Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and to carry out Bayesian inference, however, quantification of uncertainty with variational inference remains challenging from both theoretical and practical perspectives. This paper is concerned with developing uncertainty measures for variational inference by using bootstrap procedures. We first develop two general bootstrap approaches for assessing the uncertainty of a variational estimate and the study the underlying bootstrap theory in both fixed- and increasing-dimension settings. We then use the bootstrap approach and our theoretical results in the context of mixed membership modeling with multivariate binary data on functional disability from the National Long Term Care Survey. We carry out a two-sample approach to test for changes in the repeated measures of functional disability for the subset of individuals present in 1984 and 1994 waves.

Dialogue assistants are rapidly becoming an indispensable daily aid. To avoid the significant effort needed to hand-craft the required dialogue flow, the Dialogue Management (DM) module can be cast as a continuous Markov Decision Process (MDP) and trained through Reinforcement Learning (RL). Several RL models have been investigated over recent years. However, the lack of a common benchmarking framework makes it difficult to perform a fair comparison between different models and their capability to generalise to different environments. Therefore, this paper proposes a set of challenging simulated environments for dialogue model development and evaluation. To provide some baselines, we investigate a number of representative parametric algorithms, namely deep reinforcement learning algorithms - DQN, A2C and Natural Actor-Critic and compare them to a non-parametric model, GP-SARSA. Both the environments and policy models are implemented using the publicly available PyDial toolkit and released on-line, in order to establish a testbed framework for further experiments and to facilitate experimental reproducibility.

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has been increasingly popular in Bayesian learning due to its ability to deal with large data. A standard SG-MCMC algorithm simulates samples from a discretized-time Markov chain to approximate a target distribution. However, the samples are typically highly correlated due to the sequential generation process, an undesired property in SG-MCMC. In contrary, Stein variational gradient descent (SVGD) directly optimizes a set of particles, and it is able to approximate a target distribution with much fewer samples. In this paper, we propose a novel method to directly optimize particles (or samples) in SG-MCMC from scratch. Specifically, we propose efficient methods to solve the corresponding Fokker-Planck equation on the space of probability distributions, whose solution (i.e., a distribution) is approximated by particles. Through our framework, we are able to show connections of SG-MCMC to SVGD, as well as the seemly unrelated generative-adversarial-net framework. Under certain relaxations, particle optimization in SG-MCMC can be interpreted as an extension of standard SVGD with momentum.

This paper studies directed exploration for reinforcement learning agents by tracking uncertainty about the value of each available action. We identify two sources of uncertainty that are relevant for exploration. The first originates from limited data (parametric uncertainty), while the second originates from the distribution of the returns (return uncertainty). We identify methods to learn these distributions with deep neural networks, where we estimate parametric uncertainty with Bayesian drop-out, while return uncertainty is propagated through the Bellman equation as a Gaussian distribution. Then, we identify that both can be jointly estimated in one network, which we call the Double Uncertain Value Network. The policy is directly derived from the learned distributions based on Thompson sampling. Experimental results show that both types of uncertainty may vastly improve learning in domains with a strong exploration challenge.

We analyse multimodal time-series data corresponding to weight, sleep and steps measurements. We focus on predicting whether a user will successfully achieve his/her weight objective. For this, we design several deep long short-term memory (LSTM) architectures, including a novel cross-modal LSTM (X-LSTM), and demonstrate their superiority over baseline approaches. The X-LSTM improves parameter efficiency by processing each modality separately and allowing for information flow between them by way of recurrent cross-connections. We present a general hyperparameter optimisation technique for X-LSTMs, which allows us to significantly improve on the LSTM and a prior state-of-the-art cross-modal approach, using a comparable number of parameters. Finally, we visualise the model's predictions, revealing implications about latent variables in this task.

The TensorFlow Distributions library implements a vision of probability theory adapted to the modern deep-learning paradigm of end-to-end differentiable computation. Building on two basic abstractions, it offers flexible building blocks for probabilistic computation. Distributions provide fast, numerically stable methods for generating samples and computing statistics, e.g., log density. Bijectors provide composable volume-tracking transformations with automatic caching. Together these enable modular construction of high dimensional distributions and transformations not possible with previous libraries (e.g., pixelCNNs, autoregressive flows, and reversible residual networks). They are the workhorse behind deep probabilistic programming systems like Edward and empower fast black-box inference in probabilistic models built on deep-network components. TensorFlow Distributions has proven an important part of the TensorFlow toolkit within Google and in the broader deep learning community.

Labeling training data is increasingly the largest bottleneck in deploying machine learning systems. We present Snorkel, a first-of-its-kind system that enables users to train state-of-the-art models without hand labeling any training data. Instead, users write labeling functions that express arbitrary heuristics, which can have unknown accuracies and correlations. Snorkel denoises their outputs without access to ground truth by incorporating the first end-to-end implementation of our recently proposed machine learning paradigm, data programming. We present a flexible interface layer for writing labeling functions based on our experience over the past year collaborating with companies, agencies, and research labs. In a user study, subject matter experts build models 2.8x faster and increase predictive performance an average 45.5% versus seven hours of hand labeling. We study the modeling tradeoffs in this new setting and propose an optimizer for automating tradeoff decisions that gives up to 1.8x speedup per pipeline execution. In two collaborations, with the U.S. Department of Veterans Affairs and the U.S. Food and Drug Administration, and on four open-source text and image data sets representative of other deployments, Snorkel provides 132% average improvements to predictive performance over prior heuristic approaches and comes within an average 3.60% of the predictive performance of large hand-curated training sets.

We present a formalization of nested Monte Carlo (NMC) estimation, whereby terms in an outer estimator themselves involve calculation of separate, nested, Monte Carlo (MC) estimators. We demonstrate that, under mild conditions, NMC can provide consistent estimates of nested expectations, including cases involving arbitrary levels of nesting; establish corresponding rates of convergence; and provide empirical evidence that these rates are observed in practice. We further establish a number of pitfalls that can arise from naïve nesting of MC estimators, provide guidelines about how these can be avoided, and lay out novel methods for reformulating certain classes of nested expectation problems into single expectations, leading to improved convergence rates. Finally, we use one of these reformulations to derive a new estimator for use in discrete Bayesian experimental design problems which has a better convergence rate than existing methods. Our results have implications for a wide range of fields from probabilistic programming to deep generative models and serve both as an invitation for further inquiry and a caveat against careless use.

We address the problem of bootstrapping language acquisition for an artificial system similarly to what is observed in experiments with human infants. Our method works by associating meanings to words in manipulation tasks, as a robot interacts with objects and listens to verbal descriptions of the interactions. The model is based on an affordance network, i.e., a mapping between robot actions, robot perceptions, and the perceived effects of these actions upon objects. We extend the affordance model to incorporate spoken words, which allows us to ground the verbal symbols to the execution of actions and the perception of the environment. The model takes verbal descriptions of a task as the input and uses temporal co-occurrence to create links between speech utterances and the involved objects, actions, and effects. We show that the robot is able form useful word-to-meaning associations, even without considering grammatical structure in the learning process and in the presence of recognition errors. These word-to-meaning associations are embedded in the robot's own understanding of its actions. Thus, they can be directly used to instruct the robot to perform tasks and also allow to incorporate context in the speech recognition task. We believe that the encouraging results with our approach may afford robots with a capacity to acquire language descriptors in their operation's environment as well as to shed some light as to how this challenging process develops with human infants.

Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms.