theta}\mathcal{L}_{\mathcal{T}_{u}}(\mathcal{\theta},\mathcal{S}_{u}),\mathcal{Q}_{u}),$
(1)

where $\nabla_{\theta}$ denotes the gradient w.r.t parameters $\theta$ of a
preference prediction model, and $\alpha$ is the meta-learning rate, and
$\mathcal{\theta}-\alpha\nabla_{\theta}\mathcal{L}_{\mathcal{T}_{u}}(\mathcal{\theta},\mathcal{S}_{u}$
is the task-specific parameters adapted to the task $\mathcal{T}_{u}$ after
one gradient step from the global $\theta$. The algorithm locally updates
parameters $\theta$ based on the gradient with $\mathcal{S}_{u}$, and then
globally updates $\theta$ based on $\mathcal{Q}_{u}$, so that the globally
updated parameters adapt to various tasks[4]. During meta-testing, the meta-
learner adapts the learned $\theta$ to $\mathcal{T}_{u}\in\mathbb{T}_{te}$
with its support set $\mathcal{S}_{u}$, and then the adapted parameters
$\theta$ is used to predict ratings and evaluate the recommendation
performance in its query set $\mathcal{Q}_{u}$[52].

##  IV Methodology

In this section, we propose a novel method Diverse Preference Augmentation
with multiple domains (MetaDPA) for cold-start recommendations as illustrated
in Fig. 2. Our method consists of three blocks: Multi-source Domain
Adaptation, Diverse Preference Augmentation, and Preference Meta-learning.

Firstly, we conduct multi-source domain adaptation between the source domains
and the target domain with Dual CVAEs, and align the representations of the
source and target domains by the principle of InfoMax[37] in Section IV-A.
Then, we employ the learned encoder-decoders to generate diverse ratings,
which is named as diverse preference augmentation in Section IV-B. Next, these
augmented diverse ratings together with the original true ratings are fed into
the preference meta-learning procedure in Section IV-C. Finally, we test the
recommendation performances under three cold-start settings separately.

###  IV-A Multi-source Domain Adaptation

In this section, our objective is to conduct domain adaptation from multiple
source domains to the target domains. As users’/items’ content information is
commonly used for alleviating cold-start issues, and the content data
including items’ images, descriptions and users’ profile, user-item review
texts. Most of the content data are not shared by different domains. In
TDAR[46], it takes the review texts as domain-invariant features to align the
latent space for domain adaptation. To facilitate the domain adaptation, we
also adopt the domain-invariant reviews as the content data. Specifically, the
user content $\mathbf{c}_{u}$ is the collection of reviews from items rated by
the user $u$. We first encode the user’s content into a dense low-dimensional
embeddings $\mathbf{x}_{u}$. We denote $\mathbf{x}_{u}^{(s)}$ and
$\mathbf{x}_{u}^{(t)}$ as the user content vectors in the source domain and in
the target domain, respectively. For simplicity, we use $\mathbf{x}_{s}$ and
$\mathbf{x}_{t}$ to represent them. Similarly, we denote $\mathbf{r}_{s}$ and
$\mathbf{r}_{t}$ as ratings rated by the shared user $u$ to items in the
source domain and the target domain, respectively.

We use a Dual-CVAE network to learn users’ latent representations and
reconstruct ratings $\mathbf{r}_{s}$ and $\mathbf{r}_{t}$. In the Dual-CVAE,
we add conditions $\mathbf{x}_{s}$ ($\mathbf{x}_{t}$) on the latent
representations in a similar way with HCVAE[53]. Firstly, the input
$\mathbf{x}_{s}$ and $\mathbf{x}_{t}$ are encoded into a distribution
$q_{\phi_{s}}(\mathbf{z}_{s}|\mathbf{r}_{s},\mathbf{x}_{s})$ and
$q_{\phi_{t}}(\mathbf{z}_{t}|\mathbf{r}_{t},\mathbf{x}_{t})$, respectively.
The encoders of the Dual-CVAE maps ratings $\mathbf{r}_{s}$ and
$\mathbf{r}_{t}$ to latent representations $\mathbf{z}_{s}$ and
$\mathbf{z}_{t}$, respectively. The optimization objective of the Dual-CVAE is
the evidence lower bound (ELOB)[54], which consists of the sum of the
reconstruction error, namely, maximizing the likelihood estimation of the
decoders $\log p_{\theta_{s}}(\mathbf{r}_{s}|\mathbf{z}_{s},\mathbf{x}_{s})$
and $\log p_{\theta_{t}}(\mathbf{r}_{t}|\mathbf{z}_{t},\mathbf{x}_{t})$, and
the negative KL-divergence between the variational posterior and the prior. So
the loss function in the source domain and the target domain can be written as
follows[53]:

$\displaystyle\mathcal{L}_{\textit{ELBO}}$
$\displaystyle=\mathcal{L}(\mathbf{r}_{s},\mathbf{x}_{s};\theta_{s},\phi_{s})+\mathcal{L}(r_{t},\mathbf{x}_{t};\theta_{t},\phi_{t})$
$\displaystyle=\mathbb{E}_{q_{\phi_{s}}(\mathbf{z}_{s}|\mathbf{r}_{s},\mathbf{x}_{s})}[\log
p_{\theta_{s}}(\mathbf{r}_{s}|\mathbf{z}_{s},\mathbf{x}_{s})]$
$\displaystyle+\mathbb{E}_{q_{\phi_{t}}(\mathbf{z}_{t}|\mathbf{r}_{t},\mathbf{x}_{t})}[\log
p_{\theta_{t}}(\mathbf{r}_{t}|\mathbf{z}_{t},\mathbf{x}_{t})]$ $\displaystyle-
D_{KL}[q_{\phi_{s}}(\mathbf{z}_{s}|\mathbf{r}_{s},\mathbf{x}_{s})||p(\mathbf{z}_{s})]$
$\displaystyle-
D_{KL}[q_{\phi_{t}}(\mathbf{z}_{t}|\mathbf{r}_{t},\mathbf{x}_{t})||p(\mathbf{z}_{t})].$
(2)

We employ the softmax function as the activation function in the output layer
that maps the reconstructed output into the range of [0,1], which is
consistent with the range of reconstructed ratings. The reconstruction loss
between the predictions and true ratings could be MSE if the user-item
interactions are explicit feedback and binary cross entropy if the user-item
interactions are implicit feedbacks[55]. In this paper, we use the implicit
feedback as ratings, so we adopt the binary cross-entropy as the
reconstruction loss.

The KL divergence loss of the Dual-CVAE can be estimated using the Stochastic
Gradient Variational Bayes (SGVB) estimator[56]. Besides, we hope to learn
latent representations from the content embeddings $\mathbf{x}_{s}$ and
$\mathbf{x}_{t}$, and so the learned distributions of latent representations
store preference information from both ratings and content, which makes it
capable of reconstructing ratings only using content. So we have the following
objective:

$\displaystyle\mathcal{L}_{\textit{KL}}=$
$\displaystyle-\frac{1}{2}\sum_{l=1}^{L}[\mathbf{\sigma}_{s_{l}}^{2}+(\mathbf{\mu}_{s_{l}}-\mathbf{z}_{s_{l}}^{x})^{2}-{\rm\log}\mathbf{\sigma}_{s_{l}}^{2}-1]$
$\displaystyle+\frac{1}{2}\sum_{l=1}^{L}[\mathbf{\sigma}_{t_{l}}^{2}+(\mathbf{\mu}_{t_{l}}-\mathbf{z}_{t_{l}}^{x})^{2}-{\rm\log}\mathbf{\sigma}_{t_{l}}^{2}-1].$
(3)

where $L$ is the dimension of the latent sampled representations. For the
source domain, $\mathbf{u}_{s}$ and $\mathbf{\sigma}_{s}$ are the mean and
variance of the approximate posterior, and $\mathbf{z}_{s}^{x}$ is the output
of a dense embedding encoder $E_{s}^{x}$, parameterized by $\phi_{x_{s}}$. The
notations $\mathbf{u}_{t}$, $\mathbf{\sigma}_{t}$, $\mathbf{z}_{t}^{x}$,
$E_{t}^{x}$, and $\phi_{x_{t}}$ in the target domain have similar meanings.

To reconstruct ratings only using content, we align the latent representations
of the Dual-CVAE to the output dense embedding vector of encoder $E_{s}^{x}$
by the following mean square error (MSE) loss:

$\mathcal{L}_{\textit{MSE}}=||\mathbf{z}_{s}-q_{\phi_{x_{s}}}(\mathbf{z}_{s}^{x}|\mathbf{x}_{s})||^{2}+||\mathbf{z}_{t}-q_{\phi_{x_{t}}}(\mathbf{x}_{t}^{x}|\mathbf{x}_{t})||^{2}.$
(4)

For domain adaptation, we construct the cross-domain reconstruction objectives
by generating ratings $\mathbf{r}_{s}$ of the source domain with the latent
representation of the target domain $\mathbf{z}_{t}$, and reconstructing
ratings $\mathbf{r}_{t}$ of the target domain with the latent factors of the
source domain $\mathbf{z}_{s}$. To align the latent representations
$\mathbf{z}_{s}$ and $\mathbf{z}_{t}$, we have the following cross-domain
reconstruction loss,

$\displaystyle\mathcal{L}_{\textit{Rec}}=$
$\displaystyle\frac{1}{2m}\sum_{i=1}^{m}[r_{si}\log(\hat{r}_{ti})+(1-r_{si})\log(1-\hat{r}_{ti})]$
$\displaystyle+\frac{1}{2m}\sum_{i=1}^{m}[r_{ti}\log(\hat{r}_{si})+(1-r_{ti})\log(1-\hat{r}_{si})],$
(5)

where $\hat{r}_{ti}$ is the reconstructed rating of user $u$ to item $i$ by
feeding the latent representation of target domain $\mathbf{z}_{t}$ into the
decoder $D_{s}$ in the target domain as shown in the Fig. 1, and
$\hat{r}_{si}$ is the generated rating of user $u$ to item $i$ by injecting
the latent representation of source domain $\mathbf{z}_{s}$ into the decoder
of target domain $D_{t}$.

To maximize the mutual information from the source and target domains and
preserve the domain-specific properties, we impose the MDI constraint with the
InfoMax principle[57] on sampled latent representations $\mathbf{z}_{s}$ and
$\mathbf{z}_{t}$. Since the MDI constraint does not discard superfluous
information of each domain for predicting ratings. So it allows the
reconstructed user’s preference to have the capacity of preserving the domain-
specific properties as well as the domain-shared properties. The MDI
constraint is written as follows:

$\mathcal{L}_{\textit{MDI}}(\phi_{s},\phi_{t})=-I_{\phi_{s},\phi_{t}}(\mathbf{z}_{s},\mathbf{z}_{t}),$
(6)

where the function $I(\cdot)$ denotes the mutual information between
inputs[37]. The MDI is employed here because we consider each user’s latent
preferences $\mathbf{z}_{s}$ and $\mathbf{z}_{t}$ encoded from different
domains should have both domain-shared and domain-specific properties. So the
MDI advocates the decoders of each domains to generate domain-specific
ratings, which is consistent with the goal of generating diverse ratings by
the content in the target domain.

###  IV-B Diverse Preference Augmentation

As introduced in Section I, the goal of diverse preference augmentation is to
generate diverse ratings by the learned encoder-decoders (highlighted with red
line shown in Fig. 1) of target domain given the input $\mathbf{x}_{t}$. If
there are $k$ source domains, we have $k$ Dual-CVAEs for the multi-source
domain adaptation, then we generate $k$ ratings for each user in the target
domain by his/her content $\mathbf{x}_{t}$. Due to the integrated effect of
MDI constraint imposed on the latent representations, the reconstruction loss
(IV-A) and the cross-domain reconstruction loss (IV-A), the Dual-CVAE can
learn domain-shared preference information well enough. Thus, these generated
$k$ ratings from $k$ Dual-CVAEs are similar because all source domains adapts
to the target domain. To avoid overfitting, we impose the ME constraints on
the outputs of $k$ decoders $D_{t}$ to generate ratings as different as
possible from each other. With the ME constraint, we force the generated
rating from the decoder $D_{t}$ as close to the reconstructed ratings as
possible from the decoder $D_{s}$. Thus, the generated ratings preserve
domain-specific preference patterns of multiple source domains, so we can
generate diverse ratings by $k$ encoder-decoder frameworks of Dual-CVAEs. The
ME constraint is realized by maximizing the mutual information between two
generated ratings $\mathbf{r}_{s}$ and $\mathbf{r}_{t}$ of a shared user $u$
as follows:

$\mathcal{L}_{\textit{ME}}=-I(\mathbf{r}_{s},\mathbf{r}_{t}),$ (7)

where $I(\cdot)$ denotes the mutual information between two inputs, that is
implemented by InfoNCE[58].

By enforcing ME and MDI constraints on the Dual-CVAE, the objective of cross-
domain adaptation can be derived by summing up objectives (IV-A), (4), (IV-A),
and two constraints (6), (7) together. Single-source cross-domain adaptation
is one special case of multi-source cross-domain adaptation. We can obtain the
multi-source cross-domain objective by integrating the following cross-domain
objective together,

$\mathcal{L}_{\textit{Dual-
CVAE}}=\mathcal{L}_{\textit{ELBO}}+\mathcal{L}_{\textit{MSE}}+\mathcal{L}_{\textit{Rec}}+\beta_{1}\mathcal{L}_{\textit{MDI}}+\beta_{2}\mathcal{L}_{\textit{ME}}.$
(8)

We train the Dual-CVAE shown in Fig. 1 by minimizing the objective (8) of
cross-domain adaptation. The multi-source cross-domain adaptation can be
implemented by training multiple Dual-CVAEs in parallel. Suppose we have $k$
source domains, then we learn $k$ Dual-CVAEs independently. After that, we
obtain the learned $k$ encoders $E_{t}^{x}$ and $k$ decoders $D_{t}$, and then
employ them to generate $k$ diverse ratings
$\mathbf{r}_{t1},\mathbf{r}_{t2},\cdots,\mathbf{r}_{tk}$ with the content
$\mathbf{x}_{t}$. It’s worth note that these generated ratings are in the
continuous scale of $[0,1]$ because we focus on implicit feedback in this
paper.

By taking users’ preferences / ratings prediction as meta-learning tasks, the
meta-learner trained on these generated ratings and original ratings is
expected to avoid overfitting as introduced in Section I. In Section II, we
know that the meta-learning optimization scheme MAML[49] can fast adapt to new
tasks. In recommendations, the meta-learner can fast adapt to cold-start
recommendations with MAML.

###  IV-C Preference Meta-learning

This block focuses on training a preference prediction model based on meta-
learning in the target domain by generated diverse ratings
$\mathbf{r}_{t1},\mathbf{r}_{t2},\cdots,\mathbf{r}_{tk}$. Firstly, we encode
the original content $\mathbf{c}_{u}$ and $\mathbf{c}_{i}$ to their dense
embedding $\mathbf{x}_{u}$ and $\mathbf{x}_{i}$. We denote $\mathbf{c}_{t}$ as
the combination of $\mathbf{c}_{u}$ and $\mathbf{c}_{i}$ in the following
paper. Then, we construct the meta-learning task $\mathcal{T}_{u}$ and the
augmented tasks $\mathcal{T}_{u}^{1},\cdots,\mathcal{T}_{u}^{k}$ as follows:

$\displaystyle\mathcal{T}_{u}$
$\displaystyle={(\mathbf{c}_{t},\mathbf{r}_{t})}$ (9)
$\displaystyle\mathcal{T}_{u_{1}}$
$\displaystyle={(\mathbf{c}_{t},\hat{\mathbf{r}}_{t1})},\cdots,\mathcal{T}_{u_{k}}={(\mathbf{c}_{t},\hat{\mathbf{r}}_{tk})},$
(10)

where $\mathbf{r}_{t}$ is the original ratings in the target domain. Next, we
learn the preference prediction model via the meta-learning framework MAML.

As shown in Fig. 2, we firstly employ a fully connected embedding layer to
encode content vectors $\mathbf{c}_{u}$ and $\mathbf{c}_{i}$ into dense
embeddings $\mathbf{x}_{u}$ and $\mathbf{x}_{i}$, and then we adopt a multi-
layer neural architecture[29] to predict rating scores by the concatenation of
$\mathbf{x}_{u}$ and $\mathbf{x}_{i}$. As implicit feedback we considered in
this paper, so we use the binary cross-entropy loss on the top of multi-layer
neural network to predict ratings.

The embedding layer and the multi-layer architecture constitute the preference
prediction model. We train the model with diverse tasks to avoid overfitting
via the meta-learning framework MAML. The objective can be written as:

$\hat{\mathbf{r}}_{ui}=f(\theta_{l},\theta_{e},\mathbf{c}_{u},\mathbf{c}_{i}),$
(11)

where $\theta_{e}$ is the parameters of the fully connected embedding layer
that encodes the content vector $\mathbf{c}_{u}$ and $\mathbf{c}_{i}$ into
dense embeddings $\mathbf{x}_{u}$ and $\mathbf{x}_{i}$, and $\theta_{l}$ is
the parameters of the multi-layer neural network.

As shown in Fig. 2, MAML includes the inner loop for local update of the model
and the outer loop for global update of the model. In this work, we train the
MAML on training task set $\mathbb{T}_{tr}$, which includes the original tasks
$\mathcal{T}_{u}$ and augmented tasks
$\mathcal{T}_{u1},\cdots,\mathcal{T}_{uk}$. We divide samples of each task
$\mathcal{T}\in\mathbb{T}_{tr}$ randomly into a support set $\mathcal{S}_{u}$
and a query set $\mathbf{Q}_{u}$ as follows:

$\displaystyle\mathcal{T}=\\{\mathcal{S}_{u},\mathcal{Q}_{u}\\}.$ (12)

In the meta-testing phase, meta-testing tasks $\mathcal{T}\in\mathbb{T}_{te}$
includes only original tasks constituted from original ratings of the target
domain. Samples of each $\mathcal{T}$ are also split into a support set
$\mathcal{S}_{u}$ for fine-tuning the preference model and a query set
$\mathbf{Q}_{u}$ for testing the recommendation performance.

###  IV-D Time Complexity Analysis

Our model consists of three blocks (Fig.2). (1) the Dual-CVAE (Fig. 1) is
trained in parallel for multiple source domains. It encodes users’ ratings and
users’ content into latent vectors $\mathbf{z}_{s},\mathbf{z}_{t}$ with
2-layer networks and then decodes the latent vectors into users’ ratings with
2-layer networks. The dimensions of users’ content, hidden layers and the
latent vectors are constant with the data size
$\mathcal{O}\\{\text{max}\\{n,m\\}\\}$, where $n$ and $m$ are numbers of users
and items. If we denote $B$, $l$ and $m$ as the batch size, the numbers of
items in the source and target domains, then the dimensions of inputs
$\mathbf{r}_{s}$ and $\mathbf{r}_{t}$ are $l$ and $m$, respectively. So the
time complexity is $\mathcal{O}(B(l+m))$. (2) The second block forwards the
encoder and decoder (red line in Fig. 1) one-pass to generate ratings, so the
time complexity is $\mathcal{O}(B)$. (3) The third block learns a 2-layer
network, and the dimension of users’ (items’) content is constant with the
data size, so the time complexity is $\mathcal{O}(B)$. Overall, the time
complexity is $\mathcal{O}(B(l+m))$, so it scales linearly with the data size.

TABLE I: Statistics of datasets for multiple source domains. Source ($S$) | #shared users ($T$) | #items | #ratings | sparsity
---|---|---|---|---
Books | CDs
Electronics | 28,505 | 6,260 | 63,001 | 1,687,993 | 99.98%
Movies | 37,387 | 18,031 | 50,052 | 1,697,438 | 99.97%
Music | 1,952 | 5,331 | 3,568 | 64,705 | 99.67%
TABLE II: Statistics of datasets for target domains. Datasets | #users | #items | #ratings | sparsity
---|---|---|---|---
Books | 603,374 | 348,957 | 8,575,000 | 99.99%
CDs | 25,400 | 24,904 | 43,903 | 99.99%

##  V Experiments

In this work, we claim that (1) diverse preference augmentation can handle
overfitting in the case of sparse interactions to improve the performance of
four recommendation problems defined in Section III-A; (2) learning a
preference model via a meta-learning scheme can alleviate cold-start issues.
The goal of experiments is to evaluate the effectiveness of the proposed
MetaDPA to avoid overfitting and solve the recommendation problems including
‘Warm-start’, ‘C-U’, ‘C-I’, and ‘C-UI’. In addition, the experiments study the
impact of two constraints added in the model. To be specific, we analyze the
effectiveness from the following aspects:

  * •

RQ1: Does our method outperforms the state-of-the-art cross-domain baselines?

  * •

RQ2: Does our method handle overfitting on sparse interactions?

  * •

RQ3: How is the scalability of our method?

  * •

RQ4: How do the two constraints MDI and ME affect the performances of
recommendations under different settings?

  * •

RQ5: How do the hyper-parameters, such as $\beta_{1}$ of MDI, and $\beta_{2}$
of ME, affect the effectiveness of DPA?

Figure 3: Performance comparison on Books. Figure 4: Performance comparisons
on CDs.

###  V-A Experimental Settings

####  V-A1 Datasets

We evaluate the performance of our method against the state-of-the-art
baselines on public Amazon datasets111http://jmcauley.ucsd.edu/data/amazon/.
Among the largest categories, we choose Electronics, Movies and Music as three
source domains, and Books and CDs as two target domains. As this paper focuses
provide recommendations based on implicit feedbacks, we transform explicit
ratings greater than 0 as the positive feedbacks ’1’ and others as negative
feedbacks ’0’. Statistics for the source domains and the target domains are
shown in Table I and Table II, respectively.

Experiments of our method contains three phases: (1) multi-source domain
adaptation from three source to two target domains, (2) diverse preference
augmentation, and (2) preference meta-learning in the two target domains. In
the first phase, we train three independent Dual-CVAEs of multi-source domain
adaptation. In this phase, we discard users or items with fewer than 20
positive ratings for both source and target domains. We randomly split ratings
into 80% as training set and the remaining 20% as evaluation set for the
domain adaptation. Then, we generate diverse ratings from three decoders of
Dual-CVAEs for users in the target domains by their content data. In the third
phase, we train preference model with the generated ratings and the original
ratings in the target domains, and test the performances of four problems
defined in Section III-A.

####  V-A2 Evaluation Protocols

In this paper, we only test performances on target domains. Recommendation
problems consist of ‘C-U’, ‘C-I’, ‘C-UI’, and ‘Warm-start’ introduced in
Section III-A. We first train our model on training tasks $\mathcal{T}_{tr}$
constructed of ratings in $\mathbf{R}_{w}$. For solving ‘Warm-start’, we test
the performance on the query set of $\mathcal{T}_{tr}$. For cold-start
problems ‘C-U’, ‘C-I’, and ‘C-UI’, we first finetune the trained model on
training tasks $\mathcal{T}_{tr}$ by the support set of testing tasks
$\mathcal{T}_{te}$, and then we test the performance on the query set of
$\mathcal{T}_{te}$. Taking ‘C-U’ as an example, $\mathcal{T}_{te}$ is
constructed from ratings $\\{r_{ui}:u\in U_{n},i\in I_{e}\\}$. Similarly, we
can construct testing tasks $\mathcal{T}_{te}$ for other two cold-start
settings.

Following the common strategy of implicit feedbacks[29], we adopt the similar
leave-one-out evaluation protocols for evaluating the performance of
recommendations. Specifically, we sample 99 negative unobserved items for each
positive item to evaluate MetaDPA and other baselines. Then we report the
performance of top-k recommendations under four common metrics: hit ratio
(HR)[59], mean reciprocal rank (MRR)[60], normalized discounted cumulative
gain (NDCG)[4], and area under ROC curve (AUC)[61].

####  V-A3 Baselines

TABLE III: The overall performance comparison of MetaDPA (the proposed model) and baselines. Best performance marked as bold font, the second best marked as o. Dataset | Books | CDs
---|---|---
Metric | HR@10 | MRR@10 | NDCG@10 | AUC | HR@10 | MRR@10 | NDCG@10 | AUC
C-U | NeuMF | 0.1159 | 0.0327 | 0.0515 | 0.5009 | 0.1069 | 0.0300 | 0.0478 | 0.5054
MeLU | 0.1524 | 0.0630 | 0.0834 | 0.5819 | 0.1278 | 0.042 | 0.0617 | 0.5635
CoNN | 0.1515 | 0.0437 | 0.0683 | 0.5810 | 0.1696 | 0.0549 | 0.0813 | 0.5853
TDAR | 0.0641 | 0.0195 | 0.0298 | 0.3852 | 0.1417 | 0.0549 | 0.0748 | 0.5451
CATN | 0.1071 | 0.0329 | 0.0500 | 0.5376 | 0.1346 | 0.0364 | 0.0585 | 0.5910o
DAML | 0.1756 | 0.0596 | 0.086 | 0.5454 | 0.1789o | 0.0618 | 0.0886o | 0.5876
MetaCF | 0.1607 | 0.0746o | 0.1014o | 0.5383 | 0.1535 | 0.0807o | 0.0979 | 0.5024
| MetaDPA | 0.1702o | 0.0848 | 0.1042 | 0.5803o | 0.2648 | 0.1371 | 0.1660 | 0.6364
C-I | NeuMF | 0.1248 | 0.0329 | 0.0536 | 0.5043 | 0.117 | 0.0416 | 0.0589 | 0.5054
MeLU | 0.1846o | 0.0610 | 0.0891o | 0.5977 | 0.1326 | 0.0404 | 0.0616 | 0.577
CoNN | 0.1660 | 0.0438 | 0.0716 | 0.6014o | 0.1871 | 0.0651 | 0.09319 | 0.6092
TDAR | 0.1275 | 0.0343 | 0.0556 | 0.5169 | 0.1423 | 0.0472 | 0.0688 | 0.5324
CATN | 0.1280 | 0.0373 | 0.0581 | 0.5628 | 0.1195 | 0.0347 | 0.0539 | 0.5670
DAML | 0.1766 | 0.0561 | 0.0839 | 0.5466 | 0.2008o | 0.0738 | 0.1030 | 0.6143o
MetaCF | 0.1393 | 0.0631o | 0.0807 | 0.5298 | 0.1930 | 0.1041o | 0.1252o | 0.5108
| MetaDPA | 0.2178 | 0.0775 | 0.1101 | 0.6392 | 0.3119 | 0.1359 | 0.1762 | 0.6808
C-UI | NeuMF | 0.0843 | 0.0277 | 0.0408 | 0.5387 | 0.1240 | 0.0371 | 0.0568 | 0.5144
MeLU | 0.1742o | 0.0621o | 0.0872o | 0.5699o | 0.1240 | 0.0265 | 0.048 | 0.5733
CoNN | 0.1011 | 0.0223 | 0.0404 | 0.5493 | 0.1473 | 0.0570 | 0.0776 | 0.6045
TDAR | 0.1180 | 0.0308 | 0.0504 | 0.5076 | 0.1705 | 0.0809 | 0.1016 | 0.5560
CATN | 0.1209 | 0.0391 | 0.0579 | 0.5315 | 0.0916 | 0.0314 | 0.0451 | 0.5256
DAML | 0.1292 | 0.0379 | 0.0590 | 0.5340 | 0.1550 | 0.0543 | 0.0774 | 0.6053o
MetaCF | 0.1236 | 0.0462 | 0.0644 | 0.5351 | 0.1860o | 0.0876o | 0.1104o | 0.5221
| MetaDPA | 0.1910 | 0.0694 | 0.0971 | 0.5921 | 0.2558 | 0.1069 | 0.1407 | 0.6515
Warm-start | NeuMF | 0.1292 | 0.0415 | 0.0616 | 0.5107 | 0.1106 | 0.0336 | 0.0512 | 0.5014
MeLU | 0.1512 | 0.0929 | 0.1059 | 0.5562 | 0.1470 | 0.0465 | 0.0696 | 0.5826
CoNN | 0.1773 | 0.0528 | 0.0813 | 0.6023 | 0.1922 | 0.0645 | 0.0940 | 0.6029
TDAR | 0.2798 | 0.0749 | 0.1219o | 0.6331 | 0.1501 | 0.0489 | 0.0722 | 0.5843
CATN | 0.1363 | 0.0386 | 0.0610 | 0.5539 | 0.1505 | 0.0440 | 0.0684 | 0.6183o
DAML | 0.2011 | 0.0696 | 0.1000 | 0.5710 | 0.2007 | 0.0691 | 0.0995 | 0.6062
MetaCF | 0.1775 | 0.0857o | 0.1070 | 0.5127 | 0.2084o | 0.1511o | 0.1859o | 0.5472
| MetaDPA | 0.2099o | 0.0829 | 0.1396 | 0.6211o | 0.2866 | 0.1994 | 0.2187 | 0.6481

To investigate whether MetaDPA can improve the recommendation performance
under cold-start settings or not, we compare it with several state-of-the-art
baselines, including the competitive NeuMF, content-aware recommender systems
(CoNN, DAML), meta-learning based methods (Melu, MetaCF), cross-domain
recommendation frameworks (TDAR, CATN).

  * •

NeuMF: Neural collaborative filtering[29] is the most favorite technique in
recommender systems.

  * •

MeLU: Meta-learned user preference estimator[62] demonstrates satisfactory
performance when applied to a wide range of users for providing personalized
recommendations due to the generalization ability.

  * •

MetaCF:  Fast adaptation for recommendations with meta-learning[51] is
formulated with a dynamic subgraph sampling that accounts for the dynamic
arrival of new users by dynamically generating representative adaptation tasks
for existing users.

  * •

CoNN: Deep cooperative neural networks[39] learns item properties and user
behaviors from reviews consisting of two parallel neural networks with the
shared last layer.

  * •

DAML: Dual attention mutual learning[40] adapts local and mutual attention
network to extract the rating and review features. With such features, neural
factorization machine can effectively make predictions.

  * •

TDAR: Text-enhanced domain adaptation recommendation (TDAR)[46] extracts the
textual features in word semantic space for each user and item and feds them
into a collaborative filtering model for predicting ratings.

  * •

CATN: Cross-domain recommendation framework via aspect transfer network[45]
learns cross-domain aspect-level preference matching by bridging multiple
user’s inherent traits via reviews in different domains.

Figure 5: Effectiveness of Mutually-Exclusive (ME) and Multi-domain InfoMax
(MDI) constraints.

####  V-A4 Hyper-parameter Settings

To obtain the optimal hyper-parameters $\beta_{1}$ and $\beta_{2}$ in Eq.(8),
we apply the grid search in the range of
$\\{1e^{-2},1e^{-1},1,1e^{1},1e^{2}\\}\bigotimes\\{1e^{-2},1e^{-1},1,1e^{1},1e^{2}\\}$
on Books and CDs, respectively. After searching, we set $\beta_{1}=0.1$,
$\beta_{2}=1$ on CDs, and $\beta_{1}=0.1$, $\beta_{2}=1$ on Books, because
these settings can achieve best performance.

###  V-B Overall Performance Compared with Baselines (RQ1 & RQ2)

We compare our model MetaDPA with other competitive baselines to show the
performance improvements under NDCG@k in Fig. 3 and Fig. 4 on Books and CDs,
respectively. The results under other metrics are shown in Table III. We
conclude that the performance of the proposed MetaDPA is significantly
superior to all competing baselines. The overwhelming advantages over
baselines attribute to the following three points:

  * (1)

Compared with cross-domain recommendations CATN and TDAR: By transferring
preference properties from multiple source domains to the target domain via
augmented diverse ratings, the proposed model can capture more preference
properties, which is helpful to avoid overfitting and improve the
recommendation accuracy, so it performs much better than cross-domain
recommender systems;

  * (2)

Compared with content-aware recommendations CoNN and DAML: The diverse
preference augmentation block aims to reduce the gap between content and
preference that exists in content-aware recommender systems, so most of the
time, it performs better than content-aware recommender systems;

  * (3)

Compared with meta-learning based recommender systems Melu and MetaCF: With
the diverse ratings fed into the preference meta-learning, MetaDPA avoids
overfitting to the insufficient interactive training set, so it performs much
better than meta-learning based recommender systems for solving recommendation
problems.

Figure 6: Training time cost varies with Data size. Figure 7: The impact of
hyper-parameter $\beta_{1}$. Figure 8: The impact of hyper-parameter
$\beta_{2}$.

Specifically, both CoNN and DAML are content-aware recommendations with deep
models. The difference is that CoNN uses a parallel neural network to learn
user behaviors and item properties while DAML learns rating and review
features by local and mutual attention networks. In our experiments, DAML
shows a little better than CoNN. Both methods show middle performance in all
scenarios. Actually, this indicates that content information can effectively
deal with cold-start problems and work well in warm-start scenarios.

Besides, TDAR and CATN perform worse than content-based methods CoNN and DAML
in most scenarios. However, the performance of TDAR is unstable. In some
cases, it performs very well, e.g., the warm-start scenario on Books and CDs.
The possible reason is that TDAR is designed for warm-start recommendations
instead of cold-start settings, and the training datasets are very sparse for
cold-start users/items, so it performs inferior to other baselines under cold-
start settings and achieves better performance under warm-start settings.

In addition, MeLU and MetaCF are effective meta-learning recommendations that
are designed for solving cold-start issues with meta-learning frameworks. Both
of them demonstrate powerful performances, which outperforms almost all other
baselines in cold-start settings, and both perform well in the warm-start
scenarios on Books as well. However, MeLU performs badly in all scenarios on
CDs. A possible reason is that it easily sticks into the serious meta-
overfitting on sparse user-item interactions. In contrast, MetaCF performs
much better than other baselines on CDs, which indicates that incorporating
potential interactions by neighborhood users / items can enrich users’
preference information.

To explore the reasons why the performances of other baselines’ on CDs are
worse than the performances on Books, we calculate the proportion of users who
have no less than 40 interactions, and we obtain 13% for CDs and 16% for
Books, which may account for the different results of baselines. We are known
that the recommendation performance is heavily dependent on the rating
sparsity. When we learn models by a batch of users, the performances rely on
the rating sparsity of a batch of users. If more users rated more items (such
as more than 40 items), the recommendation problems would converges to a
better solution, so the performances would be better.

Overall, under both cold-start and warm-start scenarios, MetaDPA outperforms
all baselines significantly w.r.t NDCG@k metric. Regarding other metrics,
MetaDPA outperforms almost all baselines except HR@10 and AUC for solving user
cold-start problem (‘C-U’), MRR@10 for solving ‘Warm-start’ issue on Books.
However, MetaDPA obtains the second-best performance on these problems. This
indicates that meta-learning-based recommendations significantly improve cold-
start recommendations and warm-start recommendations by addressing the meta-
overfitting problem.

###  V-C Scalability (RQ3)

In this section, we run a series of experiments on the source domain
Electronics and the target domain Books. To evaluate the scalability, we
choose items in Books randomly with different percentages, 10%, 20%, …, 100%
to create 10 group new datasets. To speed up the computation, we train our
model on GPU platform (NVIDIA GeForce RTX 3090). In the experiments, we set
batch size $B=32$ heuristically similar to the work[63], and we report the
training time costs of 1 epoch in each block. As shown in Fig. 6, the training
procedure scales linearly with the data size for the first block (Block-1 in
Fig. 6), and the training time costs are constant with the data size for the
second block (Block-2) and third block (Block-3). Which is consistent with the
time analysis in Section IV-D. So the proposed framework can be extended to
larger datasets.

###  V-D Significance Test

We use the one-sided test, Wilcoxon signed-rank test[64], to test the
significance of our method surpassing the second-best methods, which has the
null hypothesis that the median of the differences of two results
$x_{i}-y_{i}$ under an evaluation metric ($x_{i}$ and $y_{i}$ denote the
results of our method and the second-best method) is negative against the
alternative that it is positive. For different metrics, we obtain different
p-values. By randomly splitting training set and testing set 30 times
independently, we obtain two sets of 30 results for our method and the second-
best method, respectively.

By comparing with the second-best method MeLU, we test the significance on
Books and get $p$-values are $5.96e^{-8},1.23e^{-5},1.78e^{-7},5.96e^{-8}$ for
HR@10, MRR@10, NDCG@10, AUC under cold-start user (‘C-U’). Similarly, for
cold-start item (‘C-I’), $p$-values are
$5.96e^{-8},2.98e^{-7},5.96e^{-8},5.96e^{-8}$. For ‘C-UI’ and ‘Warm-start’,
all $p$-values are $5.96e^{-8}$ except $p$-value is $2.15e^{-4}$ under AUC for
’Warm-start’ setting. Besides, we get all $p$-values are $1.19e^{-7}$ on CDs
under all recommendation settings. Similarly, we obtain similar results when
we compare the second-best methods MetaCF, DAML, TDAR, and CATN under specific
settings. So we conclude that our method significantly outperforms other
baselines with $p$-values<0.05 under all evaluation metrics.

###  V-E Ablation Studies (RQ4)

In this subsection, we discuss the effectiveness of MDI and ME constraints. We
test two variants of MetaDPA to validate the effectiveness of the two
constraints.

  * •

MetaDPA-ME: MetaDPA only with the ME constraint.

  * •

MetaDPA-MDI: MetaDPA only with the MDI constraint.

MetaDPA-ME only considers making the preference distribution of the target
domain close to the source and ignores how to learn domain-specific and
domain-shared preference properties for domain adaptation. MetaDPA-ME
generates more diverse but less meaningful ratings for the target domain. In
contrast, MetaDPA-MDI considers learning domain-specific and domain-shared
properties as other cross-domain methods and ignores diverse requirements. The
results on all four scenarios on CDs are shown in Fig. 5. Obviously, both
MetaDPA-ME and MetaDPA-MDI suffer performance declines. MetaDPA-ME performs
worst due to it generating meaningless ratings and introducing useless bias to
the meta-training tasks. MetaDPA-MDI performs worse than MetaDPA because it
generates ratings that are too close to the true ratings and lack diversity.
However, both variants still perform better than MeLU and other baselines
since the Dual-CVAE framework brings weak but good enough diversity and domain
adaptation.

###  V-F The Impact of Hyper-parameters (RQ5)

In this subsection, we test the sensitivity of our framework w.r.t the hyper-
parameters $\beta_{1}$ and $\beta_{2}$ on CDs by grid search introduced in
Section V-A. The results for $\beta_{1}$ and $\beta_{2}$ are respectively
shown in Fig. 7 and Fig. 8. We conclude that $\beta_{1}$ is more sensitive
than $\beta_{2}$. Actually, $\beta_{1}$ and $\beta_{2}$ weigh the importances
of constraints MDI and ME, respectively. MDI affects both domain adaptation
and diverse ratings generation; while ME only affects the latter, so the
variation of $\beta_{1}$ affects the recommendation performance more seriously
than $\beta_{2}$, i.e., $\beta_{1}$ is more sensitive than $\beta_{2}$.
Besides, we find that warm-start scenarios are more sensitive than cold-start
scenarios. As introduced in Section V-A, we use a few samples to finetune the
model (trained in the warm-start setting) for cold-start testings, so it has a
better generalization ability than that for warm-start testing. That’s why
warm-start scenarios are more sensitive than cold-start scenarios.

##  VI Conclusion

In this paper, we propose a Diverse Preference Augmentation based on meta-
learning (MetaDPA) method by multiple source domains for solving cold-start
issues in recommendation tasks. The proposed MetaDPA consists of three blocks.
The first block is multi-source domain adaptation, formulated with multiple
Dual-CVAEs. To preserve both domain-shared and domain-specific preference
properties in the latent space, we add the MDI constraint with the principle
of Info-Max, which is effective to maintain domain-shared properties without
discarding domain-specific information. Besides, we impose the ME constraint
on the outputs of decoders for generating diverse ratings from different
source domains. The second block is diverse preference augmentation, which is
realized by feeding the content data in the target domain into the content
encoder $E_{t}^{x}$ and the decoder $D_{t}$. The last block, preference meta-
learning, optimizes the preference model which is formulated with a multi-
layer neural network based on the model-agnostic meta-learning scheme.
Experimental results clearly show that MetaDPA significantly outperforms
state-of-the-art baselines including content-aware, cross-domain, and meta-
learning methods on public datasets. Besides, we conduct ablation studies to
evaluate the effectiveness of two constraints MDI and ME. Finally, we also
evaluate the impacts of hyper-parameters $\beta_{1}$ and $\beta_{2}$ on the
recommendation performance.

## Acknowledgments

This work is supported by the Major Project for New Generation of AI under
Grant No. 2018AAA0100400, the National Natural Science Foundation of China
(Grant No. 62002052, 61801060, 62176047, 62172075, 61832001), the Sichuan
Science and Technology Program (Grant No. 2022YFG0189, 2021JDRC0079). Besides,
this work is supported in part by Australian Research Council (Grant No.
FT210100624, DP180100106, DP200101328, DP190101985), the Beijing Natural
Science Foundation (Grant No. Z190023), the China Postdoctoral Science
Foundation (Grant No. 2019TQ0051), the Open Fund of Intelligent Terminal Key
Laboratory of Sichuan Province (Grant No. SCITLAB-1017).

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