A Bayesian neural network (BNN) refers to extending standard networks with posterior inference. Standard NN training via optimization is (from a probabilistic perspective) equivalent to maximum likelihood estimation (MLE) for the weights. For many reasons this is unsatisfactory. One reason is that it lacks proper theoretical justification from a probabilistic perspective: why maximum likelihood? Using MLE ignores any uncertainty that we may have in the proper weight values.

Artificial Intelligence has become a buzzword for investors of late, many of whom recognize its enormous potential to become the most game-changing technology since the industrial revolution. Indeed, the projected impact of AI is likely to be greater than all prior tech trends combined, and savvy investors would be wise not to miss out. From an investor's point of view, you can divide the AI sector into a few major sub-sectors: infrastructure, algorithms, platforms, and applications. The infrastructure segment includes technologies and companies that provide the underpinnings enabling AI: machine learning, deep learning, natural language processing, and computer vision, including cloud infrastructure, specialized semiconductors, large-volume storage devices, low-latency databases, edge-based computing elements, and more. On the algorithm side, one would primarily count neural nets, classification, and clustering algorithms, good old Bayesian networks, and hidden Markov models.

Matrix decomposition is a popular and fundamental approach in machine learning and data mining. It has been successfully applied into various fields. Most matrix decomposition methods focus on decomposing a data matrix from one single source. However, it is common that data are from different sources with heterogeneous noise. A few of matrix decomposition methods have been extended for such multi-view data integration and pattern discovery. While only few methods were designed to consider the heterogeneity of noise in such multi-view data for data integration explicitly. To this end, we propose a joint matrix decomposition framework (BJMD), which models the heterogeneity of noise by Gaussian distribution in a Bayesian framework. We develop two algorithms to solve this model: one is a variational Bayesian inference algorithm, which makes full use of the posterior distribution; and another is a maximum a posterior algorithm, which is more scalable and can be easily paralleled. Extensive experiments on synthetic and real-world datasets demonstrate that BJMD considering the heterogeneity of noise is superior or competitive to the state-of-the-art methods.

Direct acoustics-to-word (A2W) models in the end-to-end paradigm have received increasing attention compared to conventional sub-word based automatic speech recognition models using phones, characters, or context-dependent hidden Markov model states. This is because A2W models recognize words from speech without any decoder, pronunciation lexicon, or externally-trained language model, making training and decoding with such models simple. Prior work has shown that A2W models require orders of magnitude more training data in order to perform comparably to conventional models. Our work also showed this accuracy gap when using the English Switchboard-Fisher data set. This paper describes a recipe to train an A2W model that closes this gap and is at-par with state-of-the-art sub-word based models. We achieve a word error rate of 8.8%/13.9% on the Hub5-2000 Switchboard/CallHome test sets without any decoder or language model. We find that model initialization, training data order, and regularization have the most impact on the A2W model performance. Next, we present a joint word-character A2W model that learns to first spell the word and then recognize it. This model provides a rich output to the user instead of simple word hypotheses, making it especially useful in the case of words unseen or rarely-seen during training.

The rising interest in pattern recognition and data analytics has spurred the development of innovative machine learning algorithms and tools. However, as each algorithm has its strengths and limitations, one is motivated to judiciously fuse multiple algorithms in order to find the "best" performing one, for a given dataset. Ensemble learning aims at such high-performance meta-algorithm, by combining the outputs from multiple algorithms. The present work introduces a blind scheme for learning from ensembles of classifiers, using a moment matching method that leverages joint tensor and matrix factorization. Blind refers to the combiner who has no knowledge of the ground-truth labels that each classifier has been trained on. A rigorous performance analysis is derived and the proposed scheme is evaluated on synthetic and real datasets.

Deep learning (DL), a new-generation artificial neural network research, has made profound strides in recent years. This review paper is intended to provide water resources scientists with a simple technical overview, trans-disciplinary progress update, and potentially inspirations about DL. Effective architectures, more accessible data, advances in regularization, and new computing power enabled the success of DL. A trans-disciplinary review reveals that DL is rapidly transforming myriad scientific disciplines including high-energy physics, astronomy, chemistry, genomics and remote sensing, where systematic DL toolkits, innovative customizations, and sub-disciplines have emerged. However, with a few exceptions, its adoption in hydrology has so far been gradual. The literature suggests that novel regularization techniques can effectively prevent high-capacity deep networks from overfitting. As a result, in most scientific disciplines, DL models demonstrated superior predictive and generalization performance to conventional methods. Meanwhile, less noticed is that DL may also serve as a scientific exploratory tool. A new area termed "AI neuroscience", has been born. This budding sub-discipline is accumulating a significant body of work, e.g., distilling knowledge obtained in DL networks to interpretable models, attributing decisions to inputs via back-propagation of relevance, or visualization of activations. These methods are designed to interpret the decision process of deep networks and derive insights. While scientists so far have mostly been using customized, ad-hoc methods for interpretation, vast opportunities await for DL to propel advancement in water science.

Various applications involve assigning discrete label values to a collection of objects based on some pairwise noisy data. Due to the discrete---and hence nonconvex---structure of the problem, computing the optimal assignment (e.g.~maximum likelihood assignment) becomes intractable at first sight. This paper makes progress towards efficient computation by focusing on a concrete joint alignment problem---that is, the problem of recovering $n$ discrete variables $x_i \in \{1,\cdots, m\}$, $1\leq i\leq n$ given noisy observations of their modulo differences $\{x_i - x_j~\mathsf{mod}~m\}$. We propose a low-complexity and model-free procedure, which operates in a lifted space by representing distinct label values in orthogonal directions, and which attempts to optimize quadratic functions over hypercubes. Starting with a first guess computed via a spectral method, the algorithm successively refines the iterates via projected power iterations. We prove that for a broad class of statistical models, the proposed projected power method makes no error---and hence converges to the maximum likelihood estimate---in a suitable regime. Numerical experiments have been carried out on both synthetic and real data to demonstrate the practicality of our algorithm. We expect this algorithmic framework to be effective for a broad range of discrete assignment problems.

We present new excess risk bounds for general unbounded loss functions including log loss and squared loss, where the distribution of the losses may be heavy-tailed. The bounds hold for general estimators, but they are optimized when applied to $\eta$-generalized Bayesian, MDL, and ERM estimators. When applied with log loss, the bounds imply convergence rates for generalized Bayesian inference under misspecification in terms of a generalization of the Hellinger metric as long as the learning rate $\eta$ is set correctly. For general loss functions, our bounds rely on two separate conditions: the $v$-GRIP (generalized reversed information projection) conditions, which control the lower tail of the excess loss; and the newly introduced witness condition, which controls the upper tail. The parameter $v$ in the $v$-GRIP conditions determines the achievable rate and is akin to the exponent in the well-known Tsybakov margin condition and the Bernstein condition for bounded losses, which the $v$-GRIP conditions generalize; favorable $v$ in combination with small model complexity leads to $\tilde{O}(1/n)$ rates. The witness condition allows us to connect the excess risk to an 'annealed' version thereof, by which we generalize several previous results connecting Hellinger and R\'enyi divergence to KL divergence.

Graphical models provide powerful tools to uncover complicated patterns in multivariate data and are commonly used in Bayesian statistics and machine learning. In this paper, we introduce an R package BDgraph which performs Bayesian structure learning for general undirected graphical models with either continuous or discrete variables. The package efficiently implements recent improvements in the Bayesian literature. To speed up computations, the computationally intensive tasks have been implemented in C++ and interfaced with R. In addition, the package contains several functions for simulation and visualization, as well as two multivariate datasets taken from the literature and are used to describe the package capabilities. The paper includes a brief overview of the statistical methods which have been implemented in the package. The main body of the paper explains how to use the package. Furthermore, we illustrate the package's functionality in both real and artificial examples, as well as in an extensive simulation study.

In this paper, we propose a new algorithm for learning general latent-variable probabilistic graphical models using the techniques of predictive state representation, instrumental variable regression, and reproducing-kernel Hilbert space embeddings of distributions. Under this new learning framework, we first convert latent-variable graphical models into corresponding latent-variable junction trees, and then reduce the hard parameter learning problem into a pipeline of supervised learning problems, whose results will then be used to perform predictive belief propagation over the latent junction tree during the actual inference procedure. We then give proofs of our algorithm's correctness, and demonstrate its good performance in experiments on one synthetic dataset and two real-world tasks from computational biology and computer vision -- classifying DNA splice junctions and recognizing human actions in videos.