Abstract--Bayesian networks are powerful statistical models to study the probabilistic relationships among set random variables with major applications in disease modeling and prediction. Here, we propose a continuous time Bayesian network with conditional dependencies, represented as Poisson regression, to model the impact of exogenous variables on the conditional dependencies of the network. We also propose an adaptive regularization method with an intuitive early stopping feature based on density based clustering for efficient learning of the structure and parameters of the proposed network. Using a dataset of patients with multiple chronic conditions extracted from electronic health records of the Department of Veterans Affairs we compare the performance of the proposed approach with some of the existing methods in the literature for both short-term (one-year ahead) and long-term (multi-year ahead) predictions. The proposed approach provides a sparse intuitive representation of the complex functional relationships between multiple chronic conditions. It also provides the capability of analyzing multiple disease trajectories over time given any combination of prior conditions.

The effective representation, processing, analysis, and visualization of large-scale structured data, especially those related to complex domains such as networks and graphs, are one of the key questions in modern machine learning. Graph signal processing (GSP), a vibrant branch of signal processing models and algorithms that aims at handling data supported on graphs, opens new paths of research to address this challenge. In this article, we review a few important contributions made by GSP concepts and tools, such as graph filters and transforms, to the development of novel machine learning algorithms. In particular, our discussion focuses on the following three aspects: exploiting data structure and relational priors, improving data and computational efficiency, and enhancing model interpretability. Furthermore, we provide new perspectives on future development of GSP techniques that may serve as a bridge between applied mathematics and signal processing on one side, and machine learning and network science on the other. Cross-fertilization across these different disciplines may help unlock the numerous challenges of complex data analysis in the modern age.

In mobile health (mHealth) smart devices deliver behavioral treatments repeatedly over time to a user with the goal of helping the user adopt and maintain healthy behaviors. Reinforcement learning appears ideal for learning how to optimally make these sequential treatment decisions. However, significant challenges must be overcome before reinforcement learning can be effectively deployed in a mobile healthcare setting. In this work we are concerned with the following challenges: 1) individuals who are in the same context can exhibit differential response to treatments 2) only a limited amount of data is available for learning on any one individual, and 3) non-stationary responses to treatment. To address these challenges we generalize Thompson-Sampling bandit algorithms to develop IntelligentPooling. IntelligentPooling learns personalized treatment policies thus addressing challenge one. To address the second challenge, IntelligentPooling updates each user's degree of personalization while making use of available data on other users to speed up learning. Lastly, IntelligentPooling allows responsivity to vary as a function of a user's time since beginning treatment, thus addressing challenge three. We show that IntelligentPooling achieves an average of 26% lower regret than state-of-the-art. We demonstrate the promise of this approach and its ability to learn from even a small group of users in a live clinical trial.

In high-dimensions, the prior tails can have a significant effect on both posterior computation and asymptotic concentration rates. To achieve optimal rates while keeping the posterior computations relatively simple, an empirical Bayes approach has recently been proposed, featuring thin-tailed conjugate priors with data-driven centers. While conjugate priors ease some of the computational burden, Markov chain Monte Carlo methods are still needed, which can be expensive when dimension is high. In this paper, we develop a variational approximation to the empirical Bayes posterior that is fast to compute and retains the optimal concentration rate properties of the original. In simulations, our method is shown to have superior performance compared to existing variational approximations in the literature across a wide range of high-dimensional settings.

Solutions to most complex tasks can be decomposed into simpler, intermediate skills, reusable across wider ranges of problems. We follow this concept and introduce Hindsight Off-policy Options (HO2), a new algorithm for efficient and robust option learning. The algorithm relies on critic-weighted maximum likelihood estimation and an efficient dynamic programming inference procedure over off-policy trajectories. We can backpropagate through the inference procedure through time and the policy components for every time-step, making it possible to train all component's parameters off-policy, independently of the data-generating behavior policy. Experimentally, we demonstrate that HO2 outperforms competitive baselines and solves demanding robot stacking and ball-in-cup tasks from raw pixel inputs in simulation. We further compare autoregressive option policies with simple mixture policies, providing insights into the relative impact of two types of abstractions common in the options framework: action abstraction and temporal abstraction. Finally, we illustrate challenges caused by stale data in off-policy options learning and provide effective solutions.

Systems that are based on recursive Bayesian updates for classification limit the cost of evidence collection through certain stopping/termination criteria and accordingly enforce decision making. Conventionally, two termination criteria based on pre-defined thresholds over (i) the maximum of the state posterior distribution; and (ii) the state posterior uncertainty are commonly used. In this paper, we propose a geometric interpretation over the state posterior progression and accordingly we provide a point-by-point analysis over the disadvantages of using such conventional termination criteria. For example, through the proposed geometric interpretation we show that confidence thresholds defined over maximum of the state posteriors suffer from stiffness that results in unnecessary evidence collection whereas uncertainty based thresholding methods are fragile to number of categories and terminate prematurely if some state candidates are already discovered to be unfavorable. Moreover, both types of termination methods neglect the evolution of posterior updates. We then propose a new stopping/termination criterion with a geometrical insight to overcome the limitations of these conventional methods and provide a comparison in terms of decision accuracy and speed. We validate our claims using simulations and using real experimental data obtained through a brain computer interfaced typing system.

We introduce a class of acquisition functions for sample selection that leads to faster convergence in applications related to Bayesian experimental design and uncertainty quantification. The approach follows the paradigm of active learning, whereby existing samples of a black-box function are utilized to optimize the next most informative sample. The proposed method aims to take advantage of the fact that some input directions of the black-box function have a larger impact on the output than others, which is important especially for systems exhibiting rare and extreme events. The acquisition functions introduced in this work leverage the properties of the likelihood ratio, a quantity that acts as a probabilistic sampling weight and guides the active-learning algorithm towards regions of the input space that are deemed most relevant. We demonstrate superiority of the proposed approach in the uncertainty quantification of a hydrological system as well as the probabilistic quantification of rare events in dynamical systems and the identification of their precursors.

We introduce a new incremental preference elicitation procedure able to deal with noisy responses of a Decision Maker (DM). The originality of the contribution is to propose a Bayesian approach for determining a preferred solution in a multiobjective decision problem involving a combinatorial set of alternatives. We assume that the preferences of the DM are represented by an aggregation function whose parameters are unknown and that the uncertainty about them is represented by a density function on the parameter space. Pairwise comparison queries are used to reduce this uncertainty (by Bayesian revision). The query selection strategy is based on the solution of a mixed integer linear program with a combinatorial set of variables and constraints, which requires to use columns and constraints generation methods. Numerical tests are provided to show the practicability of the approach.

This paper applies probabilistic model checking techniques for discrete Markov chains to inference in Bayesian networks. We present a simple translation from Bayesian networks into tree-like Markov chains such that inference can be reduced to computing reachability probabilities. Using a prototypical implementation on top of the Storm model checker, we show that symbolic data structures such as multi-terminal BDDs (MTBDDs) are very effective to perform inference on large Bayesian network benchmarks. We compare our result to inference using probabilistic sentential decision diagrams and vtrees, a scalable symbolic technique in AI inference tools.

We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of the positions of the particles, in either continuous or discrete time, along multiple independent trajectories. We introduce a nonparametric inference approach to this inverse problem, based on a regularized maximum likelihood estimator constrained to suitable hypothesis spaces adaptive to data. We show that a coercivity condition enables us to control the condition number of this problem and prove the consistency of our estimator, and that in fact it converges at a near-optimal learning rate, equal to the min-max rate of $1$-dimensional non-parametric regression. In particular, this rate is independent of the dimension of the state space, which is typically very high. We also analyze the discretization errors in the case of discrete-time observations, showing that it is of order $1/2$ in terms of the time gaps between observations. This term, when large, dominates the sampling error and the approximation error, preventing convergence of the estimator. Finally, we exhibit an efficient parallel algorithm to construct the estimator from data, and we demonstrate the effectiveness of our algorithm with numerical tests on prototype systems including stochastic opinion dynamics and a Lennard-Jones model.