Markov chain Monte Carlo (MCMC) algorithms are generally regarded as the gold standard technique for Bayesian inference. They are theoretically well-understood and conceptually simple to apply in practice. The drawback of MCMC is that in general performing exact inference requires all of the data to be processed at each iteration of the algorithm. For large data sets, the computational cost of MCMC can be prohibitive, which has led to recent developments in scalable Monte Carlo algorithms that have a significantly lower computational cost than standard MCMC. In this paper, we focus on a particular class of scalable Monte Carlo algorithms, stochastic gradient Markov chain Monte Carlo (SGMCMC) which utilises data subsampling techniques to reduce the per-iteration cost of MCMC. We provide an introduction to some popular SGMCMC algorithms and review the supporting theoretical results, as well as comparing the efficiency of SGMCMC algorithms against MCMC on benchmark examples. The supporting R code is available online.

Parameterized state space models in the form of recurrent networks are often used in machine learning to learn from data streams exhibiting temporal dependencies. To break the black box nature of such models it is important to understand the dynamical features of the input driving time series that are formed in the state space. We propose a framework for rigorous analysis of such state representations in vanishing memory state space models such as echo state networks (ESN). In particular, we consider the state space a temporal feature space and the readout mapping from the state space a kernel machine operating in that feature space. We show that: (1) The usual ESN strategy of randomly generating input-to-state, as well as state coupling leads to shallow memory time series representations, corresponding to cross-correlation operator with fast exponentially decaying coefficients; (2) Imposing symmetry on dynamic coupling yields a constrained dynamic kernel matching the input time series with straightforward exponentially decaying motifs or exponentially decaying motifs of the highest frequency; (3) Simple cycle high-dimensional reservoir topology specified only through two free parameters can implement deep memory dynamic kernels with a rich variety of matching motifs. We quantify richness of feature representations imposed by dynamic kernels and demonstrate that for dynamic kernel associated with cycle reservoir topology, the kernel richness undergoes a phase transition close to the edge of stability.

We explore a general framework in Markov chain Monte Carlo (MCMC) sampling where sequential proposals are tried as a candidate for the next state of the Markov chain. This sequential-proposal framework can be applied to various existing MCMC methods, including Metropolis-Hastings algorithms using random proposals and methods that use deterministic proposals such as Hamiltonian Monte Carlo or the bouncy particle sampler. Sequential-proposal MCMC methods construct the same Markov chains as those constructed by the delayed rejection method under certain circumstances. We demonstrate that applications of the sequential-proposal framework to Hamiltonian Monte Carlo (HMC) methods can lead to improved numerical efficiency compared to standard HMC methods and the No-U-Turn sampler. Finally, we show that the sequential-proposal bouncy particle sampler enables the constructed Markov chain to pass through regions of low target density and thus facilitates better mixing of the chain when the target density is multimodal.

By and large the process of learning concepts that are embedded in time is regarded as quite a mature research topic. Hidden Markov models, recurrent neural networks are, amongst others, successful approaches to learning from temporal data. In this paper, we claim that the dominant approach minimizing appropriate risk functions defined over time by classic stochastic gradient might miss the deep interpretation of time given in other fields like physics. We show that a recent reformulation of learning according to the principle of Least Cognitive Action is better suited whenever time is involved in learning. The principle gives rise to a learning process that is driven by differential equations, that can somehow descrive the process within the same framework as other laws of nature.

Compared with the classical policy gradient algorithm 1992), actor-critic tracks the action-value function (critic) in policy gradient in an online(Williams, manner, and alternatively updates the policy (actor) and the critic. On the one hand, the online update of critic significantly reduces the variance of policy gradient and hence leads to faster convergence. On the other hand, it also introduces algorithmic instability, which is often observed in practice (Islam et al., 2017) and parallels the notoriously unstable training of generative adversarial and Vinyals, 2016). Such instability of actor-critic originates from severalnetworks (Pfau intertwining challenges, including(i) function approximation of actor and critic, (ii) improper choice of stepsizes, (iii) the noise arising from stochastic approximation, (iv) the asynchrony between actor and critic, and (v) possibly off-policy data used in the update of critic. As a result, the convergence of actor-critic remains much less well understood than that of policy gradient, which itself is open. Consequently, the practical use of actor-critic often lacks theoretical guidance. In this paper, we aim to theoretically understand the algorithmic instability of actor-critic.

We present new techniques for automatically constructing probabilistic programs for data analysis, interpretation, and prediction. These techniques work with probabilistic domain-specific data modeling languages that capture key properties of a broad class of data generating processes, using Bayesian inference to synthesize probabilistic programs in these modeling languages given observed data. We provide a precise formulation of Bayesian synthesis for automatic data modeling that identifies sufficient conditions for the resulting synthesis procedure to be sound. We also derive a general class of synthesis algorithms for domain-specific languages specified by probabilistic context-free grammars and establish the soundness of our approach for these languages. We apply the techniques to automatically synthesize probabilistic programs for time series data and multivariate tabular data. We show how to analyze the structure of the synthesized programs to compute, for key qualitative properties of interest, the probability that the underlying data generating process exhibits each of these properties. Second, we translate probabilistic programs in the domain-specific language into probabilistic programs in Venture, a general-purpose probabilistic programming system. The translated Venture programs are then executed to obtain predictions of new time series data and new multivariate data records. Experimental results show that our techniques can accurately infer qualitative structure in multiple real-world data sets and outperform standard data analysis methods in forecasting and predicting new data.

Generalization is one of the most important goals in statistical machine learning problems [1]. In various standard machine learning techniques, given a particular data set, we fit our probabilistic learning model to the empirical distribution (or the data distribution) of the data set. When our learning model is sufficiently flexible, it can fit the empirical distribution exactly via an appropriate learning method. A learning model that is too close to the empirical distribution frequently gives poor results for new data points. This situation is known as over-fitting. Over-fitting impedes generalization; therefore, techniques that can suppress over-fitting are needed to achieve good generalizations.

We study a formalization of the grammar induction problem that models sentences as being generated by a compound probabilistic context-free grammar. In contrast to traditional formulations which learn a single stochastic grammar, our context-free rule probabilities are modulated by a per-sentence continuous latent variable, which induces marginal dependencies beyond the traditional context-free assumptions. Inference in this grammar is performed by collapsed variational inference, in which an amortized variational posterior is placed on the continuous variable, and the latent trees are marginalized with dynamic programming. Experiments on English and Chinese show the effectiveness of our approach compared to recent state-of-the-art methods for grammar induction from words with neural language models.

This paper addresses two challenges facing sampling-based kinodynamic motion planning: a way to identify good candidate states for local transitions and the subsequent computationally intractable steering between these candidate states. Through the combination of sampling-based planning, a Rapidly Exploring Randomized Tree (RRT) and an efficient kinodynamic motion planner through machine learning, we propose an efficient solution to long-range planning for kinodynamic motion planning. First, we use deep reinforcement learning to learn an obstacle-avoiding policy that maps a robot's sensor observations to actions, which is used as a local planner during planning and as a controller during execution. Second, we train a reachability estimator in a supervised manner, which predicts the RL policy's time to reach a state in the presence of obstacles. Lastly, we introduce RL-RRT that uses the RL policy as a local planner, and the reachability estimator as the distance function to bias tree-growth towards promising regions. We evaluate our method on three kinodynamic systems, including physical robot experiments. Results across all three robots tested indicate that RL-RRT outperforms state of the art kinodynamic planners in efficiency, and also provides a shorter path finish time than a steering function free method. The learned local planner policy and accompanying reachability estimator demonstrate transferability to the previously unseen experimental environments, making RL-RRT fast because the expensive computations are replaced with simple neural network inference. Video: https://youtu.be/dDMVMTOI8KY

Partially Observable Markov Decision Processes (POMDPs) are a popular formalism for sequential decision making in partially observable environments. Since solving POMDPs to optimality is a difficult task, point-based value iteration methods are widely used. These methods compute an approximate POMDP solution, and in some cases they even provide guarantees on the solution quality, but these algorithms have been designed for problems with an infinite planning horizon. In this paper we discuss why state-of-the-art point-based algorithms cannot be easily applied to finite-horizon problems that do not include discounting. Subsequently, we present a general point-based value iteration algorithm for finite-horizon problems which provides solutions with guarantees on solution quality. Furthermore, we introduce two heuristics to reduce the number of belief points considered during execution, which lowers the computational requirements. In experiments we demonstrate that the algorithm is an effective method for solving finite-horizon POMDPs.