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.

We explore a collaborative multi-agent reinforcement learning setting where a team of agents attempts to solve cooperative tasks in partially-observable environments. In this scenario, learning an effective communication protocol is key. We propose a communication architecture that allows for targeted communication, where agents learn both what messages to send and who to send them to, solely from downstream task-specific reward without any communication supervision. Additionally, we introduce a multi-stage communication approach where the agents co-ordinate via multiple rounds of communication before taking actions in the environment. We evaluate our approach on a diverse set of cooperative multi-agent tasks, of varying difficulties, with varying number of agents, in a variety of environments ranging from 2D grid layouts of shapes and simulated traffic junctions to complex 3D indoor environments. We demonstrate the benefits of targeted as well as multi-stage communication. Moreover, we show that the targeted communication strategies learned by agents are both interpretable and intuitive.

Learning of RBMs using standard algorithms such as CD(k) involves gradient descent on negative log-likelihood. One of the terms in the gradient, which is expectation of visible and hidden units is intractable and is obtained through an MCMC estimate. In this work we show that the Hessian of the log-likelihood can be written in terms of covariances of hidden and visible units and hence all elements of the Hessian can also be estimated using the same MCMC samples with minimal extra computational costs. Since inverting the Hessian may be computationally expensive, we propose an algorithm that uses inverse of the diagonal approximation of the Hessian. This essentially results in parameter-specific adaptive learning rates for the gradient descent process. We show that this algorithm improves the efficiency of learning RBMs compared to state-of-art methods. Specifically we show that using the inverse of diagonal approximation of Hessian in the stochastic DC (difference of convex functions) program approach results in very efficient learning of RBMs. We use different evaluation metrics to test the probability distribution learnt by the RBM along with the traditional criterion of average test and train log-likelihood.

We present a statistical-modelling method for piano reduction, i.e. converting an ensemble score into piano scores, that can control performance difficulty. While previous studies have focused on describing the condition for playable piano scores, it depends on player's skill and can change continuously with the tempo. We thus computationally quantify performance difficulty as well as musical fidelity to the original score, and formulate the problem as optimization of musical fidelity under constraints on difficulty values. First, performance difficulty measures are developed by means of probabilistic generative models for piano scores and the relation to the rate of performance errors is studied. Second, to describe musical fidelity, we construct a probabilistic model integrating a prior piano-score model and a model representing how ensemble scores are likely to be edited. An iterative optimization algorithm for piano reduction is developed based on statistical inference of the model. We confirm the effect of the iterative procedure; we find that subjective difficulty and musical fidelity monotonically increase with controlled difficulty values; and we show that incorporating sequential dependence of pitches and fingering motion in the piano-score model improves the quality of reduction scores in high-difficulty cases.

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.

Disease progression models are instrumental in predicting individual-level health trajectories and understanding disease dynamics. Existing models are capable of providing either accurate predictions of patients' prognoses or clinically interpretable representations of disease pathophysiology, but not both. In this paper, we develop the phased attentive state space (PASS) model of disease progression, a deep probabilistic model that captures complex representations for disease progression while maintaining clinical interpretability. Unlike Markovian state space models which assume memoryless dynamics, PASS uses an attention mechanism to induce "memoryful" state transitions, whereby repeatedly updated attention weights are used to focus on past state realizations that best predict future states. This gives rise to complex, non-stationary state dynamics that remain interpretable through the generated attention weights, which designate the relationships between the realized state variables for individual patients. PASS uses phased LSTM units (with time gates controlled by parametrized oscillations) to generate the attention weights in continuous time, which enables handling irregularly-sampled and potentially missing medical observations. Experiments on data from a real-world cohort of patients show that PASS successfully balances the tradeoff between accuracy and interpretability: it demonstrates superior predictive accuracy and learns insightful individual-level representations of disease progression.