Bayesian inference is used extensively to infer and to quantify the uncertainty in a field of interest from a measurement of a related field when the two are linked by a physical model. Despite its many applications, Bayesian inference faces challenges when inferring fields that have discrete representations of large dimension, and/or have prior distributions that are difficult to represent mathematically. In this manuscript we consider the use of Generative Adversarial Networks (GANs) in addressing these challenges. A GAN is a type of deep neural network equipped with the ability to learn the distribution implied by multiple samples of a given field. Once trained on these samples, the generator component of a GAN maps the iid components of a low-dimensional latent vector to an approximation of the distribution of the field of interest. In this work we demonstrate how this approximate distribution may be used as a prior in a Bayesian update, and how it addresses the challenges associated with characterizing complex prior distributions and the large dimension of the inferred field. We demonstrate the efficacy of this approach by applying it to the problem of inferring and quantifying uncertainty in the initial temperature field in a heat conduction problem from a noisy measurement of the temperature at later time.

Decentralized consensus-based optimization is a general computational framework where a network of nodes cooperatively minimizes a sum of locally available cost functions via only local computation and communication. In this article, we survey recent advances on this topic, particularly focusing on decentralized, consensus-based, first-order gradient methods for large-scale stochastic optimization. The class of consensus-based stochastic optimization algorithms is communication-efficient, able to exploit data parallelism, robust in random and adversarial environments, and simple to implement, thus providing scalable solutions to a wide range of large-scale machine learning problems. We review different state-of-the-art decentralized stochastic optimization formulations, different variants of consensus-based procedures, and demonstrate how to obtain decentralized counterparts of centralized stochastic first-order methods. We provide several intuitive illustrations of the main technical ideas as well as applications of the algorithms in the context of decentralized training of machine learning models.

We present a new method for computing ASR word confidences that effectively mitigates ASR errors for diverse downstream applications, improves the word error rate of the 1-best result, and allows better comparison of scores across different models. We propose 1) a new method for modeling word confidence using a Heterogeneous Word Confusion Network (HWCN) that addresses some key flaws in conventional Word Confusion Networks, and 2) a new score calibration method for facilitating direct comparison of scores from different models. Using a bidirectional lattice recurrent neural network to compute the confidence scores of each word in the HWCN, we show that the word sequence with the best overall confidence is more accurate than the default 1-best result of the recognizer, and that the calibration method greatly improves the reliability of recognizer combination.

In this paper we present an incremental variant of the Twin Support Vector Machine (TWSVM) called Fuzzy Bounded Twin Support Vector Machine (FBTWSVM) to deal with large datasets and learning from data streams. We combine the TWSVM with a fuzzy membership function, so that each input has a different contribution to each hyperplane in a binary classifier. To solve the pair of quadratic programming problems (QPPs) we use a dual coordinate descent algorithm with a shrinking strategy, and to obtain a robust classification with a fast training we propose the use of a Fourier Gaussian approximation function with our linear FBTWSVM. Inspired by the shrinking technique, the incremental algorithm re-utilizes part of the training method with some heuristics, while the decremental procedure is based on a scored window. The FBTWSVM is also extended for multi-class problems by combining binary classifiers using a Directed Acyclic Graph (DAG) approach. Moreover, we analyzed the theoretical foundations properties of the proposed approach and its extension, and the experimental results on benchmark datasets indicate that the FBTWSVM has a fast training and retraining process while maintaining a robust classification performance.

Matrix-variate distributions can intuitively model the dependence structure of matrix-valued observations that arise in applications with multivariate time series, spatio-temporal or repeated measures. This paper develops an Expectation-Maximization algorithm for discriminant analysis and classification with matrix-variate $t$-distributions. The methodology shows promise on simulated datasets or when applied to the forensic matching of fractured surfaces or the classification of functional Magnetic Resonance, satellite or hand gestures images.

We study distributed algorithms for expected loss minimization where the datasets are large and have to be stored on different machines. Often we deal with minimizing the average of a set of convex functions where each function is the empirical risk of the corresponding part of the data. In the distributed setting where the individual data instances can be accessed only on the local machines, there would be a series of rounds of local computations followed by some communication among the machines. Since the cost of the communication is usually higher than the local machine computations, it is important to reduce it as much as possible. However, we should not allow this to make the computation too expensive to become a burden in practice. Using second-order methods could make the algorithms converge faster and decrease the amount of communication needed. There are some successful attempts in developing distributed second-order methods. Although these methods have shown fast convergence, their local computation is expensive and could enjoy more improvement for practical uses. In this study we modify an existing approach, DANE (Distributed Approximate NEwton), in order to improve the computational cost while maintaining the accuracy. We tackle this problem by using iterative methods for solving the local subproblems approximately instead of providing exact solutions for each round of communication. We study how using different iterative methods affect the behavior of the algorithm and try to provide an appropriate tradeoff between the amount of local computation and the required amount of communication. We demonstrate the practicality of our algorithm and compare it to the existing distributed gradient based methods such as SGD.

Stochastic (sub)gradient methods require step size schedule tuning to perform well in practice. Classical tuning strategies decay the step size polynomially and lead to optimal sublinear rates on (strongly) convex problems. An alternative schedule, popular in nonconvex optimization, is called \emph{geometric step decay} and proceeds by halving the step size after every few epochs. In recent work, geometric step decay was shown to improve exponentially upon classical sublinear rates for the class of \emph{sharp} convex functions. In this work, we ask whether geometric step decay similarly improves stochastic algorithms for the class of sharp nonconvex problems. Such losses feature in modern statistical recovery problems and lead to a new challenge not present in the convex setting: the region of convergence is local, so one must bound the probability of escape. Our main result shows that for a large class of stochastic, sharp, nonsmooth, and nonconvex problems a geometric step decay schedule endows well-known algorithms with a local linear rate of convergence to global minimizers. This guarantee applies to the stochastic projected subgradient, proximal point, and prox-linear algorithms. As an application of our main result, we analyze two statistical recovery tasks---phase retrieval and blind deconvolution---and match the best known guarantees under Gaussian measurement models and establish new guarantees under heavy-tailed distributions.

Accurately forecasting urban development and its environmental and climate impacts critically depends on realistic models of the spatial structure of the built environment, and of its dependence on key factors such as population and economic development. Scenario simulation and sensitivity analysis, i.e., predicting how changes in underlying factors at a given location affect urbanization outcomes at other locations, is currently not achievable at a large scale with traditional urban growth models, which are either too simplistic, or depend on detailed locally-collected socioeconomic data that is not available in most places. Here we develop a framework to estimate, purely from globally-available remote-sensing data and without parametric assumptions, the spatial sensitivity of the (\textit{static}) rate of change of urban sprawl to key macroeconomic development indicators. We formulate this spatial regression problem as an image-to-image translation task using conditional generative adversarial networks (GANs), where the gradients necessary for comparative static analysis are provided by the backpropagation algorithm used to train the model. This framework allows to naturally incorporate physical constraints, e.g., the inability to build over water bodies. To validate the spatial structure of model-generated built environment distributions, we use spatial statistics commonly used in urban form analysis. We apply our method to a novel dataset comprising of layers on the built environment, nightlighs measurements (a proxy for economic development and energy use), and population density for the world's most populous 15,000 cities.

Today, despite decades of developments in medicine and the growing interest in precision healthcare, vast majority of diagnoses happen once patients begin to show noticeable signs of illness. Early indication and detection of diseases, however, can provide patients and carers with the chance of early intervention, better disease management, and efficient allocation of healthcare resources. The latest developments in machine learning (more specifically, deep learning) provides a great opportunity to address this unmet need. In this study, we introduce BEHRT: A deep neural sequence transduction model for EHR (electronic health records), capable of multitask prediction and disease trajectory mapping. When trained and evaluated on the data from nearly 1.6 million individuals, BEHRT shows a striking absolute improvement of 8.0-10.8%, in terms of Average Precision Score, compared to the existing state-of-the-art deep EHR models (in terms of average precision, when predicting for the onset of 301 conditions). In addition to its superior prediction power, BEHRT provides a personalised view of disease trajectories through its attention mechanism; its flexible architecture enables it to incorporate multiple heterogeneous concepts (e.g., diagnosis, medication, measurements, and more) to improve the accuracy of its predictions; and its (pre-)training results in disease and patient representations that can help us get a step closer to interpretable predictions.

The reservoir computing paradigm is employed to classify heartbeat anomalies online based on electrocardiogram signals. Inspired by the principles of information processing in the brain, reservoir computing provides a framework to design, train, and analyze recurrent neural networks (RNNs) for processing time-dependent information. Due to its computational efficiency and the fact that training amounts to a simple linear regression, this supervised learning algorithm has been variously considered as a strategy to implement useful computations not only on digital computers but also on emerging unconventional hardware platforms such as neuromorphic microchips. Here, this biological-inspired learning framework is exploited to devise an accurate patient-adaptive model that has the potential to be integrated into wearable cardiac events monitoring devices. The proposed patient-customized model was trained and tested on ECG recordings selected from the MIT-BIH arrhythmia database. Restrictive inclusion criteria were used to conduct the study only on ECGs including, at least, two classes of heartbeats with highly unequal number of instances. The results of extensive simulations showed this model not only provides accurate, cheap and fast patient-customized heartbeat classifier but also circumvents the problem of "imbalanced classes" when the readout weights are trained using weighted ridge-regression.