Machine learning techniques have been successfully applied to super-resolution tasks on natural images where visually pleasing results are sufficient. However in many scientific domains this is not adequate and estimations of errors and uncertainties are crucial. To address this issue we propose a Bayesian framework that decomposes uncertainties into epistemic and aleatoric uncertainties. We test the validity of our approach by super-resolving images of the Sun's magnetic field and by generating maps measuring the range of possible high resolution explanations compatible with a given low resolution magnetogram.

We develop amortized population Gibbs (APG) samplers, a new class of autoencoding variational methods for deep probabilistic models. APG samplers construct high-dimensional proposals by iterating over updates to lower-dimensional blocks of variables. Each conditional update is a neural proposal, which we train by minimizing the inclusive KL divergence relative to the conditional posterior. To appropriately account for the size of the input data, we develop a new parameterization in terms of neural sufficient statistics, resulting in quasi-conjugate variational approximations. Experiments demonstrate that learned proposals converge to the known analytical conditional posterior in conjugate models, and that APG samplers can learn inference networks for highly-structured deep generative models when the conditional posteriors are intractable. Here APG samplers offer a path toward scaling up stochastic variational methods to models in which standard autoencoding architectures fail to produce accurate samples.

Consider a loss function G ( a,θ) ( a,θ) G ( a,θ) R, where a A R s is a decision/design variable and θ Θ R d is a model parameter space. Given a set of observations X n {ξ 1,...,ξ n} drawn from a distribution with unknown parameter θ 0, p( X n θ 0), our goal is to compute the Bayes optimal decision rule a ( X n) arg min a A E π[G ( a,θ)] ΘG ( a,θ) π ( θ X n) dθ, (1) where π ( θ X n) is the posterior distribution. The latter results when a Bayesian decision-maker places a prior distribution π ( θ) over the parameter space Θ, capturing a priori information about θ such as location or spread. Given X n, the prior and likelihood p ( X n θ) together define a posterior distribution π ( θ X n) p ( X n θ) π ( θ) p( θ, X n), the conditional distribution over θ given observations. The posterior distribution represents uncertainty over the unknown parameter θ, and contains all information required for further inferences or optimization. In general, under most realistic modeling assumptions, closed-form analytic expressions are unavailable for π ( θ X n), making the subsequent integration and optimization problems intractable. In practice, therefore, one uses an approximation to the posterior in the integration in (1). It is easy to see that posterior computation can be expressed as a convex optimization problem: min q () M KL( q ( θ) π ( θ X n)) KL( q ( θ) p ( θ, X n)) log p( X n) (2) KL( q ( θ) π ( θ)) Θlog p( X n θ) q ( θ) dθ log p ( X n) where KL is the Kullback-Leibler divergence and M is the space of all distributions that are absolutely continuous with respect to the posterior (or, equivalently, the prior).

How secure automatic speaker verification (ASV) technology is? More concretely, given a specific target speaker, how likely is it to find another person who gets falsely accepted as that target? This question may be addressed empirically by studying naturally confusable pairs of speakers within a large enough corpus. To this end, one might expect to find at least some speaker pairs that are indistinguishable from each other in terms of ASV. To a certain extent, such aim is mirrored in the standardized ASV evaluation benchmarks. However, the number of speakers in such evaluation benchmarks represents only a small fraction of all possible human voices, making it challenging to extrapolate performance beyond a given corpus. Furthermore, the impostors used in performance evaluation are usually selected randomly. A potentially more meaningful definition of an impostor - at least in the context of security-driven ASV applications - would be closest (most confusable) other speaker to a given target. We put forward a novel performance assessment framework to address both the inadequacy of the random-impostor evaluation model and the size limitation of evaluation corpora by addressing ASV security against closest impostors on arbitrarily large datasets. The framework allows one to make a prediction of the safety of given ASV technology, in its current state, for arbitrarily large speaker database size consisting of virtual (sampled) speakers. As a proof-of-concept, we analyze the performance of two state-of-the-art ASV systems, based on i-vector and x-vector speaker embeddings (as implemented in the popular Kaldi toolkit), on the recent VoxCeleb 1 & 2 corpora. We found that neither the i-vector or x-vector system is immune to increased false alarm rate at increased impostor database size.

Machine learning algorithms are extensively used to make increasingly more consequential decisions, so that achieving optimal predictive performance can no longer be the only focus. This paper explores intersectional fairness, that is fairness when intersections of multiple sensitive attributes -- such as race, age, nationality, etc. -- are considered. Previous research has mainly been focusing on fairness with respect to a single sensitive attribute, with intersectional fairness being comparatively less studied despite its critical importance for modern machine learning applications. We introduce intersectional fairness metrics by extending prior work, and provide different methodologies to audit discrimination in a given dataset or model outputs. Secondly, we develop novel post-processing techniques to mitigate any detected bias in a classification model. Our proposed methodology does not rely on any assumptions regarding the underlying model and aims at guaranteeing fairness while preserving good predictive performance. Finally, we give guidance on a practical implementation, showing how the proposed methods perform on a real-world dataset.

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Monte Carlo methods are a class of techniques for randomly sampling a probability distribution. There are many problem domains where describing or estimating the probability distribution is relatively straightforward, but calculating a desired quantity is intractable. This may be due to many reasons, such as the stochastic nature of the domain or an exponential number of random variables. Instead, a desired quantity can be approximated by using random sampling, referred to as Monte Carlo methods. These methods were initially used around the time that the first computers were created and remain pervasive through all fields of science and engineering, including artificial intelligence and machine learning.

Machine learning algorithms relying on deep neural networks recently allowed a great leap forward in artificial intelligence. Despite the popularity of their applications, the efficiency of these algorithms remains largely unexplained from a theoretical point of view. The mathematical description of learning problems involves very large collections of interacting random variables, difficult to handle analytically as well as numerically. This complexity is precisely the object of study of statistical physics. Its mission, originally pointed towards natural systems, is to understand how macroscopic behaviors arise from microscopic laws. Mean-field methods are one type of approximation strategy developed in this view. We review a selection of classical mean-field methods and recent progress relevant for inference in neural networks. In particular, we remind the principles of derivations of high-temperature expansions, the replica method and message passing algorithms, highlighting their equivalences and complementarities. We also provide references for past and current directions of research on neural networks relying on mean-field methods.

Thanks to its generality, RL has been widely studied in many areas, such as control theory, game theory, operations research, multi-agent systems, machine learning, artificial intelligence, and statistics [23]. In recent years, combining with deep learning, RL has demonstrated its great potential in addressing challenging practical control and optimization problems [17, 21]. Among all possible algorithms, the temporal difference (TD) learning has arguably become one of the most popular RL algorithms so far, which is further dominated by the celebrated TD(0) algorithm [22]. TD learning provides an iterative process to update an estimate of the so-termed value function v π(s) with respect to a given policy π based on temporally successive samples. Dealing with a finite state space, the classical version of the TD(0) algorithm adopts a tabular representation for v π(s), which stores entry-wise value estimates on a per state basis. J. Sun and Q. Yang are with the College of Control Science and Engineering, and the State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, China. G. Wang and G. B. Giannakis are with the Digital Technology Center and the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA. Z. Yang is with the Department of Mechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen, China.

For many applications it is critical to know the uncertainty of a neural network's predictions. While a variety of neural network parameter estimation methods have been proposed for uncertainty estimation, they have not been rigorously compared across uncertainty measures. We assess four of these parameter estimation methods to calibrate uncertainty estimation using four different uncertainty measures: entropy, mutual information, aleatoric uncertainty and epistemic uncertainty. We also evaluate their calibration using expected calibration error. We additionally propose a novel method of neural network parameter estimation called RECAST, which combines cosine annealing with warm restarts with Stochastic Gradient Langevin Dynamics, capturing more diverse parameter distributions. When benchmarked against mutilated data from MNIST, we show that RECAST is well-calibrated and when combined with predictive entropy and epistemic uncertainty it offers the best calibrated measure of uncertainty when compared to recent methods.