The recent explosion of genetic and high dimensional biobank and 'omic' data has provided researchers with the opportunity to investigate the shared genetic origin (pleiotropy) of hundreds to thousands of related phenotypes. However, existing methods for multi-phenotype genome-wide association studies (GWAS) do not model pleiotropy, are only applicable to a small number of phenotypes, or provide no way to perform inference. To add further complication, raw genetic and phenotype data are rarely observed, meaning analyses must be performed on GWAS summary statistics whose statistical properties in high dimensions are poorly understood. We therefore developed a novel model, theoretical framework, and set of methods to perform Bayesian inference in GWAS of high dimensional phenotypes using summary statistics that explicitly model pleiotropy, beget fast computation, and facilitate the use of biologically informed priors. We demonstrate the utility of our procedure by applying it to metabolite GWAS, where we develop new nonparametric priors for genetic effects on metabolite levels that use known metabolic pathway information and foster interpretable inference at the pathway level.

The Wasserstein distance between mixing measures has come to occupy a central place in the statistical analysis of mixture models. This work proposes a new canonical interpretation of this distance and provides tools to perform inference on the Wasserstein distance between mixing measures in topic models. We consider the general setting of an identifiable mixture model consisting of mixtures of distributions from a set $\mathcal{A}$ equipped with an arbitrary metric $d$, and show that the Wasserstein distance between mixing measures is uniquely characterized as the most discriminative convex extension of the metric $d$ to the set of mixtures of elements of $\mathcal{A}$. The Wasserstein distance between mixing measures has been widely used in the study of such models, but without axiomatic justification. Our results establish this metric to be a canonical choice. Specializing our results to topic models, we consider estimation and inference of this distance. Though upper bounds for its estimation have been recently established elsewhere, we prove the first minimax lower bounds for the estimation of the Wasserstein distance in topic models. We also establish fully data-driven inferential tools for the Wasserstein distance in the topic model context. Our results apply to potentially sparse mixtures of high-dimensional discrete probability distributions. These results allow us to obtain the first asymptotically valid confidence intervals for the Wasserstein distance in topic models.

As autonomous vehicles (AVs) become more prevalent on public roads, they will inevitably interact with human-driven vehicles (HVs) in mixed traffic scenarios. To ensure safe interactions between AVs and HVs, it is crucial to account for the uncertain behaviors of HVs when developing control strategies for AVs. In this paper, we propose an efficient learning-based modeling approach for HVs that combines a first-principles model with a Gaussian process (GP) learning-based component. The GP model corrects the velocity prediction of the first-principles model and estimates its uncertainty. Utilizing this model, a model predictive control (MPC) strategy, referred to as GP-MPC, was designed to enhance the safe control of a mixed vehicle platoon by integrating the uncertainty assessment into the distance constraint. We compare our GP-MPC strategy with a baseline MPC that uses only the first-principles model in simulation studies. We show that our GP-MPC strategy provides more robust safe distance guarantees and enables more efficient travel behaviors (higher travel speeds) for all vehicles in the mixed platoon. Moreover, by incorporating a sparse GP technique in HV modeling and a dynamic GP prediction in MPC, we achieve an average computation time for GP-MPC at each time step that is only 5% longer than the baseline MPC, which is approximately 100 times faster than our previous work that did not use these approximations. This work demonstrates how learning-based modeling of HVs can enhance safety and efficiency in mixed traffic involving AV-HV interaction.

We study learning in periodic Markov Decision Process (MDP), a special type of non-stationary MDP where both the state transition probabilities and reward functions vary periodically, under the average reward maximization setting. We formulate the problem as a stationary MDP by augmenting the state space with the period index, and propose a periodic upper confidence bound reinforcement learning-2 (PUCRL2) algorithm. We show that the regret of PUCRL2 varies linearly with the period $N$ and as $\mathcal{O}(\sqrt{Tlog T})$ with the horizon length $T$. Utilizing the information about the sparsity of transition matrix of augmented MDP, we propose another algorithm PUCRLB which enhances upon PUCRL2, both in terms of regret ($O(\sqrt{N})$ dependency on period) and empirical performance. Finally, we propose two other algorithms U-PUCRL2 and U-PUCRLB for extended uncertainty in the environment in which the period is unknown but a set of candidate periods are known. Numerical results demonstrate the efficacy of all the algorithms.

Prescriptive Process Monitoring is a prominent problem in Process Mining, which consists in identifying a set of actions to be recommended with the goal of optimising a target measure of interest or Key Performance Indicator (KPI). One challenge that makes this problem difficult is the need to provide Prescriptive Process Monitoring techniques only based on temporally annotated (process) execution data, stored in, so-called execution logs, due to the lack of well crafted and human validated explicit models. In this paper we aim at proposing an AI based approach that learns, by means of Reinforcement Learning (RL), an optimal policy (almost) only from the observation of past executions and recommends the best activities to carry on for optimizing a KPI of interest. This is achieved first by learning a Markov Decision Process for the specific KPIs from data, and then by using RL training to learn the optimal policy. The approach is validated on real and synthetic datasets and compared with off-policy Deep RL approaches. The ability of our approach to compare with, and often overcome, Deep RL approaches provides a contribution towards the exploitation of white box RL techniques in scenarios where only temporal execution data are available.

The issue of distinguishing between the same-source and different-source hypotheses based on various types of traces is a generic problem in forensic science. This problem is often tackled with Bayesian approaches, which are able to provide a likelihood ratio that quantifies the relative strengths of evidence supporting each of the two competing hypotheses. Here, we focus on distance-based approaches, whose robustness and specifically whose capacity to deal with high-dimensional evidence are very different, and need to be evaluated and optimized. A unified framework for direct methods based on estimating the likelihoods of the distance between traces under each of the two competing hypotheses, and indirect methods using logistic regression to discriminate between same-source and different-source distance distributions, is presented. Whilst direct methods are more flexible, indirect methods are more robust and quite natural in machine learning. Moreover, indirect methods also enable the use of a vectorial distance, thus preventing the severe information loss suffered by scalar distance approaches.Direct and indirect methods are compared in terms of sensitivity, specificity and robustness, with and without dimensionality reduction, with and without feature selection, on the example of hand odor profiles, a novel and challenging type of evidence in the field of forensics. Empirical evaluations on a large panel of 534 subjects and their 1690 odor traces show the significant superiority of the indirect methods, especially without dimensionality reduction, be it with or without feature selection.

Partially Observable Monte Carlo Planning (POMCP) is an efficient solver for Partially Observable Markov Decision Processes (POMDPs). It allows scaling to large state spaces by computing an approximation of the optimal policy locally and online, using a Monte Carlo Tree Search based strategy. However, POMCP suffers from sparse reward function, namely, rewards achieved only when the final goal is reached, particularly in environments with large state spaces and long horizons. Recently, logic specifications have been integrated into POMCP to guide exploration and to satisfy safety requirements. However, such policy-related rules require manual definition by domain experts, especially in real-world scenarios. In this paper, we use inductive logic programming to learn logic specifications from traces of POMCP executions, i.e., sets of belief-action pairs generated by the planner. Specifically, we learn rules expressed in the paradigm of answer set programming. We then integrate them inside POMCP to provide soft policy bias toward promising actions. In the context of two benchmark scenarios, rocksample and battery, we show that the integration of learned rules from small task instances can improve performance with fewer Monte Carlo simulations and in larger task instances. We make our modified version of POMCP publicly available at https://github.com/GiuMaz/pomcp_clingo.git.

Concept bottleneck model (CBM) is a ubiquitous method that can interpret neural networks using concepts. In CBM, concepts are inserted between the output layer and the last intermediate layer as observable values. This helps in understanding the reason behind the outputs generated by the neural networks: the weights corresponding to the concepts from the last hidden layer to the output layer. However, it has not yet been possible to understand the behavior of the generalization error in CBM since a neural network is a singular statistical model in general. When the model is singular, a one to one map from the parameters to probability distributions cannot be created. This non-identifiability makes it difficult to analyze the generalization performance. In this study, we mathematically clarify the Bayesian generalization error and free energy of CBM when its architecture is three-layered linear neural networks. We also consider a multitask problem where the neural network outputs not only the original output but also the concepts. The results show that CBM drastically changes the behavior of the parameter region and the Bayesian generalization error in three-layered linear neural networks as compared with the standard version, whereas the multitask formulation does not.

Continuous-time Markov decision processes (CTMDPs) are canonical models to express sequential decision-making under dense-time and stochastic environments. When the stochastic evolution of the environment is only available via sampling, model-free reinforcement learning (RL) is the algorithm-of-choice to compute optimal decision sequence. RL, on the other hand, requires the learning objective to be encoded as scalar reward signals. Since doing such translations manually is both tedious and error-prone, a number of techniques have been proposed to translate high-level objectives (expressed in logic or automata formalism) to scalar rewards for discrete-time Markov decision processes (MDPs). Unfortunately, no automatic translation exists for CTMDPs. We consider CTMDP environments against the learning objectives expressed as omega-regular languages. Omega-regular languages generalize regular languages to infinite-horizon specifications and can express properties given in popular linear-time logic LTL. To accommodate the dense-time nature of CTMDPs, we consider two different semantics of omega-regular objectives: 1) satisfaction semantics where the goal of the learner is to maximize the probability of spending positive time in the good states, and 2) expectation semantics where the goal of the learner is to optimize the long-run expected average time spent in the ``good states" of the automaton. We present an approach enabling correct translation to scalar reward signals that can be readily used by off-the-shelf RL algorithms for CTMDPs. We demonstrate the effectiveness of the proposed algorithms by evaluating it on some popular CTMDP benchmarks with omega-regular objectives.

Multi-agent reinforcement learning (MARL) is the study of the learning dynamics of strategic agents that coexist in a shared environment, and is one of the important frontiers of machine learning and control. In this paper, we study MARL in stochastic games, also known as Markov games, a multi-agent generalization of Markov decision problems (MDPs) in which the cost-relevant history of the system is summarized by a state variable Shapley [1953]. Due to its ability to model both dynamic inter-temporal choice as well as strategic interaction, the stochastic games model has long been a popular framework for studying multi-agent learning Littman [1994]. In comparison to single-agent reinforcement learning, analysis of MARL is difficult due to several challenges inherent to multi-agent systems, including non-stationarity, conflicting interests, and decentralized information. As a result, fundamental understanding of multi-agent reinforcement learning theory has lagged behind its single-agent counterpart Zhang et al. [2021].