Sequence generation models such as recurrent networks can be trained with a diverse set of learning algorithms. For example, maximum likelihood learning is simple and efficient, yet suffers from the exposure bias problem. Reinforcement learning like policy gradient addresses the problem but can have prohibitively poor exploration efficiency. A variety of other algorithms such as RAML, SPG, and data noising, have also been developed from different perspectives. This paper establishes a formal connection between these algorithms. We present a generalized entropy regularized policy optimization formulation, and show that the apparently divergent algorithms can all be reformulated as special instances of the framework, with the only difference being the configurations of reward function and a couple of hyperparameters. The unified interpretation offers a systematic view of the varying properties of exploration and learning efficiency. Besides, based on the framework, we present a new algorithm that dynamically interpolates among the existing algorithms for improved learning. Experiments on machine translation and text summarization demonstrate the superiority of the proposed algorithm.

Bayesian optimization usually assumes that a Bayesian prior is given. However, the strong theoretical guarantees in Bayesian optimization are often regrettably compromised in practice because of unknown parameters in the prior. In this paper, we adopt a variant of empirical Bayes and show that, by estimating the Gaussian process prior from offline data sampled from the same prior and constructing unbiased estimators of the posterior, variants of both GP-UCB and probability of improvement achieve a near-zero regret bound, which decreases to a constant proportional to the observational noise as the number of offline data and the number of online evaluations increase. Empirically, we have verified our approach on challenging simulated robotic problems featuring task and motion planning.

Parallel tempering addresses some of the drawbacks of canonical Markov Chain Monte-Carlo methods for Bayesian neural learning with the ability to utilize high performance computing. However, certain challenges remain given the large range of network parameters and big data. Surrogate-assisted optimization considers the estimation of an objective function for models given computational inefficiency or difficulty to obtain clear results. We address the inefficiency of parallel tempering for large-scale problems by combining parallel computing features with surrogate assisted estimation of likelihood function that describes the plausibility of a model parameter value, given specific observed data. In this paper, we present surrogate-assisted parallel tempering for Bayesian neural learning where the surrogates are used to estimate the likelihood. The estimation via the surrogate becomes useful rather than evaluating computationally expensive models that feature large number of parameters and datasets. Our results demonstrate that the methodology significantly lowers the computational cost while maintaining quality in decision making using Bayesian neural learning. The method has applications for a Bayesian inversion and uncertainty quantification for a broad range of numerical models.

Likelihood-free inference refers to inference when a likelihood function cannot be explicitly evaluated, which is often the case for models based on simulators. While much of the literature is concerned with sample-based'Approximate Bayesian Computation' methods, recent work suggests that approaches relying on deep neural conditional density estimators can obtain state-of-the-art results with fewer simulations. The neural approaches vary in how they choose which simulations to run and what they learn: an approximate posterior or a surrogate likelihood. This work provides some direct controlled comparisons between these choices.

The method of block coordinate gradient descent (BCD) has been a powerful method for large-scale optimization. This paper considers the BCD method that successively updates a series of blocks selected according to a Markov chain. This kind of block selection is neither i.i.d. random nor cyclic. On the other hand, it is a natural choice for some applications in distributed optimization and Markov decision process, where i.i.d. random and cyclic selections are either infeasible or very expensive. By applying mixing-time properties of a Markov chain, we prove convergence of Markov chain BCD for minimizing Lipschitz differentiable functions, which can be nonconvex. When the functions are convex and strongly convex, we establish both sublinear and linear convergence rates, respectively. We also present a method of Markov chain inertial BCD. Finally, we discuss potential applications.

Scalable Bayesian sampling is playing an important role in modern machine learning, especially in the fast-developed unsupervised-(deep)-learning models. While tremendous progresses have been achieved via scalable Bayesian sampling such as stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD), the generated samples are typically highly correlated. Moreover, their sample-generation processes are often criticized to be inefficient. In this paper, we propose a novel self-adversarial learning framework that automatically learns a conditional generator to mimic the behavior of a Markov kernel (transition kernel). High-quality samples can be efficiently generated by direct forward passes though a learned generator. Most importantly, the learning process adopts a self-learning paradigm, requiring no information on existing Markov kernels, e.g., knowledge of how to draw samples from them. Specifically, our framework learns to use current samples, either from the generator or pre-provided training data, to update the generator such that the generated samples progressively approach a target distribution, thus it is called self-learning. Experiments on both synthetic and real datasets verify advantages of our framework, outperforming related methods in terms of both sampling efficiency and sample quality.

State-space models (SSMs) provide a flexible framework for modelling time-series data. Consequently, SSMs are ubiquitously applied in areas such as engineering, econometrics and epidemiology. In this paper we provide a fast approach for approximate Bayesian inference in SSMs using the tools of deep learning and variational inference.

Today we are going to implement a Bayesian linear regression in R from scratch and use it to forecast US GDP growth. This post is based on a very informative manual from the Bank of England on Applied Bayesian Econometrics. I have translated the original Matlab code into R since its open source and widely used in data analysis/science. My main goal in this post is to try and give people a better understanding of Bayesian statistics, some of it's advantages and also some scenarios where you might want to use it. Let's take a moment to think about why we would we even want to use Bayesian techniques in the first place.

A GPS-denied UAV (Agent B) is localised through INS alignment with the aid of a nearby GPS-equipped UAV (Agent A), which broadcasts its position at several time instants. Agent B measures the signals' direction of arrival with respect to Agent B's inertial navigation frame. Semidefinite programming and the Orthogonal Procrustes algorithm are employed, and accuracy is improved through maximum likelihood estimation. The method is validated using flight data and simulations. A three-agent extension is explored.

Although Neural Machine Translation (NMT) models have advanced state-of-the-art performance in machine translation, they face problems like the inadequate translation. We attribute this to that the standard Maximum Likelihood Estimation (MLE) cannot judge the real translation quality due to its several limitations. In this work, we propose an adequacy-oriented learning mechanism for NMT by casting translation as a stochastic policy in Reinforcement Learning (RL), where the reward is estimated by explicitly measuring translation adequacy. Benefiting from the sequence-level training of RL strategy and a more accurate reward designed specifically for translation, our model outperforms multiple strong baselines, including (1) standard and coverage-augmented attention models with MLE-based training, and (2) advanced reinforcement and adversarial training strategies with rewards based on both word-level BLEU and character-level chrF3. Quantitative and qualitative analyses on different language pairs and NMT architectures demonstrate the effectiveness and universality of the proposed approach.