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We propose and investigate new complementary methodologies for estimating predictive variance networks in regression neural networks. We derive a locally aware mini-batching scheme that result in sparse robust gradients, and show how to…

When random label noise is added to a training dataset, the prediction error of a neural network on a label-noise-free test dataset initially improves during early training but eventually deteriorates, following a U-shaped dependence on…

Point estimators for the shearing of galaxy images induced by gravitational lensing involve a complex inverse problem in the presence of noise, pixelization, and model uncertainties. We present a probabilistic forward modeling approach to…

Current person image retrieval methods have achieved great improvements in accuracy metrics. However, they rarely describe the reliability of the prediction. In this paper, we propose an Uncertainty-Aware Learning (UAL) method to remedy…

Over recent years, deep learning based image registration has achieved impressive accuracy in many domains, including medical imaging and, specifically, human neuroimaging with magnetic resonance imaging (MRI). However, the uncertainty…

Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…

The problem of developing binary classifiers from positive and unlabeled data is often encountered in machine learning. A common requirement in this setting is to approximate posterior probabilities of positive and negative classes for a…

We consider fully connected and feedforward deep neural networks with dependent and possibly heavy-tailed weights, as introduced in [26], to address limitations of the standard Gaussian prior. It has been proved in [26] that, as the number…

Deep Bayesian neural networks (BNNs) are a powerful tool, though computationally demanding, to perform parameter estimation while jointly estimating uncertainty around predictions. BNNs are typically implemented using arbitrary…

How to develop slim and accurate deep neural networks has become crucial for real- world applications, especially for those employed in embedded systems. Though previous work along this research line has shown some promising results, most…

Deep learning models frequently make incorrect predictions with high confidence when presented with test examples that are not well represented in their training dataset. We propose a novel and straightforward approach to estimate…

Noisy PN learning is the problem of binary classification when training examples may be mislabeled (flipped) uniformly with noise rate rho1 for positive examples and rho0 for negative examples. We propose Rank Pruning (RP) to solve noisy PN…

We study the impact that uncertainties on assumed relations between galaxy bias parameters have on constraints of the local PNG $f_{\rm NL}$ parameter. We focus on the relation between the linear density galaxy bias $b_1$ and local PNG bias…

In the general signal+noise model we construct an empirical Bayes posterior which we then use for uncertainty quantification for the unknown, possibly sparse, signal. We introduce a novel excessive bias restriction (EBR) condition, which…

Measuring the structural parameters (size, total brightness, light concentration, etc.) of galaxies is a significant first step towards a quantitative description of different galaxy populations. In this work, we demonstrate that a Bayesian…

We analyze gradient descent with randomly weighted data points in a linear regression model, under a generic weighting distribution. This includes various forms of stochastic gradient descent, importance sampling, but also extends to…

The use of Deep Neural Network (DNN) models in risk-based decision-making has attracted extensive attention with broad applications in medical, finance, manufacturing, and quality control. To mitigate prediction-related risks in decision…

The distribution of the weights of modern deep neural networks (DNNs) - crucial for uncertainty quantification and robustness - is an eminently complex object due to its extremely high dimensionality. This paper proposes one of the first…

Methods for reasoning under uncertainty are a key building block of accurate and reliable machine learning systems. Bayesian methods provide a general framework to quantify uncertainty. However, because of model misspecification and the use…

Supremum norm loss is intuitively more meaningful to quantify function estimation error in statistics. In the context of multivariate nonparametric regression with unknown error, we propose a Bayesian procedure based on spike-and-slab prior…