Efficient exploration is an unsolved problem in Reinforcement Learning. We introduce Model-Based Active eXploration (MAX), an algorithm that actively explores the environment. It minimizes data required to comprehensively model the environment by planning to observe novel events, instead of merely reacting to novelty encountered by chance. Non-stationarity induced by traditional exploration bonus techniques is avoided by constructing fresh exploration policies only at time of action. In semi-random toy environments where directed exploration is critical to make progress, our algorithm is at least an order of magnitude more efficient than strong baselines.

A theoretical performance analysis of the graph neural network (GNN) is presented. For classification tasks, the neural network approach has the advantage in terms of flexibility that it can be employed in a data-driven manner, whereas Bayesian inference requires the assumption of a specific model. A fundamental question is then whether GNN has a high accuracy in addition to this flexibility. Moreover, whether the achieved performance is predominately a result of the backpropagation or the architecture itself is a matter of considerable interest. To gain a better insight into these questions, a mean-field theory of a minimal GNN architecture is developed for the graph partitioning problem. This demonstrates a good agreement with numerical experiments.

The Expectation-Maximization (EM) algorithm for mixture models often results in slow or invalid convergence. The popular convergence proof affirms that the likelihood increases with Q; Q is increasing in the M -step and non-decreasing in the E-step. The author found that (1) Q may and should decrease in some E-steps; (2) The Shannon channel from the E-step is improper and hence the expectation is improper. The author proposed the CM-EM algorithm (CM means Channel's Matching), which adds a step to optimize the mixture ratios for the proper Shannon channel and maximizes G, average log-normalized-likelihood, in the M-step. Neal and Hinton's Maximization-Maximization (MM) algorithm use F instead of Q to speed the convergence. Maximizing G is similar to maximizing F. The new convergence proof is similar to Beal's proof with the variational method. It first proves that the minimum relative entropy equals the minimum R-G (R is mutual information), then uses variational and iterative methods that Shannon et al. use for rate-distortion functions to prove the global convergence. Some examples show that Q and F should and may decrease in some E-steps. For the same example, the EM, MM, and CM-EM algorithms need about 36, 18, and 9 iterations respectively.

However Deep neural networks recently have achieved impressive results for different tasks, they suffer from poor uncertainty prediction. Temperature Scaling (TS) is an efficient post-processing method for calibrating DNNs toward to have more accurate uncertainty prediction. TS relies on a single parameter T which softens the logit layer of a DNN and the optimal value of it is found by minimizing on Negative Log Likelihood (NLL) loss function. In this paper, we discuss about weakness of NLL loss function, especially for DNNs with high accuracy and propose a new loss function called Attended-NLL which can improve TS calibration ability significantly.

Development of interpretable machine learning models for clinical healthcare applications has the potential of changing the way we understand, treat, and ultimately cure, diseases and disorders in many areas of medicine. Interpretable ML models for clinical healthcare can serve not only as sources of predictions and estimates, but also as discovery tools for clinicians and researchers to reveal new knowledge from the data. High dimensionality of patient information (e.g., phenotype, genotype, and medical history), lack of objective measurements, and the heterogeneity in patient populations often create significant challenges in developing interpretable machine learning models for clinical psychiatry in practice. In this paper we take a step towards the development of such interpretable models. First, by developing a novel categorical rule mining method based on Multivariate Correspondence Analysis (MCA) capable of handling datasets with large numbers of feature categories, and second, by applying this method to build a transdiagnostic Bayesian Rule List model to screen for neuropsychiatric disorders using Consortium for Neuropsychiatric Phenomics dataset. We show that our method is not only at least 100 times faster than state-of-the-art rule mining techniques for datasets with 50 features, but also provides interpretability and comparable prediction accuracy across several benchmark datasets.

Expectation Maximization (EM) is among the most popular algorithms for maximum likelihood estimation, but it is generally only guaranteed to find its stationary points of the log-likelihood objective. The goal of this article is to present theoretical and empirical evidence that over-parameterization can help EM avoid spurious local optima in the log-likelihood. We consider the problem of estimating the mean vectors of a Gaussian mixture model in a scenario where the mixing weights are known. Our study shows that the global behavior of EM, when one uses an over-parameterized model in which the mixing weights are treated as unknown, is better than that when one uses the (correct) model with the mixing weights fixed to the known values. For symmetric Gaussians mixtures with two components, we prove that introducing the (statistically redundant) weight parameters enables EM to find the global maximizer of the log-likelihood starting from almost any initial mean parameters, whereas EM without this over-parameterization may very often fail. For other Gaussian mixtures, we provide empirical evidence that shows similar behavior. Our results corroborate the value of over-parameterization in solving non-convex optimization problems, previously observed in other domains.

We develop deep Poisson-gamma dynamical systems (DPGDS) to model sequentially observed multivariate count data, improving previously proposed models by not only mining deep hierarchical latent structure from the data, but also capturing both first-order and long-range temporal dependencies. Using sophisticated but simple-to-implement data augmentation techniques, we derived closed-form Gibbs sampling update equations by first backward and upward propagating auxiliary latent counts, and then forward and downward sampling latent variables. Moreover, we develop stochastic gradient MCMC inference that is scalable to very long multivariate count time series. Experiments on both synthetic and a variety of real-world data demonstrate that the proposed model not only has excellent predictive performance, but also provides highly interpretable multilayer latent structure to represent hierarchical and temporal information propagation.

It is somewhat surprising that among all the high-flying buzzwords of machine learning, we don't hear much about the one phrase which fuses some of the core concepts of statistical learning, information theory, and natural philosophy into a single three-word-combo. Moreover, it is not just an obscure and pedantic phrase meant for machine learning (ML) Ph.Ds and theoreticians. It has a precise and easily accessible meaning for anyone interested to explore, and a practical pay-off for the practitioners of ML and data science. I am talking about Minimum Description Length. Let's peel the layers off and see how useful it is… We start with (not chronologically) with Reverend Thomas Bayes, who by the way, never published his idea about how to do statistical inference, but was later immortalized by the eponymous theorem. It was the second half of the 18th century, and there was no branch of mathematical sciences called "Probability Theory".

We define a new method to estimate centroid for text classification based on the symmetric KL-divergence between the distribution of words in training documents and their class centroids. Experiments on several standard data sets indicate that the new method achieves substantial improvements over the traditional classifiers.

Bayesian inference and Gaussian processes are widely used in applications ranging from robotics and control to biological systems. Many of these applications are safety-critical and require a characterization of the uncertainty associated with the learning model and formal guarantees on its predictions. In this paper we define a robustness measure for Bayesian inference against input perturbations, given by the probability that, for a test point and a compact set in the input space containing the test point, the prediction of the learning model will remain $\delta-$close for all the points in the set, for $\delta>0.$ Such measures can be used to provide formal guarantees for the absence of adversarial examples. By employing the theory of Gaussian processes, we derive tight upper bounds on the resulting robustness by utilising the Borell-TIS inequality, and propose algorithms for their computation. We evaluate our techniques on two examples, a GP regression problem and a fully-connected deep neural network, where we rely on weak convergence to GPs to study adversarial examples on the MNIST dataset.