We introduce a novel framework for causal explanations of stochastic, sequential decision-making systems built on the well-studied structural causal model paradigm for causal reasoning. This single framework can identify multiple, semantically distinct explanations for agent actions -- something not previously possible. In this paper, we establish exact methods and several approximation techniques for causal inference on Markov decision processes using this framework, followed by results on the applicability of the exact methods and some run time bounds. We discuss several scenarios that illustrate the framework's flexibility and the results of experiments with human subjects that confirm the benefits of this approach.

Abstract: Probabilistic graphical models play a crucial role in machine learning and have wide applications in various fields. One pivotal subset is undirected graphical models, also known as Markov random fields. In this work, we investigate the structure learning methods of Markov random fields on quantum computers. We propose a quantum algorithm for structure learning of an r-wise Markov Random Field with a bounded degree underlying graph, based on a nearly optimal classical greedy algorithm. The quantum algorithm provides a polynomial speed-up over the classical counterpart in terms of the number of variables.

Data-driven control algorithms use observations of system dynamics to construct an implicit model for the purpose of control. However, in practice, data-driven techniques often require excessive sample sizes, which may be infeasible in real-world scenarios where only limited observations of the system are available. Furthermore, purely data-driven methods often neglect useful a priori knowledge, such as approximate models of the system dynamics. We present a method to incorporate such prior knowledge into data-driven control algorithms using kernel embeddings, a nonparametric machine learning technique based in the theory of reproducing kernel Hilbert spaces. Our proposed approach incorporates prior knowledge of the system dynamics as a bias term in the kernel learning problem. We formulate the biased learning problem as a least-squares problem with a regularization term that is informed by the dynamics, that has an efficiently computable, closed-form solution. Through numerical experiments, we empirically demonstrate the improved sample efficiency and out-of-sample generalization of our approach over a purely data-driven baseline. We demonstrate an application of our method to control through a target tracking problem with nonholonomic dynamics, and on spring-mass-damper and F-16 aircraft state prediction tasks.

Automatic differentiation (AD), a technique for constructing new programs which compute the derivative of an original program, has become ubiquitous throughout scientific computing and deep learning due to the improved performance afforded by gradient-based optimization. However, AD systems have been restricted to the subset of programs that have a continuous dependence on parameters. Programs that have discrete stochastic behaviors governed by distribution parameters, such as flipping a coin with probability $p$ of being heads, pose a challenge to these systems because the connection between the result (heads vs tails) and the parameters ($p$) is fundamentally discrete. In this paper we develop a new reparameterization-based methodology that allows for generating programs whose expectation is the derivative of the expectation of the original program. We showcase how this method gives an unbiased and low-variance estimator which is as automated as traditional AD mechanisms. We demonstrate unbiased forward-mode AD of discrete-time Markov chains, agent-based models such as Conway's Game of Life, and unbiased reverse-mode AD of a particle filter. Our code package is available at https://github.com/gaurav-arya/StochasticAD.jl.

Recent work on unsupervised speech segmentation has used self-supervised models with phone and word segmentation modules that are trained jointly. This paper instead revisits an older approach to word segmentation: bottom-up phone-like unit discovery is performed first, and symbolic word segmentation is then performed on top of the discovered units (without influencing the lower level). To do this, I propose a new unit discovery model, a new symbolic word segmentation model, and then chain the two models to segment speech. Both models use dynamic programming to minimize segment costs from a self-supervised network with an additional duration penalty that encourages longer units. Concretely, for acoustic unit discovery, duration-penalized dynamic programming (DPDP) is used with a contrastive predictive coding model as the scoring network. For word segmentation, DPDP is applied with an autoencoding recurrent neural as the scoring network. The two models are chained in order to segment speech. This approach gives comparable word segmentation results to state-of-the-art joint self-supervised segmentation models on an English benchmark. On French, Mandarin, German and Wolof data, it outperforms previous systems on the ZeroSpeech benchmarks. Analysis shows that the chained DPDP system segments shorter filler words well, but longer words might require some external top-down signal.

Abstract: We adapt concepts, methodology, and theory originally developed in the areas of multidimensional scaling and dimensionality reduction for multivariate data to the functional setting. We focus on classical scaling and Isomap -- prototypical methods that have played important roles in these area -- and showcase their use in the context of functional data analysis. Abstract: During Deep Brain Stimulation(DBS) surgery for treating Parkinson's disease, one vital task is to detect a specific brain area called the Subthalamic Nucleus(STN) and a sub-territory within the STN called the Dorsolateral Oscillatory Region(DLOR). Accurate detection of the STN borders is crucial for adequate clinical outcomes. Currently, the detection is based on human experts, guided by supervised machine learning detection algorithms.

Non-intrusive load monitoring (NILM) or energy disaggregation is an inverse problem whereby the goal is to extract the load profiles of individual appliances, given an aggregate load profile of the mains of a home. NILM could help identify the power usage patterns of individual appliances in a home, and thus, could help realize novel energy conservation schemes for smart homes. In this backdrop, this work proposes a novel deep-learning approach to solve the NILM problem and a few related problems as follows. 1) We build upon the reputed seq2-point convolutional neural network (CNN) model to come up with the proposed seq2-[3]-point CNN model to solve the (home) NILM problem and site-NILM problem (basically, NILM at a smaller scale). 2) We solve the related problem of appliance identification by building upon the state-of-the-art (pre-trained) 2D-CNN models, i.e., AlexNet, ResNet-18, and DenseNet-121, which are trained upon two custom datasets that consist of Wavelets and short-time Fourier transform (STFT)-based 2D electrical signatures of the appliances. 3) Finally, we do some basic qualitative inference about an individual appliance's health by comparing the power consumption of the same appliance across multiple homes. Low-frequency REDD dataset is used to train and test the proposed deep learning models for all problems, except site-NILM where REFIT dataset has been used. As for the results, we achieve a maximum accuracy of 94.6\% for home-NILM, 81\% for site-NILM, and 88.9\% for appliance identification (with Resnet-based model).

Given $X_1,\cdot ,X_N$ random variables whose joint distribution is given as $\mu$ we will use the Martingale Method to show any Lipshitz Function $f$ over these random variables is subgaussian. The Variance parameter however can have a simple expression under certain conditions. For example under the assumption that the random variables follow a Markov Chain and that the function is Lipschitz under a Weighted Hamming Metric. We shall conclude with certain well known techniques from concentration of suprema of random processes with applications in Reinforcement Learning

We study the constrained reinforcement learning problem, in which an agent aims to maximize the expected cumulative reward subject to a constraint on the expected total value of a utility function. In contrast to existing model-based approaches or model-free methods accompanied with a `simulator', we aim to develop the first model-free, simulator-free algorithm that achieves a sublinear regret and a sublinear constraint violation even in large-scale systems. To this end, we consider the episodic constrained Markov decision processes with linear function approximation, where the transition dynamics and the reward function can be represented as a linear function of some known feature mapping. We show that $\tilde{\mathcal{O}}(\sqrt{d^3H^3T})$ regret and $\tilde{\mathcal{O}}(\sqrt{d^3H^3T})$ constraint violation bounds can be achieved, where $d$ is the dimension of the feature mapping, $H$ is the length of the episode, and $T$ is the total number of steps. Our bounds are attained without explicitly estimating the unknown transition model or requiring a simulator, and they depend on the state space only through the dimension of the feature mapping. Hence our bounds hold even when the number of states goes to infinity. Our main results are achieved via novel adaptations of the standard LSVI-UCB algorithms. In particular, we first introduce primal-dual optimization into the LSVI-UCB algorithm to balance between regret and constraint violation. More importantly, we replace the standard greedy selection with respect to the state-action function in LSVI-UCB with a soft-max policy. This turns out to be key in establishing uniform concentration for the constrained case via its approximation-smoothness trade-off. We also show that one can achieve an even zero constraint violation while still maintaining the same order with respect to $T$.

To integrate high amounts of renewable energy resources, electrical power grids must be able to cope with high amplitude, fast timescale variations in power generation. Frequency regulation through demand response has the potential to coordinate temporally flexible loads, such as air conditioners, to counteract these variations. Existing approaches for discrete control with dynamic constraints struggle to provide satisfactory performance for fast timescale action selection with hundreds of agents. We propose a decentralized agent trained with multi-agent proximal policy optimization with localized communication. We explore two communication frameworks: hand-engineered, or learned through targeted multi-agent communication. The resulting policies perform well and robustly for frequency regulation, and scale seamlessly to arbitrary numbers of houses for constant processing times.