IEEE Geoscience and Remote Sensing Magazine - June 2023 - 75

over a series of predictions. In particular, ensemble methods
construct a set of deterministic models as ensemble members
that each generate a prediction with the input sample. Based
on the predictions from multiple decision makers, ensemble
methods provide an intuitive way for representing the uncertainty
by evaluating the variety among the member's predictions.
For example, Feng et al. [115] developed an object-based
change detection model using rotation forest and coarse-tofine
uncertainty analysis from multitemporal RS images. The
ensemble members segmented multitemporal images into
pixelwise classes of changed, unchanged, and uncertain classes
according to the defined uncertainty threshold in a coarseto-fine
manner. Change maps were then generated using the
rotation forest, and all the maps were combined into a final
change map by major voting, which quantifies the uncertainty
by calculating the variety of decisions from different ensembles.
Following a similar idea, Tan et al. [116] proposed an
ensemble, object-level change detection model with multiscale
uncertainty analysis based on object-based Dempster-Shafer
fusion in active learning. Moreover, Schroeder et al. [117]
proposed an ensemble model consisting of several artificial
neural networks, quantifying uncertainty through utilization
of computation prediction variance lookup tables.
BAYESIAN INFERENCE
Bayesian learning can be used to interpret model parameters
and uncertainty quantification based on the ability to
combine the scalability, expressiveness, and predictive performance
of neural networks. The Bayesian method utilizes
Bayesian neural networks (BNNs) to directly infer the probability
distribution over the model parameters
)
eled by assuming a prior distribution over parameters via
the Bayes theorem [132]. The prediction distribution of y)
from an input sample x)
can then be obtained as follows:
PD PP Dii di
))
__ ^ii h
))
yx ,, .
= #
yx
(13)
However, this equation is not tractable to the calculation step
of integrating the posterior distribution of model parameters
(, )
P Di and, thus, many approximation techniques
are typically applied. In the literature, Monte Carlo (MC)
approximation has become the most widespread approach
for Bayesian methods, following the law of large numbers.
MC approximation can approximate the expected distribution
by the mean of M neural networks, ,, ,ff f M12
determined parameters, ,, ,.m12
ii f i with
ii f i Following this idea,
MC dropouts have been applied widely to sample the parameters
of a BNN by randomly dropping some connections
of the layers according to a setting probability [118], [119],
[120]. The uncertainty distribution can then be further calculated
by performing variational inference on the neural
networks with the sampling parameters [133].
Concerning the computational cost of sampling model
parameters in MC approximation, external modules are
JUNE 2023 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
utilized to quantify uncertainty, along with the predictions
in BNNs. For example, Ma et al. [121] developed a BNN
architecture with two endpoints to estimate the yield and
the corresponding predictive uncertainty simultaneously in
corn yield prediction based on RS data. Specifically, the extracted
high-level features from the former part of the BNN
are fed into two independent subnetworks to estimate the
mean and standard deviation, respectively, of the predicted
yield as a Gaussian distribution, which can be regarded intuitively
as the quantified uncertainty.
FUTURE PERSPECTIVES
Over the decades, uncertainty analysis has become a critical
topic in geoscience and RS data analysis. The literature
has seen fruitful research outcomes in uncertainty explanation
and quantification. Nevertheless, other open research
directions deserve to be given attention in future studies
concerning the development trend of AI algorithms. In the
next section, we discuss some potential topics of interest.
i . Given the
training dataset D as a prior distribution, the posterior distribution
over the model parameters (
P D;i can be modBENCHMARK
TOOLS FOR UNCERTAINTY
QUANTIFICATION
Due to the lack of a universal benchmark protocol, comparisons
of uncertainty quantification methods are rarely
performed in the literature. Despite this, the existing evaluation
metrics on related studies are usually based on measurable
quantities such as calibration, out-of-distribution
detection, or entropy metrics [132], [134]. However, the
variety of methodology settings makes it challenging to
compare the approaches quantitatively using existing comparison
metrics. Thus, developing benchmark tools, including
a standardized evaluation protocol for uncertainty
quantification, is critical in future research.
UNCERTAINTY IN UNSUPERVISED LEARNING
As data annotation is very expensive and time consuming given
the large volume of EO data, semi- and unsupervised techniques
have been employed widely in AI-based algorithms.
However, existing uncertainty quantification methods still
focus mainly on supervised learning algorithms due to the
requirement for qualification metrics. Therefore, developing
uncertainty quantification methods in the absence of available
labeled samples is a critical research topic for the future.
UNCERTAINTY ANALYSIS FOR MORE AI ALGORITHMS
Currently, most of the existing uncertainty quantification
methods focus on high-level and forecasting tasks in geoscience
and RS. Conversely, uncertainty methods for lowlevel
vision tasks, such as cloud removal, are rarely seen in
the literature due to formation of the predictions, and thus
deserve further study.
QUANTIFYING DATA AND MODEL
UNCERTAINTY SIMULTANEOUSLY
Existing uncertainty quantification methods have a very
limited scope of application. Deterministic and Bayesian
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IEEE Geoscience and Remote Sensing Magazine - June 2023

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