65,028 research outputs found
Calibrating Ensembles for Scalable Uncertainty Quantification in Deep Learning-based Medical Segmentation
Uncertainty quantification in automated image analysis is highly desired in
many applications. Typically, machine learning models in classification or
segmentation are only developed to provide binary answers; however, quantifying
the uncertainty of the models can play a critical role for example in active
learning or machine human interaction. Uncertainty quantification is especially
difficult when using deep learning-based models, which are the state-of-the-art
in many imaging applications. The current uncertainty quantification approaches
do not scale well in high-dimensional real-world problems. Scalable solutions
often rely on classical techniques, such as dropout, during inference or
training ensembles of identical models with different random seeds to obtain a
posterior distribution. In this paper, we show that these approaches fail to
approximate the classification probability. On the contrary, we propose a
scalable and intuitive framework to calibrate ensembles of deep learning models
to produce uncertainty quantification measurements that approximate the
classification probability. On unseen test data, we demonstrate improved
calibration, sensitivity (in two out of three cases) and precision when being
compared with the standard approaches. We further motivate the usage of our
method in active learning, creating pseudo-labels to learn from unlabeled
images and human-machine collaboration
A Locally Adaptive Shrinkage Approach to False Selection Rate Control in High-Dimensional Classification
The uncertainty quantification and error control of classifiers are crucial
in many high-consequence decision-making scenarios. We propose a selective
classification framework that provides an indecision option for any
observations that cannot be classified with confidence. The false selection
rate (FSR), defined as the expected fraction of erroneous classifications among
all definitive classifications, provides a useful error rate notion that trades
off a fraction of indecisions for fewer classification errors. We develop a new
class of locally adaptive shrinkage and selection (LASS) rules for FSR control
in the context of high-dimensional linear discriminant analysis (LDA). LASS is
easy-to-analyze and has robust performance across sparse and dense regimes.
Theoretical guarantees on FSR control are established without strong
assumptions on sparsity as required by existing theories in high-dimensional
LDA. The empirical performances of LASS are investigated using both simulated
and real data
Uncertainty quantification in graph-based classification of high dimensional data
Classification of high dimensional data finds wide-ranging applications. In
many of these applications equipping the resulting classification with a
measure of uncertainty may be as important as the classification itself. In
this paper we introduce, develop algorithms for, and investigate the properties
of, a variety of Bayesian models for the task of binary classification; via the
posterior distribution on the classification labels, these methods
automatically give measures of uncertainty. The methods are all based around
the graph formulation of semi-supervised learning.
We provide a unified framework which brings together a variety of methods
which have been introduced in different communities within the mathematical
sciences. We study probit classification in the graph-based setting, generalize
the level-set method for Bayesian inverse problems to the classification
setting, and generalize the Ginzburg-Landau optimization-based classifier to a
Bayesian setting; we also show that the probit and level set approaches are
natural relaxations of the harmonic function approach introduced in [Zhu et al
2003].
We introduce efficient numerical methods, suited to large data-sets, for both
MCMC-based sampling as well as gradient-based MAP estimation. Through numerical
experiments we study classification accuracy and uncertainty quantification for
our models; these experiments showcase a suite of datasets commonly used to
evaluate graph-based semi-supervised learning algorithms.Comment: 33 pages, 14 figure
Deep Anti-Regularized Ensembles provide reliable out-of-distribution uncertainty quantification
We consider the problem of uncertainty quantification in high dimensional
regression and classification for which deep ensemble have proven to be
promising methods. Recent observations have shown that deep ensemble often
return overconfident estimates outside the training domain, which is a major
limitation because shifted distributions are often encountered in real-life
scenarios. The principal challenge for this problem is to solve the trade-off
between increasing the diversity of the ensemble outputs and making accurate
in-distribution predictions. In this work, we show that an ensemble of networks
with large weights fitting the training data are likely to meet these two
objectives. We derive a simple and practical approach to produce such
ensembles, based on an original anti-regularization term penalizing small
weights and a control process of the weight increase which maintains the
in-distribution loss under an acceptable threshold. The developed approach does
not require any out-of-distribution training data neither any trade-off
hyper-parameter calibration. We derive a theoretical framework for this
approach and show that the proposed optimization can be seen as a
"water-filling" problem. Several experiments in both regression and
classification settings highlight that Deep Anti-Regularized Ensembles (DARE)
significantly improve uncertainty quantification outside the training domain in
comparison to recent deep ensembles and out-of-distribution detection methods.
All the conducted experiments are reproducible and the source code is available
at \url{https://github.com/antoinedemathelin/DARE}.Comment: 26 pages, 9 figure
Multiscale and High-Dimensional Problems
High-dimensional problems appear naturally in various scientific areas. Two primary examples are PDEs describing complex processes in computational chemistry and physics, and stochastic/ parameter-dependent PDEs arising in uncertainty quantification and optimal control. Other highly visible examples are big data analysis including regression and classification which typically encounters high-dimensional data as input and/or output. High dimensional problems cannot be solved by traditional numerical techniques, because of the so-called curse of dimensionality. Rather, they require the development of novel theoretical and computational approaches to make them tractable and to capture fine resolutions and relevant features. Paradoxically, increasing computational power may even serve to heighten this demand, since the wealth of new computational data itself becomes a major obstruction. Extracting essential information from complex structures and developing rigorous models to quantify the quality of information in a high dimensional setting constitute challenging tasks from both theoretical and numerical perspective.
The last decade has seen the emergence of several new computational methodologies which address the obstacles to solving high dimensional problems. These include adaptive methods based on mesh refinement or sparsity, random forests, model reduction, compressed sensing, sparse grid and hyperbolic wavelet approximations, and various new tensor structures. Their common features are the nonlinearity of the solution method that prioritize variables and separate solution characteristics living on different scales. These methods have already drastically advanced the frontiers of computability for certain problem classes.
This workshop proposed to deepen the understanding of the underlying mathematical concepts that drive this new evolution of computational methods and to promote the exchange of ideas emerging in various disciplines about how to treat multiscale and high-dimensional problems
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