Off-policy evaluation (OPE) in reinforcement learning is notoriously difficult in long- and infinite-horizon settings due to diminishing overlap between behavior and target policies. In this paper, we study the role of Markovian, time-invariant, and ergodic structure in efficient OPE. We first derive the efficiency limits for OPE when one assumes each of these structures. This precisely characterizes the curse of horizon: in time-variant processes, OPE is only feasible in the near-on-policy setting, where behavior and target policies are sufficiently similar. But, in ergodic time-invariant Markov decision processes, our bounds show that truly-off-policy evaluation is feasible, even with only just one dependent trajectory, and provide the limits of how well we could hope to do. We develop a new estimator based on Double Reinforcement Learning (DRL) that leverages this structure for OPE. Our DRL estimator simultaneously uses estimated stationary density ratios and $q$-functions and remains efficient when both are estimated at slow, nonparametric rates and remains consistent when either is estimated consistently. We investigate these properties and the performance benefits of leveraging the problem structure for more efficient OPE.

Markov switching models (MSMs) are probabilistic models that employ multiple sets of parameters to describe different dynamic regimes that a time series may exhibit at different periods of time. The switching mechanism between regimes is controlled by unobserved random variables that form a first-order Markov chain. Explicit-duration MSMs contain additional variables that explicitly model the distribution of time spent in each regime. This allows to define duration distributions of any form, but also to impose complex dependence between the observations and to reset the dynamics to initial conditions. Models that focus on the first two properties are most commonly known as hidden semi-Markov models or segment models, whilst models that focus on the third property are most commonly known as changepoint models or reset models. In this monograph, we provide a description of explicit-duration modelling by categorizing the different approaches into three groups, which differ in encoding in the explicit-duration variables different information about regime change/reset boundaries. The approaches are described using the formalism of graphical models, which allows to graphically represent and assess statistical dependence and therefore to easily describe the structure of complex models and derive inference routines. The presentation is intended to be pedagogical, focusing on providing a characterization of the three groups in terms of model structure constraints and inference properties. The monograph is supplemented with a software package that contains most of the models and examples described. The material presented should be useful to both researchers wishing to learn about these models and researchers wishing to develop them further.

Sampling from log-concave distributions is a well researched problem that has many applications in statistics and machine learning. We study the distributions of the form $p^{*}\propto\exp(-f(x))$, where $f:\mathbb{R}^{d}\rightarrow\mathbb{R}$ has an $L$-Lipschitz gradient and is $m$-strongly convex. In our paper, we propose a Markov chain Monte Carlo (MCMC) algorithm based on the underdamped Langevin diffusion (ULD). It can achieve $\epsilon\cdot D$ error (in 2-Wasserstein distance) in $\tilde{O}\left(\kappa^{7/6}/\epsilon^{1/3}+\kappa/\epsilon^{2/3}\right)$ steps, where $D\overset{\mathrm{def}}{=}\sqrt{\frac{d}{m}}$ is the effective diameter of the problem and $\kappa\overset{\mathrm{def}}{=}\frac{L}{m}$ is the condition number. Our algorithm performs significantly faster than the previously best known algorithm for solving this problem, which requires $\tilde{O}\left(\kappa^{1.5}/\epsilon\right)$ steps. Moreover, our algorithm can be easily parallelized to require only $O(\kappa\log\frac{1}{\epsilon})$ parallel steps. To solve the sampling problem, we propose a new framework to discretize stochastic differential equations. We apply this framework to discretize and simulate ULD, which converges to the target distribution $p^{*}$. The framework can be used to solve not only the log-concave sampling problem, but any problem that involves simulating (stochastic) differential equations.

Mixtures-of-Experts models and their maximum likelihood estimation (MLE) via the EM algorithm have been thoroughly studied in the statistics and machine learning literature. They are subject of a growing investigation in the context of modeling with high-dimensional predictors with regularized MLE. We examine MoE with Gaussian gating network, for clustering and regression, and propose an $\ell_1$-regularized MLE to encourage sparse models and deal with the high-dimensional setting. We develop an EM-Lasso algorithm to perform parameter estimation and utilize a BIC-like criterion to select the model parameters, including the sparsity tuning hyperparameters. Experiments conducted on simulated data show the good performance of the proposed regularized MLE compared to the standard MLE with the EM algorithm.

In this paper we consider the basic version of Reinforcement Learning (RL) that involves computing optimal data driven (adaptive) policies for Markovian decision process with unknown transition probabilities. We provide a brief survey of the state of the art of the area and we compare the performance of the classic UCB policy of \cc{bkmdp97} with a new policy developed herein which we call MDP-Deterministic Minimum Empirical Divergence (MDP-DMED), and a method based on Posterior sampling (MDP-PS).

Most gradient-based approaches to meta-learning do not explicitly account for the fact that different parts of the underlying model adapt by different amounts when applied to a new task. For example, the input layers of an image classification convnet typically adapt very little, while the output layers can change significantly. This can cause parts of the model to begin to overfit while others underfit. To address this, we introduce a hierarchical Bayesian model with per-module shrinkage parameters, which we propose to learn by maximizing an approximation of the predictive likelihood using implicit differentiation. Our algorithm subsumes Reptile and outperforms variants of MAML on two synthetic few-shot meta-learning problems.

While most approaches to the problem of Inverse Reinforcement Learning (IRL) focus on estimating a reward function that best explains an expert agent's policy or demonstrated behavior on a control task, it is often the case that such behavior is more succinctly described by a simple reward combined with a set of hard constraints. In this setting, the agent is attempting to maximize cumulative rewards subject to these given constraints on their behavior. We reformulate the problem of IRL on Markov Decision Processes (MDPs) such that, given a nominal model of the environment and a nominal reward function, we seek to estimate state, action, and feature constraints in the environment that motivate an agent's behavior. Our approach is based on the Maximum Entropy IRL framework, which allows us to reason about the likelihood of an expert agent's demonstrations given our knowledge of an MDP. Using our method, we can infer which constraints can be added to the MDP to most increase the likelihood of observing these demonstrations. We present an algorithm which iteratively infers the Maximum Likelihood Constraint to best explain observed behavior, and we evaluate its efficacy using both simulated behavior and recorded data of humans navigating around an obstacle.

Before we start this article on machine learning basics, let us take an example to understand the impact of machine learning in the world. We can safely assume that machine learning has been a dominant force in today's world and has accelerated our progress in all fields. No matter which industry you look at, machine learning has dramatically altered it. Let's take an example from the world of trading. Man Group's AHL Dimension programme is a $5.1 billion dollar hedge fund which is partially managed by AI. After it started off, by the year 2015, its machine learning algorithms were contributing more than half of the profits of the fund even though the assets under its management were far less. Machine learning has become a hot topic today, with professionals all over the world signing up for ML or AI courses for fear of being left behind. But exactly what is machine learning? It will be clear to you when you have reached the end of this article. Machine Learning, as the name suggests, provides machines with the ability to learn autonomously based on experiences, observations and analysing patterns within a given data set without explicitly programming. When we write a program or a code for some specific purpose, we are actually writing a definite set of instructions which the machine will follow. Whereas in machine learning, we input a data set through which the machine will learn by identifying and analysing the patterns in the data set and learn to take decisions autonomously based on its observations and learnings from the dataset.

Probability is a field of mathematics that quantifies uncertainty. It is undeniably a pillar of the field of machine learning, and many recommend it as a prerequisite subject to study prior to getting started. This is misleading advice, as probability makes more sense to a practitioner once they have the context of the applied machine learning process in which to interpret it. In this post, you will discover why machine learning practitioners should study probabilities to improve their skills and capabilities. Before we go through the reasons that you should learn probability, let's start off by taking a small look at the reason why you should not.

Cryo-electron microscopy (cryo-EM) is a powerful technique for determining the structure of proteins and other macromolecular complexes at near-atomic resolution. In single particle cryo-EM, the central problem is to reconstruct the three-dimensional structure of a macromolecule from $10^{4-7}$ noisy and randomly oriented two-dimensional projections. However, the imaged protein complexes may exhibit structural variability, which complicates reconstruction and is typically addressed using discrete clustering approaches that fail to capture the full range of protein dynamics. Here, we introduce a novel method for cryo-EM reconstruction that extends naturally to modeling continuous generative factors of structural heterogeneity. This method encodes structures in Fourier space using coordinate-based deep neural networks, and trains these networks from unlabeled 2D cryo-EM images by combining exact inference over image orientation with variational inference for structural heterogeneity. We demonstrate that the proposed method, termed cryoDRGN, can perform ab initio reconstruction of 3D protein complexes from simulated and real 2D cryo-EM image data. To our knowledge, cryoDRGN is the first neural network-based approach for cryo-EM reconstruction and the first end-to-end method for directly reconstructing continuous ensembles of protein structures from cryo-EM images.