# Forecasting formation of a Tropical Cyclone Using Reanalysis Data

Sandeep Kumar
Department of Mathematics, Shaheed Bhagat Singh College,
University of Delhi.
&
Department of Computer Science, IIIT Delhi
New Delhi, India.
<EMAIL_ADDRESS><EMAIL_ADDRESS>&Koushik Biswas
Department of Computer Science
IIIT Delhi
New Delhi, India, 110020
<EMAIL_ADDRESS>
&Ashish Kumar Pandey
Department of Mathematics
IIIT Delhi
New Delhi, India, 110020
<EMAIL_ADDRESS>

###### Abstract

The tropical cyclone formation process is one of the most complex natural
phenomena which is governed by various atmospheric, oceanographic, and
geographic factors that varies with time and space. Despite several years of
research, accurately predicting tropical cyclone formation remains a
challenging task. While the existing numerical models have inherent
limitations, the machine learning models fail to capture the spatial and
temporal dimensions of the causal factors behind TC formation. In this study,
a deep learning model has been proposed that can forecast the formation of a
tropical cyclone with a lead time of up to 60 hours with high accuracy. The
model uses the high-resolution reanalysis data ERA5 (ECMWF reanalysis $5^{th}$
generation), and best track data IBTrACS (International Best Track Archive for
Climate Stewardship) to forecast tropical cyclone formation in six ocean
basins of the world. For 60 hours lead time the models achieve an accuracy in
the range of $86.9\%-92.9\%$ across the six ocean basins. The model takes
about 5-15 minutes of training time depending on the ocean basin, and the
amount of data used and can predict within seconds, thereby making it suitable
for real-life usage.

_K_ eywords Tropical cyclone $\cdot$ Formation $\cdot$ Forecast $\cdot$
Reanalysis data

##  1 Introduction

The formation of any natural disaster is a complicated phenomenon that
involves multiple causal factors which have temporal, spatial, and altitudinal
dimensions. Understanding the evolution process of a natural disaster and
modeling it, is always a challenging task. One such natural disaster is
tropical cyclone(TC) (also known as hurricanes or typhoons) which occurs
frequently in the tropical and subtropical waters of the world. Near the
equator, the warm air rises over the surface of the sea and creates a low-
pressure system (LPS), also known as a tropical depression. This causes the
air around the LPS to move towards it, which further gets warmed and rises
above. The rising moist air cools down and forms the cloud. The process of
cloud formation and wind rotation intensifies with the help of favorable
conditions like- sea surface temperature greater than $26^{o}C$ [1], low
vertical wind shear, high relative humidity, and atmospheric instability [1,
2, 3]. The difference of temperature between the warm core with rising moist
air and the adjoining cool environment leads to rapidly rising buoyant air.
All this makes the TC development a complicated process that depends on
oceanographic, atmospheric, and geographic factors. Moreover, out of these
LPSs, only a small number developed in a full-fledged TC under the above
favorable conditions [4]. As the theory behind the development process of a TC
is still not settled, predicting TC formation is a challenging problem. TCs
bring with themselves heavy rainfall, thunderstorm, and flash floods in the
coastal areas, thereby causing huge ecological, infrastructural and human
loss. Also with climate change, the frequency, intensity, and associated
hazards of TCs are going to increase [5]. All this makes, the development of a
model that can forecast the formation of a TC well advance in time, important
from a disaster mitigation point of view. This will provide the disaster
managers adequate time to take preventive measures. In this work, a deep
learning model has been proposed to successfully forecast TC formation with a
lead time of up to 60 hours (h) using as less as 12h of preceding data for the
six ocean basins, North Atlantic (NA), North Indian (NI), South Indian (SI),
West Pacific (WP), South Pacific (SP), and East Pacific (EP) of the world.

There are mainly two approaches for detecting TCs, one is model driven
approach based on equations governing the physical phenomenon of TC
development (including numerical simulations) and the other is data driven
approach that utilizes historical data relating to TCs (including machine
learning methods). The earliest conventional way to detect a TC is early-stage
Dvorak analysis (EDA) (an extended Dvorak technique [6]) which utilizes
satellite cloud images, however this technique includes subjective
interpretation of parameters and hence not sufficiently scientific [7]. EDA is
used by the National Hurricane Center (NHC), Central Pacific Hurricane Center
(CPHC), and the Japan Meteorological Agency (JMA) to forecast typhoon
initiation, up to 48 hours before its formation, with an accuracy of up to
$57\%$ [8]. In [9], authors shows that the global ensembles models [European
Centre for Medium-Range Weather Forecasts (ECMWF), Japan Meteorological Agency
(JMA), National Centers for Environmental Prediction (NCEP), and Met Office in
the United Kingdom (UKMO)] along with EDA can be used to improve the accuracy
up to $79\%$. In [10], authors evaluated the performance of five global NWP
systems [Global Forecast System (GFS), ECMWF, Canada’s Global Environment
Multiscale Model (CMC), UKMO, and Navy Operational Global Atmospheric
Prediction System (NOGAPS)] for TC forecast in the North Atlantic (NA) ocean
for the period 2004-2011, and shows the best hit rate of $44\%$ can be
achieved. Over the years the accuracy of numerical models is improved based on
better initialization and improved computing power. But still, these models
are not suitable for long lead time forecasts as the numerical methods are
prone to error accumulation over iterations. In [11, 12] authors have used
statistical method, Linear Discriminant Analysis (LDA) to predict 24h
probability of TC formation from derived large scale environmental parameters.
But the factors that lead to a TC formation have a non-linear complex
relationship that makes these linear methods unsuitable for the TC formation
prediction task. Recently, machine learning methods and deep learning methods
have been successfully applied to answer the TC formation forecast problem,
which we will discuss more in the next section.

The rest of the paper is organized as follows: in Section 2 related work is
described, Section 3 presents the data used, Section 4 describe the proposed
deep learning model, Section 5 presents the findings of this work, and finally
in Section 6 we conclude with a summary and future directions.

##  2 Related Work

Various machine learning models have been successfully applied to a TC
formation forecast problem. In [13] Decision trees (DTs) are used to detect
developing and non-developing tropical disturbances in the North Pacific Ocean
for the months, June to September of 2004-2013, using five derived parameters
from Navy Operational Global Atmospheric Prediction System (NOGAPS). They
reported accuracy of $84.6\%$ for a lead time of 24h. They differentiate
between developing and non-developing disturbance based on relative vorticity.
In [14], DTs, random forest (RF), and support vector machine (SVM) are used to
detect the formation of TC in the western North Pacific Ocean for the period
2005-2009 using eight derived predictors from WindSat satellite data. They
classify a tropical depression as TC when the maximum sustained wind speed
(MSWS) reaches $13m/s$ (or 25 knots) and the satellite image available with at
least $60\%$ coverage in a circle with $4^{\circ}$ radius around the center of
the tropical disturbance. In [15], the authors use 13 predictors derived from
mesoscale convective system (MCS) data and ERA-Interim dataset to predict TC
formation using the following machine learning tools - Logistic Regression
(LR), Naïve Bayes (NB), DT, K-Nearest neighbors (KNN), Multilayer perceptron
(MLP), Quadratic Discriminant Analysis (QDA), SVM, AdaBoost (ADA), and RF. The
authors reported the accuracy in terms of F1-score, precision, and recall for
lead times 6h, 12h, 24h, and 48h for global (consisting of all ocean basins),
NA, and west north pacific (WNP) ocean basins.

Various deep learning studies have successfully captured the spatial and
temporal dimensions of causal factors to answer the prediction problems
related to TC’s track, intensity [16, 17, 18, 19, 20, 21] and its landfall’s
characteristics [22, 23, 24]. Recently, a few deep learning studies have been
proposed that forecast TC formation. In [25], CNN has been used to detect the
TC and its precursors in the six ocean basins of the world using 30 years of
simulated outgoing longwave radiation (OLR) data generated through a cloud-
resolving global non-hydrostatic atmospheric model. The TC and its precursors
are categorized as one class and identified based on TC tracking algorithm
[26, 27] which takes temperature, horizontal components of wind, and sea level
pressure (SLP) as inputs. The study restricted it to the limited range of
latitudes $30^{\circ}$S - $30^{\circ}$N. In [28], the authors have presented a
deep learning model to detect an ongoing TC with the help of satellite data of
eight TCs in NI ocean basin. In [29] a hybrid CNN-LSTM model is used to
predict if an ongoing TC will be intensified to the level of a typhoon (wind
speed greater than 64 knots) with a lead time of 24h, using preceding data of
6h, 12h, 18h or 24h. The International Best Track Archive for Climate
Stewardship (IBTrACS) data and ERA-Interim datasets are used for three ocean
basins WP, EP, and NA. Thus we see that very few deep learning studies exists,
and each has their own criterion of detecting TC formation.

##  3 Data

Figure 1: Location of TC and non TC formation.

Inspired by the successful usage of reanalysis dataset in the recent works
[29, 23, 30, 31, 24] to answer TC related track, intensity, and landfall’s
characteristics problems, we have used ERA5 [32] high-resolution reanalysis
dataset provided by ECMWF111https://cds.climate.copernicus.eu/, a high-
resolution data that provides hourly weather and climate data for the whole
globe. In [33], the authors show how well a TC is represented in the
reanalysis dataset. The formation process of a TC is determined by large-scale
atmospheric factors at various altitudes around the center of a LPS. For this
study we have extracted wind fields $u$, $v$, geopotential $z$, relative
humidity $r$, and temperature $t$ at three pressure levels (altitudes) 225hPa,
500hPa, and 700hPa. These variables largely determine the development process
of a TC as follows: $u$ and $v$ fields represent the east-west and north-south
movement of air along with its speed, $z$ represents the gravitational
potential energy relative to sea level, $r$ represents the water vapor
pressure, and $t$ represents the atmospheric temperature. As the atmospheric
causal factors behind TC formation may have horizontal extends up to 1000
kilometers (km) these variables are extracted for a spatial region
$5^{\circ}\times 5^{\circ}$ with a resolution of $0.25^{\circ}$ which resulted
in a grid of $41\times 41$. As one degree is around 110 km near the equator
and decreases as we move pole-wards, this resulted in a spatial extend of
around 1000 km with a resolution of around 25 km. A graphical representation
of used reanalysis data is shown in Fig 2.

Figure 2: Pictorial representation of reanalysis data. Algorithm 1 Generating
negative classes (non TC) in a ocean basin, say OB.

Input: Set $T$ and $L$ of time points and location (lat, lon) of all TC
formation in ocean basin OB.
Parameter: count (No. of positive class in OB), A Kernel Density Function say
LocGen fitted on the set $L$.
Output: Set $T1$ and $L1$ of time points and location (lat, lon) of all non TC
formation (negative classes) in ocean basin OB.

1:Let $count1=0$, $T1=\\{\\},$, $L1=\\{\\}$.

2:while $count1<count$ do

3: Generate a random time $t1$ (between 01/01/1980 and 01/09/2021) and random
location say (lat1,lon1) through LocGen.

4: if (lat1,lon1) lies over land then

5: continue

6: end if

7: if $Abs(t-t1)>$ 5days $\forall t\in T$ then

8: Add $t1$ to $T1$ and (lat1,lon1) to $L1$, $count1++$.

9: else

10: if $Abs(lat-lat1)>5^{\circ}$ and $Abs(lon-lon1)>5^{\circ}$
$\forall\,(lat,lon)\in L$. then

11: Add $t1$ to $T1$ and (lat1, lon1) to $L1$, $count1++$.

12: end if

13: end if

14:end while

15:return $T1$ and $L1$.

The IBTrACS dataset [34] maintained by National Oceanic and Atmospheric
Administration222https://www.ncdc.noaa.gov/ibtracs/ keeps three hourly global
records of all TCs in the form of its time, track (latitude and longitude),
intensity, and many more other variables from the very initiation of a TC when
it was first detected as a tropical depression or LPS. As the definition of TC
genesis time is ambiguous [35] we take the time when a TC is recorded first as
LPS in IBTrACS as TC formation time. We extracted the record of TC formation
time and corresponding location (latitude, longitude) for all TCs for the
earlier mentioned six ocean basins of the world from 1980 to September 2021.
All these TCs form the positive class in our classification problem. The total
number of positive cases are 653 (NA), 360 (NI), 832 (SI), 1431 (WP), 509
(SP), 983 (EP). To generate the negative classes (non-TC formation data), for
a particular ocean basin we followed the Algorithm 1. This way we have equal
number of positive and negative classes in our dataset. A negative class
sample represents a time $t$ and location loc such that there is no existing
TC formation in a time window of 5 days and if $t$ lies within a window of 5
days, then there is no existing TC formation in a spatial window of
$5^{\circ}$. This way we have selected all TC formation samples and non-TC
formation samples. Next, for each sample, we downloaded the above described
reanalysis data for grid size $41\times 41$ centered at the location of each
sample, for time points $t-6k$, $12\geq k\geq 4$, where $t$ is the time of TC
formation or randomly selected time of a non-TC formation sample. Thus the
reanalysis dataset is extracted for 9 time points from $t-72$h to $t-24$h at
an interval of 6 hours. The genesis location of all samples (TC formation and
non-TC formation) are shown in Fig 1 for all six ocean basins.

###  3.1 Training Dataset Preparation

For a TC, 9 data points are available at an interval of 6h as described above.
Suppose we want to use $T$ number of data points ((T-1)*6 hours of data) to
predict the formation of a TC. For this, we generate $10-T$ training data
points, where a single training point is a sequence of $T$ vectors of the
form:

$\displaystyle($
$\displaystyle\operatorname{u225}(t),\operatorname{v225}(t)\operatorname{z225}(t),\operatorname{r225}(t),\operatorname{t225}(t),$
$\displaystyle\operatorname{u500}(t),\operatorname{v500}(t)\operatorname{z500}(t),\operatorname{r500}(t),\operatorname{t500}(t),$
$\displaystyle\operatorname{u700}(t),\operatorname{v700}(t)\operatorname{7500}(t),\operatorname{r700}(t),\operatorname{t700}(t))$

where $k\leq t\leq T+k-1$ and $k$ varies from $1$ to $10-T$. For each such
training point, the target variable is 1 (positive class) or 0 (negative
class). One must note that the above process forms $10-T$ training points at
leads hours $6k$ where $4\leq k\leq 9+4-T$. All such training points for all
the TCs form the training dataset.

##  4 Model and its Implementation

Figure 3: Model description for $T=3$.

As our dataset has both spatial and temporal dimensions, the model utilizes a
combination of CNN [36, 37, 38] and LSTM [39, 40, 41, 42] networks to
effectively capture the causal factors behind a TC formation. The input
training dataset is of the dimension $(T,15,41,41)$, where $T$ stands for the
length of sequential data points (of $6*(T-1)$h), 15 stands for the number of
channels (corresponding to $u$, $v$, $z$, $r$, and $t$ fields at three
pressure levels), and $(41,41)$ is the shape of the grid centered at TC
formation location. The model consists of four alternating convolution and
max-pooling layers that generate sequential features of length $T$ using
$\operatorname{TimeDistributed}$ layer of Keras [43], which are further fed
into a stacked LSTM consisting of three LSTM layers. To avoid over-fitting
dropout 0.15 is used between two successive LSTM layers. The model and input-
output size of each layer is shown in Fig 3 for $T=3$. This resulted in a
lightweight model with just 2,83,073 trainable parameters.

###  4.1 Training and Implementation

We experimented with various configurations of above model by varying number
of layers and nodes in it, activation functions, and learning rates. The
configuration which works well across all ocean basins is reported. The
activation function $\operatorname{ReLU}(x)=\max(0,x)$ [44] is used in all
layers except the last layer which uses
$\operatorname{Sigmoid}(x)=\frac{1}{1+\exp(-x)}$ [45] activation function. The
input variables are scaled in the range $(-1,1)$ for faster and stable
training using $\operatorname{MinMaxScaler}$ of Scikit learn library [46]. The
model uses optimizer $\operatorname{Adam}$ [47], default learning rate
$0.001$, binary cross-entropy loss function, 32 batch size, and 30 epochs. The
model is implemented in $\operatorname{Keras}$ API developed over low-level
language $\operatorname{TensorFlow}$ [48] on Nvidia Tesla V100 GPU platform
with 16 GB RAM, that takes around 5-15 minutes for 30 epochs depending on
ocean basin and $T$.

###  4.2 Evaluation Metrics

As reported in [15], we have evaluated the performance of proposed model in
terms of metrics - Precision, Recall, Accuracy and F1-score (F1) which are
defined as:

$Precision(P)=\frac{TP}{TP+FP},\quad Recall(R)=\frac{TP}{TP+FN}$
$Accuracy=\frac{TP+TN}{TP+TN+FP+FN},\quad F1=\frac{2PR}{P+R}$

Table 1: Truth Table | Predicted
---|---
Actual |  Non TC |  TC
Non TC |  TN |  FP
TC |  FN |  TP

where TN, TP, FN, FP are shown in Table 1 for our classification problem. A
higher precision and recall are desirable. A higher precision indicates that a
warning from the model for a possible TC formation can not be ignored, whereas
a higher recall indicates that the model can detect a possible TC formation
with a high probability. F1 score is a measure of the balance between
precision and recall. To report the performance of the model in terms of these
metrics, we have used 5-fold validation technique, whereas the dataset is
partitioned into five equal subsets, and the model is evaluated on one subset
after it is trained on the other four subsets. Finally, the average of five
runs along with variation is reported for various leads time, which is called
5-fold validation accuracy.

##  5 Results and Analysis

Table 2: 5-fold performance ($\pm$std) of the model for T = 3 (12h). Ocean Basin |  Lead Time(h) |  Accuracy |  Precision |  Recall |  F1
---|---|---|---|---|---
NA |  24 |  0.943 $\pm$0.01 |  0.922 $\pm$0.02 |  0.965 $\pm$0.01 |  0.943 $\pm$0.01
|  36 |  0.982 $\pm$0.01 |  0.981 $\pm$0.02 |  0.983 $\pm$0.01 |  0.982 $\pm$0.01
|  48 |  0.977 $\pm$0.00 |  0.977 $\pm$0.01 |  0.976 $\pm$0.01 |  0.976 $\pm$0.00
|  60 |  0.912 $\pm$0.02 |  0.925 $\pm$0.02 |  0.901 $\pm$0.03 |  0.912 $\pm$0.02
NI |  24 |  0.977 $\pm$0.01 |  0.964 $\pm$0.02 |  0.992 $\pm$0.01 |  0.978 $\pm$0.01
|  36 |  0.990 $\pm$0.01 |  0.983 $\pm$0.01 |  0.997 $\pm$0.01 |  0.990 $\pm$0.01
|  48 |  0.989 $\pm$0.01 |  0.984 $\pm$0.02 |  0.994 $\pm$0.01 |  0.989 $\pm$0.01
|  60 |  0.929 $\pm$0.02 |  0.939 $\pm$0.03 |  0.918$\pm$0.03 |  0.928$\pm$0.02
SI |  24 |  0.955 $\pm$0.01 |  0.932 $\pm$0.02 |  0.982 $\pm$0.01 |  0.956 $\pm$0.01
|  36 |  0.993 $\pm$0.01 |  0.989 $\pm$0.01 |  0.996 $\pm$0.00 |  0.992 $\pm$0.00
|  48 |  0.991 $\pm$0.01 |  0.995 $\pm$0.00 |  0.987 $\pm$0.01 |  0.991 $\pm$0.00
|  60 |  0.913 $\pm$0.01 |  0.932 $\pm$0.02 |  0.892 $\pm$0.02 |  0.912 $\pm$0.01
WP |  24 |  0.931 $\pm$0.01 |  0.920 $\pm$0.02 |  0.944 $\pm$0.02 |  0.931 $\pm$0.01
|  36 |  0.975 $\pm$0.00 |  0.982 $\pm$0.01 |  0.968 $\pm$0.00 |  0.975 $\pm$0.00
|  48 |  0.972 $\pm$0.01 |  0.978 $\pm$0.01 |  0.966 $\pm$0.01 |  0.972 $\pm$0.01
|  60 |  0.869 $\pm$0.02 |  0.910 $\pm$0.03 |  0.818 $\pm$0.02 |  0.862 $\pm$0.02
SP |  24 |  0.930 $\pm$0.03 |  0.898 $\pm$0.06 |  0.977 $\pm$0.03 |  0.933 $\pm$0.03
|  36 |  0.964 $\pm$0.03 |  0.945 $\pm$0.05 |  0.992 $\pm$0.01 |  0.967 $\pm$0.02
|  48 |  0.954 $\pm$0.04 |  0.926 $\pm$0.07 |  0.991 $\pm$0.01 |  0.956 $\pm$0.03
|  60 |  0.899 $\pm$0.02 |  0.872 $\pm$0.05 |  0.943 $\pm$0.05 |  0.903 $\pm$0.02
EP |  24 |  0.917 $\pm$0.01 |  0.884 $\pm$0.02 |  0.959 $\pm$0.01 |  0.920 $\pm$0.02
|  36 |  0.966 $\pm$0.02 |  0.955 $\pm$0.02 |  0.979 $\pm$0.01 |  0.979 $\pm$0.01
|  48 |  0.966 $\pm$0.01 |  0.963 $\pm$0.01 |  0.971 $\pm$0.02 |  0.967 $\pm$0.01
|  60 |  0.904 $\pm$0.02 |  0.915 $\pm$0.02 |  0.891 $\pm$0.02 |  0.903 $\pm$0.02
Table 3: 5-fold performance (std) of the model for T = 5 (24h). Ocean Basin |  Lead Time(h) |  Accuracy |  Precision |  Recall |  F1
---|---|---|---|---|---
NA |  24 |  0.953 $\pm$0.01 |  0.951 $\pm$0.02 |  0.956 $\pm$0.03 |  0.953 $\pm$0.01
|  36 |  0.986 $\pm$0.01 |  0.993 $\pm$0.01 |  0.980 $\pm$0.02 |  0.987 $\pm$0.01
|  48 |  0.913 $\pm$0.02 |  0.949 $\pm$0.02 |  0.873 $\pm$0.03 |  0.909 $\pm$0.02
NI |  24 |  0.974 $\pm$0.02 |  0.959 $\pm$0.03 |  0.992 $\pm$0.01 |  0.974 $\pm$0.02
|  36 |  0.991 $\pm$0.01 |  0.988 $\pm$0.01 |  0.992 $\pm$0.01 |  0.990 $\pm$0.01
|  48 |  0.925 $\pm$0.01 |  0.964 $\pm$0.03 |  0.941 $\pm$0.02 |  0.952 $\pm$0.01
SI |  24 |  0.960 $\pm$0.02 |  0.942 $\pm$0.03 |  0.982 $\pm$0.02 |  0.961 $\pm$0.01
|  36 |  0.987 $\pm$0.01 |  0.986 $\pm$0.01 |  0.988 $\pm$0.01 |  0.987 $\pm$0.01
|  48 |  0.936 $\pm$0.01 |  0.941 $\pm$0.03 |  0.933 $\pm$0.04 |  0.936 $\pm$0.01
WP |  24 |  0.935 $\pm$0.02 |  0.912 $\pm$0.04 |  0.965 $\pm$0.01 |  0.937 $\pm$0.02
|  36 |  0.972 $\pm$0.02 |  0.966 $\pm$0.03 |  0.980 $\pm$0.01 |  0.973 $\pm$0.02
|  48 |  0.888 $\pm$0.02 |  0.899 $\pm$0.04 |  0.877 $\pm$0.02 |  0.887 $\pm$0.02
SP |  24 |  0.960 $\pm$0.01 |  0.936 $\pm$0.03 |  0.988 $\pm$0.01 |  0.961 $\pm$0.01
|  36 |  0.980 $\pm$0.02 |  0.978 $\pm$0.02 |  0.984 $\pm$0.01 |  0.980 $\pm$0.02
|  48 |  0.930 $\pm$0.01 |  0.940 $\pm$0.03 |  0.920 $\pm$0.04 |  0.928 $\pm$0.01
EP |  24 |  0.949 $\pm$0.01 |  0.933 $\pm$0.02 |  0.968 $\pm$0.01 |  0.950 $\pm$0.01
|  36 |  0.982 $\pm$0.01 |  0.980 $\pm$0.01 |  0.984 $\pm$0.01 |  0.982 $\pm$0.01
|  48 |  0.919 $\pm$0.01 |  0.936 $\pm$0.01 |  0.900 $\pm$0.01 |  0.917 $\pm$0.01

The proposed model takes any 12h, or 24h (corresponding to T = 3, or 5) of
continuous data at an interval of 6h as input from $t-72$ to $t-24$ hours,
where $t$ is the time of possible TC formation, and predicts whether a TC will
be formed or not. This way for a particular $T$, the model predicts at lead
times $6k$, $4\leq k\leq 13-T$. Thus the model predicts at a lead time of at
least 24h, which is a minimum requirement for practical utility purpose. For
various leads time the model performance is reported in terms of the 5-fold
accuracy along with the variation (std), in terms of above mentioned metrics
in Tables 2 and 3. Increasing or decreasing values of $T$ do not improve the
results further.

The accuracy for 24h lead time, vary in a range of $91.7\%-97.7\%$ and
$93.5\%-97.4\%$ for $T$ equals to 3 and 5 respectively. So for a 24h lead time
forecast, 36h (for T = 5) of data gives better results. The Precision remain
quite high in the range of $88.4\%-96.4\%$ for both $T=3,5$. This implies that
model has a very small false alarm rate and any warning by model regarding
possible TC formation can not be ignored. Also the Recall remains in the range
of $94.4\%-99.2\%$ for both $T=3,5$, which is quite high, implying that model
is detecting nearly all TC formation cases, and it can be used reliably for
practical purposes. The F1-score vary in the range of $92.0\%-97.8\%$.

The accuracy for 36h lead time is even better than 24h lead time across all
ocean basins, which is in the range $96.4\%-99.3\%$ and $97.2\%-99.1\%$ for
$T$ equals to 3 and 5 respectively. A possible reason for this is that the
reanalysis variables that we have selected in our study are more
distinguishable and represent the TC formation well at this lead time. The
Precision and Recall remain quite high again in the range of $94.5\%-99.3\%$
and $96.8\%-99.7\%$ respectively for both $T=3,5$.

The accuracy for lead time 48h is in the range $95.4\%-99.1\%$ which is
greater than lead time 24h and slightly less than lead time 36h in the case of
$T=3$. The accuracy for 48h lead time decreases by approx $5\%-9\%$ in
comparison of lead time 24h and 36h for $T=5$. This implies that for 48h lead
time prediction $T=3$ is a better choice. For $T=3$, model can predict with a
lead time of 60h, which is quite a large time for early prediction of TC
formation. In this case also model achieves an accuracy in the range of
$86.9\%-92.9\%$, which can be considered good because the dynamics of causal
factors behind TC formation change rapidly with time.

In Fig 4 the epoch wise accuracy of the train and test set is shown for NA
ocean basin. We achieved a similar train-test accuracy convergence in other
ocean basins.

###  5.1 Comparison

Table 4: Comparision with best 5-fold performance reported in [15]. Ocean Basin |  Lead Time(h) |  Precision |  Recall |  F1
---|---|---|---|---
NA |  24 |  0.937 |  0.880 |  0.908
|  |  0.951 |  0.965 |  0.953
|  48 |  0.888 |  0.683 |  0.757
|  |  0.977 |  0.976 |  0.976
WP |  24 |  0.948 |  0.754 |  0.817
|  |  0.920 |  0.965 |  0.937
|  48 |  0.889 |  0.642 |  0.701
|  |  0.978 |  0.966 |  0.972
Figure 4: Epoch wise train versus test accuracy for T = 3.

As discussed in section 2, the existing deep learning studies are not suitable
for a direct comparison, as [28, 29] deals with detecting an ongoing TC, and
in [25] the TC formation definition is based on cloud cover and uses simulated
satellite data. We will make a direct comparison with the machine learning
work [15], where the TC formation definition coincides with our definition,
and authors evaluated nine machine learning models in terms Precision, Recall,
and F1-score for lead times up to 48h in NA, and WNP ocean basins. Out of nine
classifiers, overall AdaBoost works best in all cases. In Table 4, we have
reported the AdaBoost accuracy for lead times 24h and 48h along with accuracy
achieved by our model (in bold). From Table 4, we observe that for 24h lead
time Precision is more or less same but there is a big difference in terms of
Recall, whereas we achieve a recall value of $96.5\%$ both in NA and WP ocean
basin in comparison of $88\%$ and $75.4\%$. In the case of lead time 48h, we
achieve a better performance both in WP and NA ocean basins with an
improvement of more than $9\%$ in precision and more than $28\%$ in the
recall.

##  6 Conclusion

In this work a deep learning model is proposed which can forecast a TC
formation using as less as 12h of data and lead time up to 60h with high
precision, recall, and F1-score across six ocean basins of the world. An early
information regarding potential cyclone formation has huge social, economical,
and environmental benefits. Through this work, the authors establish that the
reanalysis dataset has enough information to capture the complex and non-
linear natural phenomenon behind a cyclone formation. One can further attempt
to use the reanalysis dataset for a longer lead time forecast. The reanalysis
dataset provides many other variables like cloud cover, vorticity, sea surface
temperature, etc, one can explore these variables to further improve the
model.

One of the drawback of the proposed model is that we have taken equal number
of positive and negative samples in our study. Given any random location and
time, the chances of TC formation is very low. So a possible improvement of
the proposed study is to take large negative samples than positive samples.

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# Using AI Uncertainty Quantification to Improve Human Decision-Making

Laura R. Marusich1, Jonathan Z. Bakdash2, Yan Zhou2, Murat Kantarcioglu2

###### Abstract

AI Uncertainty Quantification (UQ) has the potential to improve human
decision-making beyond AI predictions alone by providing additional useful
probabilistic information to users. The majority of past research on AI and
human decision-making has concentrated on model explainability and
interpretability, with very little focus on understanding the impact of UQ on
human-decision making performance. Moreover, UQ is often equated to the
model’s predicted probability, hence, not carefully calibrated. In this work,
we implemented instance-based UQ for three real datasets. To achieve this, we
trained different AI models for classification for each dataset, and used
random samples generated around the neighborhood of the given instance to
create confidence intervals for UQ. The computed UQ was calibrated using a
strictly proper scoring rule as a form of quality assurance for UQ. We then
conducted two preregistered online behavioral experiments that compared
objective human decision-making performance under different AI information
conditions, including UQ. In Experiment 1 (_N_ = 445), we compared decision-
making for no AI (control), AI prediction alone, and AI prediction with a
visualization of UQ. We found UQ significantly improved decision-making beyond
the other two conditions. In Experiment 2 (_N_ = 600), we focused on comparing
different representations of UQ information: Point vs. distribution of
uncertainty and visualization type (needle vs. dotplot). We did not find
meaningful differences in decision-making performance among these different
representations of UQ. Overall, our results indicate that human decision-
making can be improved by providing UQ information along with AI predictions,
and that this benefit generalizes across a variety of representations of UQ.
Implementing instance-level UQ for AI may improve decision-making with real
systems. Future work will explore additional representations and
visualizations of AI UQ under different contexts to determine the best ways to
provide this information to users for optimal decision-making with AI
predictions.

##  1 Introduction

Using AI to improve human decision-making requires effective human-AI
interaction. Recent work on human-AI interaction guidelines focuses on
explainability and interpretability (Amershi et al. 2019), which may improve
subjective human ratings of trust in and usability of AI. However, a
quantitative synthesis of studies found explanations may not generally improve
decision accuracy beyond AI prediction alone (Schemmer et al. 2022) in many
application domains.

One less-explored possibility for promoting effective human-AI interaction is
AI Uncertainty Quantification (UQ) for predictions. AI UQ is posited to be key
for human decision-making (Abdar et al. 2021b; Jalaian, Lee, and Russell
2019). Similarly, judgment and decision-making research shows that providing
overall prediction uncertainty enhances decision-making accuracy. For example,
in weather forecasting humans demonstrate higher decision-making performance
when they receive probabilistic information (e.g., a forecast with a
probability of rain), compared to only deterministic predictions (e.g., it
will or will not rain) (Frick and Hegg 2011; Joslyn and LeClerc 2013; Morss,
Demuth, and Lazo 2008; Nadav-Greenberg and Joslyn 2009). This literature also
indicates that the way uncertainty information is represented matters for
human decision-making: communicating uncertainty with visual representations
and other intuitive methods can be especially effective (Gigerenzer et al.
2007; Hullman et al. 2018).

These findings suggest that AI Uncertainty Quantification (UQ) for
_predictions_ has the potential to improve human decision-making beyond AI
predictions alone. However, because more information, even if task-relevant,
is not always beneficial to human decision-making performance (e.g., (Marusich
et al. 2016; Gigerenzer and Brighton 2009; Alufaisan et al. 2021)), it is
critical to empirically demonstrate this potential benefit of AI UQ for
predictions.

Existing empirical work investigating the effect of AI UQ on human decision-
making tasks is somewhat limited, with varied tasks, outcome variables, and
results (Lai et al. 2021). Some work even suggests that AI UQ is not
beneficial for decision-making (Zhang, Liao, and Bellamy 2020).

It is an open question “… whether decision makers can make sense of [AI]
uncertainty estimates properly … ” and how to communicate this uncertainty
(Lai et al. 2021, p. 15). To address this question, here we focus on
empirically evaluating human decision-making for two objective measures
(response accuracy and confidence calibration with accuracy) using visual
representations of AI UQ for predictions with varying amounts of information.
Our method of estimating AI UQ reflects how we expect the prediction to change
as we repeatedly sample a small amount of noise from the vicinity of a given
instance. The high quality of UQ information was verified using a strictly
proper scoring rule (Gneiting and Raftery 2007) by leveraging true class
labels.

Our behavioral experiments show that providing AI UQ for predictions improves
human decision accuracy and confidence calibration, compared to the AI
prediction alone. At the same time, we did not find statistically significant
differences for how AI UQ was visually represented and the information
included.

In section 2, we provide the background information related to UQ. Section 3
describes our UQ technique and experimental design. In section 4, we report
findings from the behavioral experiments comparing human decision making
accuracy with or without UQ information. In section 5, we report the impact of
different visualizations of UQ information. Finally, sections 6 and 7 conclude
by discussing the implications of our results and future work.

##  2 Background and Related Work

Bhatt et al. (2021a) propose using uncertainty as a form of algorithmic
transparency. They argue that uncertainty can help build fairer models, enable
better decision-making, and improve trust. The key takeaways from their work
include that well-calibrated uncertainty is key to transparent data-driven
decision-making, and it becomes more costly to calibrate uncertainty estimates
as the complexity of the problem grows.

Predictions by AI-based systems are subject to uncertainty from different
sources. The source of uncertainty is either aleatoric, caused by noise in
data and irreducible, or epistemic because of uncertain model distribution
(Kendall and Gal 2017). Uncertainty quantification methods have been developed
to assess the reliability of AI predictions (Abdar et al. 2021a), including
Bayesian methods and ensemble methods (Abdar et al. 2021b).

Monte Carlo sampling (Neal 2012) and Markov chain Monte Carlo (Salakhutdinov
and Mnih 2008; Salimans, Kingma, and Welling 2015; Chen, Fox, and Guestrin
2014; Ding et al. 2014; Chen, Ding, and Carin 2015; Li et al. 2016; Gong et
al. 2019) are heavily used for uncertainty quantification in Bayesian
techniques (Kendall and Gal 2017; Wang et al. 2019; Liu et al. 2019a). To
estimate aleatoric uncertainty, a hidden variable is often proposed to
represent the underlying data point $x^{*}$ from which a given instance $x$ is
only one of many possible observations of $x^{*}$. Parameters modeling the
transformation from $x^{*}$ to $x$ can be sampled to obtain multiple copies of
the hidden $x^{*}$. For epistemic uncertainty, the distribution of model
parameter $\theta$ is often approximated during training by achieving certain
objective optimization, for example, the Kullback–Leibler divergence. The
distribution of the prediction can be sampled from the samples of the learned
model parameters. The predictive uncertainty can be established from the
variance or entropy of the sampled predictions of the sampled hidden states of
a given instance.

Quantifying uncertainty on learning models from a Bayesian perspective takes
many different forms. Uncertainty Posterior distribution over BNN weights can
be learned using variational inference (Subedar et al. 2019; Louizos and
Welling 2017; Farquhar, Smith, and Gal 2020; Ghosh et al. 2020). On the other
hand, Generative Adversarial Networks (GANs) are used to generate out-of-
distribution (OoD) examples (Oberdiek, Fink, and Rottmann 2022). Implicit
neural representations (INRs) are reformulated from a Bayesian perspective to
allow for uncertainty quantification (Vasconcelos et al. 2023). Similarly,
Direct Epistemic Uncertainty Prediction (DEUP) is proposed to address the
issue that using the variance of the Bayesian posterior does not capture the
epistemic uncertainty induced by model misspecification (Lahlou et al. 2023).
Aleatoric uncertainty and epistemic uncertainty have also been modeled as
universal adversarial perturbations (Liu et al. 2019a).

Ensemble models can enhance the predictive accuracy, however, it is highly
debated whether an ensemble of models can provide a good uncertainty estimate
(Abdar et al. 2021b; Wilson and Izmailov 2020; Sensoy, Kaplan, and Kandemir
2018). Recently, benefits of prior functions and bootstrapping in training
ensembles with estimate of uncertainty have been discussed (Dwaracherla et al.
2023). Maximizing Overall Diversity takes into account ensemble predictions
for possible future input when estimating uncertainty (Jain et al. 2020).
Random parameter initialization and data shuffling have also been proposed to
estimate the uncertainty of DNN ensembles (Lakshminarayanan, Pritzel, and
Blundell 2017). A Bayesian non-parametric ensemble (BNE) approach is proposed
to account for different sources of model uncertainty (Liu et al. 2019b). More
details on extensive studies on quantifying uncertainty with respect to both
Bayesian and ensemble methods, as well as in real applications can be found in
(Abdar et al. 2021b).

Lai et al. (2023) surveyed existing work on Human-AI decision-making. They
observed that many existing systems provide prediction probabilities as
classification confidence scores to human decision makers (Arshad et al. 2015;
Buçinca, Malaya, and Gajos 2021; Bussone, Stumpf, and O’Sullivan 2015; Feng
and Boyd-Graber 2019; Guo et al. 2019; Weerts, van Ipenburg, and Pechenizkiy
2019). However, prediction probabilities are prone to overconfidence in some
AI models. There is a lack of discussion on the calibration of uncertainty
estimates in the existing literature.

One contribution of our work is that we achieved efficiency of UQ estimate by
assessing the change of prediction yielded from repeatedly sampling noise
adjacent to a given instance, and carefully calibrated the uncertainty
information shown to the user by leveraging the ground truth. More precisely,
we provide well-calibrated uncertainty estimates in different visualizations
of confidence intervals to the human participants. Unlike the existing work
discussed above, our goal is to provide the uncertainty information to the
human participants to understand whether good uncertainty quantification
information helps in user decision-making. To achieve this goal, we do not
attempt to come up with a UQ method a priori. Instead, we take the liberty of
knowing the true labels of given instances, and simplify the problem as
sampling predictive confidence from instances distorted with a small amount of
random noise. The quality of the disclosed uncertainty estimate is verified
using a strictly proper scoring rule (Gneiting and Raftery 2007) prior to use
in two behavioral experiments. While there have been recent calls for research
using UQ with human decision-making (e.g., Bhatt et al. 2021b; Lai et al.
2021), the few existing studies tend to focus on qualitative or subjective
assessments of human behavior (e.g., Prabhudesai et al. 2023). Furthermore, it
is not clear how useful to decision-makers the UQ information provided in
these studies is, due to lack of proper calibration.

##  3 Current Work

We conducted two experiments to assess the effect of providing visualizations
of AI prediction UQ information upon the accuracy and confidence of human
decision-making. The first experiment compares performance when AI uncertainty
is provided to performance when only an AI prediction, or no AI information at
all, is provided. The second experiment compares decision-making performance
for different representations of AI uncertainty.

Our methods and results for the instance-level predictive UQ and behavioral
experiments are fully reproducible. See https://osf.io/cb762/ for details.

In both experiments, we assessed our research questions using three different
publicly-available and widely-used datasets: the Census, German Credit, and
Student Performance datasets from the UCI Machine Learning Repository (Dua and
Graff 2017), described in more detail below.

### Datasets

The Census dataset has 48,842 instances and 14 attributes. The missing values
in the dataset were replaced with the mode (the most frequent value), and the
dollar amounts were adjusted for inflation. The German Credit dataset has
1,000 instances and 20 attributes. The currency values were converted to
dollars and adjusted for inflation. The Student Performance has 649 instances
and 33 attributes. Three of the attributes first period grade, second period
grade, and final grade were combined into one with their average. Each dataset
was split into training (70%) and test (30%) data sets.

We selected these datasets because they involve real-world contexts that are
fairly intuitive for non-expert human participants to reason about (e.g., will
a student pass or fail a class?). In addition, using three datasets that vary
in number of features and in the overall accuracy classifiers can achieve in
their predictions ensures that our findings are not limited only to one
specific dataset.

Several machine learning models were trained on all three datasets, including
decision tree, logistic regression, random forest, and support vector machine.
The best set of hyper-parameters was determined through grid search. Random
forest was the best in terms of overall accuracy on the datasets and therefore
was selected for use as the AI model in this study. The mean accuracy on the
Census data is 85.3%, 75.7% on the German Credit data, and 85.1% on the
Student Performance data. All classification tasks were completed on an Intel®
Xeon® machine with a 2.30GHz CPU.

### Instance-Level Predictive Uncertainty Quantification

UQ methods in existing literature estimate predictive uncertainty without the
knowledge of the true labels of the test instances. These methods are subject
to complicated calculations, sometimes poor convergence, lack of scalability,
and sometimes, they are time and resource consuming (Abdar et al. 2021a). In
our study, we aim to provide predictive uncertainty quantification to human
decision-makers and use the advantage of knowing the true labels in advance.
Therefore, we simplify the problem as sampling predictive confidence from
samples of $x$ with a small random disturbance and verify the quality of the
uncertainty estimate using a strictly proper scoring rule (Gneiting and
Raftery 2007) before showing it to the human. Note that, without knowing the
ground truth, this treatment of UQ would be reckless and naive. It would
appear that we model a prior distribution over hypothesis as the distribution
over observations in the noisy neighborhood of a given instance. However,
given the true label of an instance, we can hypothesize that observations over
its $n$ neighboring noisy samples are $n$ plausible fits for this instance,
and confirm our hypothesis with a strictly proper scoring rule.

Predictive uncertainty consists of data uncertainty (aleatoric) and model
uncertainty (epistemic). To model data uncertainty, we sample $n$ instances
from a Gaussian distribution within a standard deviation $\sigma$ from a given
instance $x$, assuming $x=x^{*}+\eta$ where $x^{*}$ is the clean input of $x$
without the random disturbance $\eta$. Thus, given a prediction function
parameterized by $w$, the class label of $x$ is predicted as:

$p(y|x,w)=\int p(y|x^{*},w)p(x^{*}|x)dx^{*}$

The posterior $p(x^{*}|x)$ is generally unknown. By assuming
$\eta\sim\mathcal{N}(0,\sigma_{0}^{2},I)$, we can sample from the posterior
distribution given the noisy input $x$. In this study, we set $n=100$ and
$\sigma_{0}=0.1$.

Similarly, for model uncertainty, given a set of training data $(X,Y)$, we
assume there exists an uncertain set of $m$ models with model uncertainty
$\theta^{(m)}\sim p(\theta|X,Y)$. Hence, given an instance $x$, the
probability of the class label of $x$ is:

$p(y|x,X,Y)=\mathbb{E}_{p(\theta|X,Y)}[p(y|x,\theta)].$

In this study, we tested an ensemble of logistic regression, support vector
machine, and random forest to predict the class label. The best uncertainty
estimate, however, was obtained by using the random forest alone, assessed by
the Brier score discussed below.

Predictive uncertainty per instance was computed for 294 randomly selected
Census instances, 300 German Credit instances, and 194 Student Performance
instances. These selected instances were used for test on human subjects.

Predictive uncertainty at the instance-level was measured on random samples in
the neighborhood of the instance. More specifically, given an instance $x$,
$n$ random “clones” were sampled from a Gaussian distribution within $\delta$
standard deviation from the mean $x$. In the experiment, we let $n=100$ and
$\delta=0.1$ which provided sufficient statistical significance and
constrained neighborhood choices. Class probabilities were computed using the
trained random forest classifier for each of the 100 samples, and the 95%
confidence interval of the class probabilities was used as the predictive
uncertainty range for instance $x$. UQ computed from random forest alone was
superior to that of the ensemble of logistic regression, support vector
machine, and random forest, hence was used in the experiment on human
subjects.

Census

German Credit

Student Performance

Figure 1: The Brier score of the “cloned” instances for Census (100), German
Credit (100), and Student Performance (40) sampled for demonstration. $Y$-axis
is the Brier score. Magenta marks the samples that are correctly predicted by
the AI model, cyan marks samples incorrectly predicted by the model.
Horizontal lines illustrate the mean of the Brier score, and its 0.5, 1, and
1.5 standard deviations.

Knowing the ground truth (class label) of the instances, we can verify the
quality of the simulated predictive uncertainty using the Brier score (also
referred to as Brier loss). The Brier score measures the mean squared
difference between the predicted probability and the true outcome. For each
selected instance $x$, with $y\in\\{0,1\\}$ and the predicted probability
$p_{i}=Pr(y_{i}=1)$ for each “cloned” sample $x_{i}$, we compute the Brier
score $B=\frac{1}{n}\sum_{i}(y-p_{i})^{2}$ between the predicted probability
of the “cloned” samples and $y$—the actual label of $x$.

If the “cloned” samples are truly representative of $x$, the computed Brier
score should reflect the correctness of the prediction made for $x$ by the AI
model $M$. A smaller Brier score means more accurate predictions made for the
clones of $x$, and therefore should correspond to a correct classification for
$x$ by $M$. We verified empirically that the Brier scores of the predictive
uncertainty is highly correlated with the true prediction for $x$ by $M$, as
shown in Figure 1. Points with low Brier score corresponds to instances where
$M$ is correct. In Figure 1, points in magenta are the samples correctly
predicted by the AI model, and points in cyan are samples incorrectly
predicted by the model. As can be seen, “clones” for each correctly predicted
sample correspond to low Brier score loss, and vice versa, cloned samples for
incorrectly classified samples produce high Brier scores. Horizontal lines
illustrate the mean of the Brier score, and its 0.5, 1, and 1.5 standard
deviations. The Brier score close to mean (approximately $0.25$) is a highly
accurate indicator of the classification outcome. In essence, the Brier score
resembles the trust score (Jiang et al. 2018) that has high precision at
identifying correctly classified examples, and is adequate to assess the
quality of the estimated UQ.

### Behavioral Experiments: General Methods

We used the same experimental task across both Experiment 1 and 2, which was
developed using jsPysch (De Leeuw 2015) and hosted on MindProbe
https://mindprobe.eu/ using JATOS (Lange, Kühn, and Filevich 2015). Each trial
of this task included a description of an individual and a two-alternative
forced choice for the classification of that individual. Each choice was
correct on 50% of the trials, thus chance performance for human decision-
making accuracy was 50%. In some conditions, an AI prediction or an AI
prediction and a visualization of prediction uncertainty would also appear.
Figure 2 shows an example of the information appearing in the three AI
conditions for a trial from the German Credit dataset condition (see
https://osf.io/cb762/ for more example trials). After making a decision,
participants then entered their confidence in that choice, on a Likert scale
of 1 (No Confidence) to 5 (Full Confidence). Feedback was then displayed,
indicating whether or not the previous choice was correct.

For each dataset, we selected 50 instances with representative average AI
prediction accuracies (_Census_ : 88%, _German Credit_ : 76%, _Student
Performance_ : 82%). Then, for each participant, we randomly sampled 40 of
those 50 instances for the block of test trials, resulting in small variations
in AI accuracy for each participant.

Online participants were recruited from Prolific https://www.prolific.co. They
provided informed consent, viewed a series of instructional screens with
examples, completed 8 practice trials, followed by 40 test trials, and a brief
series of questionnaires (demographics, self-reported strategies, subjective
usability, subjective task difficulty, task understanding, and an assessment
of risk literacy (Cokely et al. 2012), see https://osf.io/cb762/). Most
participants completed the task in less than 20 minutes, and they were paid
$5.00 for their participation (i.e., above the U.S. federal minimum hourly
wage). This research received Institutional Review Board (IRB) approval.

Figure 2:  Example showing the information appearing in the three AI
conditions in Experiment 1 for a trial from the _German Credit_ dataset
condition.

##  4 Experiment 1

Experiment 1 compared participant decision-making accuracy in three
conditions: Control (no AI prediction information), AI Prediction, and AI
Uncertainty (AI prediction plus a visualized point estimate of AI
uncertainty), see Figure 2. All hypotheses and methods were pre-registered
(https://aspredicted.org/ZW9_Z54).

We hypothesized that for all three datasets, participant decision accuracy
would be highest in the AI Uncertainty condition, followed by the AI
Prediction condition, and lowest in the Control condition. Similarly, we
hypothesized that confidence calibration (positive association between
confidence and accuracy) would be strongest in the AI Uncertainty condition,
followed by the AI Prediction condition, and lowest in the Control condition.

### Participants

We recruited nearly 50 participants in each of 9 experimental conditions, for
a total of 445 participants (48.8% male, 48.5% female, 2.7% other or prefer
not to answer). The majority (68.8%) of participants were 18-44 years old.

### Results and Discussion

We excluded trials with reaction times that exceeded three standard deviations
above the mean; this resulted in the removal of 396 out of 17,800 trials
across all participants. An omnibus 3 (AI Condition) x 3 (Dataset) ANOVA for
mean accuracy indicated a significant main effect of AI condition
($F(2,436)=84.11,{p}<0.001,\eta_{p}^{2}=0.28$; see left side of Figure 3).
This large effect size is driven primarily by the differences between the
Control condition and the other two conditions. However, we also used Tukey’s
honest significance test to conduct post-hoc comparisons between individual
conditions. These comparisons showed not only that accuracy in the AI
Prediction condition was higher than in the Control condition
($t(436)=9.91,{p}<0.0001$), but also that accuracy in the AI Uncertainty
condition was further improved (although to a lesser extent) over the AI
Prediction condition ($t(436)=2.36,{p}=0.049$).

Figure 3:  Participant accuracy in Experiments 1 (left) and 2 (right). Error
bars represent 95% confidence intervals.

There was also a significant main effect of dataset upon accuracy
($F(2,436)=144.72,{p}<0.001,\eta_{p}^{2}=0.40$). Unsurprisingly, human
accuracy was lowest in the _German Credit_ dataset, for which AI accuracy is
also relatively low, and human accuracy was highest in the _Census_ dataset,
where AI accuracy is also relatively high.

To assess confidence calibration, we fit a multilevel model (Gelman and Hill
2006) that included dataset, AI condition, and confidence ratings as fixed-
effect predictors, with varying intercepts for each participant. The
multilevel model accounts for a moderate amount of variance in fixed and
varying effects, conditional Pseudo-$R^{2}$ = 0.10. This model indicated that
the relationship between confidence and accuracy interacted with both dataset
and AI condition, illustrated in Figure 4.

Figure 4:  Predicted effects (level 2/overall results of multilevel model) of
confidence ratings, dataset, and AI condition upon accuracy in Experiment 1.
Steeper, positively-sloped lines indicate better confidence calibration.
Shaded areas represent 95% confidence intervals for the predicted values.

As hypothesized, confidence was most highly calibrated with accuracy in the AI
Uncertainty condition, followed by the AI Prediction condition, and lowest in
the Control condition. See data and code at https://osf.io/cb762/ for details
of the model.

We also analyzed the impact of AI condition and dataset upon participants’
response times (RT). Using an omnibus 3 x 3 ANOVA, we found a significant main
effect of dataset upon RT ($F(2,436)=6.22,{p}=0.002,\eta_{p}^{2}=0.03$), with
participants responding slowest in the _Student Performance_ dataset (see left
side of Figure 5), perhaps due to the larger number of attributes to consider
for each instance. We did not find significant effects of AI condition
($F(2,436)=1.97,{p}=0.14,\eta_{p}^{2}=0.009$) or an interaction effect
($F(4,436)=0.13,{p}=0.97,\eta_{p}^{2}=0.001$). These results imply that the
accuracy benefit for AI UQ information is not merely due to a speed/accuracy
tradeoff among participants (Wickelgren 1977).

Figure 5:  Participant response times (RT) in milliseconds in Experiment 1
(left) and Experiment 2 (right). Error bars represent 95% confidence
intervals.

##  5 Experiment 2

Experiment 1 demonstrated that decision-making performance can be improved
with AI UQ information; we designed Experiment 2 to test if different
representations of UQ might be more or less beneficial for decision-making. We
compared performance with distributions of uncertainty probabilities to point-
estimated probabilities, as well as two different visualizations of
uncertainty (needle vs. dotplot), again using the same three datasets used in
Experiment 1 (see Figure 6). All hypotheses and methods were pre-registered
(https://aspredicted.org/CJW_71H).

Figure 6:  Example of the four conditions (point vs. distribution, and needle
vs. dotplot) in Experiment 2, using a trial from the _German Credit_ dataset.

We hypothesized that for all three datasets, both participant decision
accuracy and confidence calibration would be higher with distribution
information than for point-estimated UQ in the AI Uncertainty condition,
followed by the AI Prediction condition, and lowest in the Control condition.
We also hypothesized that, within the distribution conditions, accuracy and
confidence calibration would be higher for the dotplot visualization than for
the needle visualization, due to the more detailed information about the shape
of distributions available in the dotplot, compared to the needle which only
shows the distributions as a uniform range.

### Participants

We recruited 50 participants in each cell, for a total of 600 participants
(48.5% male, 49.3% female, 2.2% other or prefer not to answer), from the
Prolific platform. Most participants (75.3%) were 18-44 years old.

### Results and Discussion

We excluded 553 trials (out of 24,000 across all participants) with reaction
times that exceeded three standard deviations above the mean. An omnibus 2
(point vs. distribution) x 2 (needle vs. dotplot) x 3 (dataset) ANOVA for mean
accuracy indicated a significant main effect of dataset
($F(2,588)=188.77,{p}<0.001,\eta_{p}^{2}=0.39$), where performance was again
highest for the _Census_ dataset, followed by _Student Performance_ , and
lowest for _German Credit_. However, there was no significant main effects of
point vs. distribution ($F(1,588)=0.28,{p}=0.60,\eta_{p}^{2}<0.001$) or
visualization type ($F(1,588)=0.16,{p}=0.69,\eta_{p}^{2}<0.001$). Neither was
there evidence of significant first-order interaction effects among the three
manipulated variables, see right side of Figure 3).

As in Experiment 1, we fit multilevel models with varying intercepts for each
participant to assess confidence calibration. We found that the best-fitting
model (as assessed by fit statistics: AIC and BIC) had only confidence,
dataset, and their interaction as fixed-effect predictors, see Figure 7.

Figure 7:  Predicted effects (level 2/overall results of multilevel model) of
confidence ratings and dataset upon accuracy in Experiment 2. Steeper,
positively-sloped lines indicate better confidence calibration. Shaded areas
represent 95% confidence intervals for the predicted values.

The best fit model indicates confidence calibration, again, accounts for a
moderate amount of variance in fixed and varying effects, conditional
Pseudo-$R^{2}$ = 0.13. Including point vs. distribution or visualization type
did not appear to improve model fit or to predict accuracy performance above
and beyond what is predicted by dataset and confidence. See data and code at
https://osf.io/cb762/ for details of the model.

Thus, neither our accuracy or confidence calibration results indicate support
for our Experiment 2 hypotheses that performance would be better with
distribution information for UQ than for point-estimated UQ, and that within
the distribution condition, performance would be better with dotplots than
with the needle visualization.

Additionally, we analyzed RT in Experiment 2 (see right side of Figure 5) to
rule out speed/accuracy tradeoffs in the performance results. An omnibus 2 x 2
x 3 ANOVA indicated no significant effect of dataset
($F(2,588)=0.09,{p}=0.92,\eta_{p}^{2}<0.001$), point vs. distribution
($F(1,588)=0.06,{p}=0.81,\eta_{p}^{2}<0.001$), or visualization type
($F(1,588)=0.01,{p}=0.91,\eta_{p}^{2}<0.001$) upon RT. Neither was there
evidence of significant interaction effects among the three manipulated
variables.

### Exploratory Analyses

Although this work was not specifically designed to assess whether the
combination of humans plus AI generally exceeded the accuracy of AI
predictions, we conducted exploratory analyses to investigate how often this
occurred. In both experiments, we found that a small subset of participants
were able to outperform the accuracy of the AI predictions they received (see
Table 1). AI uncertainty enabled humans to outperform the AI accuracy more
frequently and with patterns of mean differences suggesting greater
improvements.

Human Accuracy | > AI (n) |  $\leq$AI (n) | > AI (Mean %)
---|---|---|---
Experiment 1 |  |  |
AI Prediction | 2 | 148 | 1.33%
AI Uncertainty | 7 | 141 | 4.73%
Experiment 2 |  |  |
Point Needle | 8 | 142 | 5.33%
Point Dotplot | 8 | 142 | 5.33%
Dist Needle | 11 | 139 | 7.33%
Dist Dotplot | 7 | 143 | 4.67%
Table 1: Number of participants who outperformed the AI

##  6 General Discussion, Limitations, and Future Work

The overall results of Experiment 1 showed that providing AI UQ to human
decision-makers improved accuracy and confidence calibration performance over
and above providing an AI prediction alone. In Experiment 2, we did not find
meaningful differences between different representations of UQ. Taken
together, our findings suggest that the benefit of AI UQ may not be overly
sensitive to the representation of the UQ information. Also, adding more
information (here, the UQ distribution), even though task-relevant, did not
improve decision-making which is consistent with prior research (Marusich et
al. 2016; Gigerenzer and Brighton 2009; Alufaisan et al. 2021).

Here, the humans and AI had identical information so we could evaluate well-
calibrated UQ. Normatively, algorithms tend to outperform human decision-
making in a variety of tasks; a clear exception is when people have knowledge
the algorithm does not (Dawes, Faust, and Meehl 1989). In such situations, it
is possible that the AI and human combined can produce better performance than
either alone (Cummings 2014). Exploratory results suggested AI uncertainty may
increase the frequency of people exceeding AI accuracy, although this was not
a common occurrence; likely because both the human and the AI had the same
information.

In this work, we did not compare different UQ techniques but did demonstrate
that, using Brier score, our UQ technique performed well in practice. It is
possible that UQ techniques that do not perform as well as ours may not
improve human decision-making accuracy. In future work, we plan to use other
UQ techniques, including less effective ones to understand the impact of UQ
quality on human decision-making accuracy. Similarly, behavioral experiments
were limited to comparing point versus distributions and two visualizations of
predictive uncertainty. It is possible that other visualizations may make
providing distribution information more effective, and we plan to conduct
future work assessing more UQ visualization techniques.

Finally, we used a relatively simple binary classification decision-making
task. In more complex application domains, where humans encounter multi-class
classification problems, the impact of UQ information on human decision making
could be different. We plan to run future experiments using multi-class
classification problems. Additionally, future work could investigate the use
of AI UQ for complex tasks where people, such as experts, have knowledge
unknown to the AI model.

##  7 Conclusion and Broader Impact

Recently, understanding how humans and AI systems can work better together has
emerged as an important challenge. Although there has been some previous work
on understanding how and when explainable AI may help human decision making,
the impact of providing uncertainty information to humans has not been
explored in depth in the context of AI systems. To address this challenge, in
this work, we explore whether providing uncertainty information to humans may
improve decision making and potentially correct errors caused by the AI
models.

As a starting point, we developed a UQ technique where we used the points
sampled around the neighborhood of a given instance, and investigated the
efficacy of using various learning models and their ensemble to provide
prediction confidence intervals at the instance level. Using the existing
labels of the test instances and Brier score criteria, we show that our
developed technique provides accurate UQ information.

On one hand, the extensive behavioral experiments show that providing AI
uncertainty information using our UQ technique improves human decision
accuracy and confidence calibration over the AI prediction alone. On the other
hand, we did not find meaningful differences among four representations of
uncertainty.

## Acknowledgments

The views and conclusions contained in this document are those of the authors
and should not be interpreted as representing the official policies, either
expressed or implied of the U.S. DEVCOM Army Research Laboratory or the U.S.
Government. The U.S. Government is authorized to reproduce and distribute
reprints for Government purposes notwithstanding any copyright notation. M.K.
and Y.Z. were supported in part by NSF awards OAC-1828467, DMS-1925346,
CNS-2029661, OAC-2115094, ARO award W911NF-17-1-0356, and a gift from Cisco
Inc.

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