Among existing uncertainty estimation approaches, Dirichlet Prior Network (DPN) distinctly models different predictive uncertainty types. However, for in-domain examples with high data uncertainties among multiple classes, even a DPN model often produces indistinguishable representations from the out-of-distribution (OOD) examples, compromising their OOD detection performance. We address this shortcoming by proposing a novel loss function for DPN to maximize the \textit{representation gap} between in-domain and OOD examples. Experimental results demonstrate that our proposed approach consistently improves OOD detection performance.

Attention modules, as simple and effective tools, have not only enabled deep neural networks to achieve state-of-the-art results in many domains, but also enhanced their interpretability. Most current models use deterministic attention modules due to their simplicity and ease of optimization. Stochastic counterparts, on the other hand, are less popular despite their potential benefits. The main reason is that stochastic attention often introduces optimization issues or requires significant model changes. In this paper, we propose a scalable stochastic version of attention that is easy to implement and optimize. We construct simplex-constrained attention distributions by normalizing reparameterizable distributions, making the training process differentiable. We learn their parameters in a Bayesian framework where a data-dependent prior is introduced for regularization. We apply the proposed stochastic attention modules to various attention-based models, with applications to graph node classification, visual question answering, image captioning, machine translation, and language understanding. Our experiments show the proposed method brings consistent improvements over the corresponding baselines.

Understanding systems by forward and inverse modeling is a recurrent topic of research in many domains of science and engineering. In this context, Monte Carlo methods have been widely used as powerful tools for numerical inference and optimization. They require the choice of a suitable proposal density that is crucial for their performance. For this reason, several adaptive importance sampling (AIS) schemes have been proposed in the literature. We here present an AIS framework called Regression-based Adaptive Deep Importance Sampling (RADIS). In RADIS, the key idea is the adaptive construction via regression of a non-parametric proposal density (i.e., an emulator), which mimics the posterior distribution and hence minimizes the mismatch between proposal and target densities. RADIS is based on a deep architecture of two (or more) nested IS schemes, in order to draw samples from the constructed emulator. The algorithm is highly efficient since employs the posterior approximation as proposal density, which can be improved adding more support points. As a consequence, RADIS asymptotically converges to an exact sampler under mild conditions. Additionally, the emulator produced by RADIS can be in turn used as a cheap surrogate model for further studies. We introduce two specific RADIS implementations that use Gaussian Processes (GPs) and Nearest Neighbors (NN) for constructing the emulator. Several numerical experiments and comparisons show the benefits of the proposed schemes. A real-world application in remote sensing model inversion and emulation confirms the validity of the approach.

Non-negative matrix factorization (NMF) has become a well-established class of methods for the analysis of non-negative data. In particular, a lot of effort has been devoted to probabilistic NMF, namely estimation or inference tasks in probabilistic models describing the data, based for example on Poisson or exponential likelihoods. When dealing with time series data, several works have proposed to model the evolution of the activation coefficients as a non-negative Markov chain, most of the time in relation with the Gamma distribution, giving rise to so-called temporal NMF models. In this paper, we review four Gamma Markov chains of the NMF literature, and show that they all share the same drawback: the absence of a well-defined stationary distribution. We then introduce a fifth process, an overlooked model of the time series literature named BGAR(1), which overcomes this limitation. These temporal NMF models are then compared in a MAP framework on a prediction task, in the context of the Poisson likelihood.

Artificial intelligence (AI), machine learning (ML), and predictive analytics (PA) are current buzzwords eclipsing the tech industry hype curve. At this point, most tech savvy people are tired of hearing how these techniques will save the day. Let's eliminate some of the hype and paint a more realistic picture of what's happening with these technologies. All three are surprisingly old concepts. Predictive analytics can trace its origins back to Thomas Bayes, who laid the foundation to Bayesian probability theory in 1736. Nothing new here, except within the last 50 years, computers have made it much easier to work with the math.

We investigate the problem of reliably assessing group fairness when labeled examples are few but unlabeled examples are plentiful. We propose a general Bayesian framework that can augment labeled data with unlabeled data to produce more accurate and lower-variance estimates compared to methods based on labeled data alone. Our approach estimates calibrated scores for unlabeled examples in each group using a hierarchical latent variable model conditioned on labeled examples. This in turn allows for inference of posterior distributions with associated notions of uncertainty for a variety of group fairness metrics. We demonstrate that our approach leads to significant and consistent reductions in estimation error across multiple well-known fairness datasets, sensitive attributes, and predictive models. The results show the benefits of using both unlabeled data and Bayesian inference in terms of assessing whether a prediction model is fair or not.

A multiple-view clustering method is a powerful analytical tool for high-dimensional data, such as functional magnetic resonance imaging (fMRI). It can identify clustering patterns of subjects depending on their functional connectivity in specific brain areas. However, when one applies an existing method to fMRI data, there is a need to simplify the data structure, independently dealing with elements in a functional connectivity matrix, that is, a correlation matrix. In general, elements in a correlation matrix are closely associated. Hence, such a simplification may distort the clustering results. To overcome this problem, we propose a novel multiple-view clustering method based on the Wishart mixture model, which preserves the correlation matrix structure. The uniqueness of this method is that the multiple-view clustering of subjects is based on particular networks of nodes (or regions of interest (ROIs) in fMRI), optimized in a data-driven manner. Hence, it can identify multiple underlying pairs of associations between a subject cluster solution and a ROI network. The key assumption of the method is independence among networks, which is effectively addressed by whitening correlation matrices. We applied the proposed method to synthetic and fMRI data, demonstrating the usefulness and power of the proposed method.

We propose an adaptively weighted stochastic gradient Langevin dynamics algorithm (SGLD), so-called contour stochastic gradient Langevin dynamics (CSGLD), for Bayesian learning in big data statistics. The proposed algorithm is essentially a \emph{scalable dynamic importance sampler}, which automatically \emph{flattens} the target distribution such that the simulation for a multi-modal distribution can be greatly facilitated. Theoretically, we prove a stability condition and establish the asymptotic convergence of the self-adapting parameter to a {\it unique fixed-point}, regardless of the non-convexity of the original energy function; we also present an error analysis for the weighted averaging estimators. Empirically, the CSGLD algorithm is tested on multiple benchmark datasets including CIFAR10 and CIFAR100. The numerical results indicate its superiority over the existing state-of-the-art algorithms in training deep neural networks.

Many real-life problems are represented as a black-box, i.e., the internal workings are inaccessible or a closed-form mathematical expression of the likelihood function cannot be defined. For continuous random variables likelihood-free inference problems can be solved by a group of methods under the name of Approximate Bayesian Computation (ABC). However, a similar approach for discrete random variables is yet to be formulated. Here, we aim to fill this research gap. We propose to use a population-based MCMC ABC framework. Further, we present a valid Markov kernel, and propose a new kernel that is inspired by Differential Evolution. We assess the proposed approach on a problem with the known likelihood function, namely, discovering the underlying diseases based on a QMR-DT Network, and three likelihood-free inference problems: (i) the QMR-DT Network with the unknown likelihood function, (ii) learning binary neural network, and (iii) Neural Architecture Search. The obtained results indicate the high potential of the proposed framework and the superiority of the new Markov kernel.

In machine learning and computer vision, optimal transport has had significant success in learning generative models and defining metric distances between structured and stochastic data objects, that can be cast as probability measures. The key element of optimal transport is the so called lifting of an \emph{exact} cost (distance) function, defined on the sample space, to a cost (distance) between probability measures over the sample space. However, in many real life applications the cost is \emph{stochastic}: e.g., the unpredictable traffic flow affects the cost of transportation between a factory and an outlet. To take this stochasticity into account, we introduce a Bayesian framework for inferring the optimal transport plan distribution induced by the stochastic cost, allowing for a principled way to include prior information and to model the induced stochasticity on the transport plans. Additionally, we tailor an HMC method to sample from the resulting transport plan posterior distribution.