Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

“Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”の学習報告

Model-free deep reinforcement learning (RL) algorithms have been demonstrated on a range of challenging decision making and control tasks. However, these methods typically suffer from two major challenges: very high sample complexity and brittle convergence properties, which necessitate meticulous hyperparameter tuning. Both of these challenges severely limit the applicability of such methods to complex, real-world domains. In this paper, we propose soft actor-critic, an off-policy actor-critic deep RL algorithm based on the maximum entropy reinforcement learning framework. In this framework, the actor aims to maximize expected reward while also maximizing entropy. That is, to succeed at the task while acting as randomly as possible. Prior deep RL methods based on this framework have been formulated as Q-learning methods. By combining off-policy updates with a stable stochastic actor-critic formulation, our method achieves state-of-the-art performance on a range of continuous control benchmark tasks, outperforming prior on-policy and off-policy methods. Furthermore, we demonstrate that, in contrast to other off-policy algorithms, our approach is very stable, achieving very similar performance across different random seeds.

Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor

There are two major types of uncertainty one can model. Aleatoric uncertainty captures noise inherent in the observations. On the other hand, epistemic uncertainty accounts for uncertainty in the model -- uncertainty which can be explained away given enough data. Traditionally it has been difficult to model epistemic uncertainty in computer vision, but with new Bayesian deep learning tools this is now possible. We study the benefits of modeling epistemic vs. aleatoric uncertainty in Bayesian deep learning models for vision tasks. For this we present a Bayesian deep learning framework combining input-dependent aleatoric uncertainty together with epistemic uncertainty. We study models under the framework with per-pixel semantic segmentation and depth regression tasks. Further, our explicit uncertainty formulation leads to new loss functions for these tasks, which can be interpreted as learned attenuation. This makes the loss more robust to noisy data, also giving new state-of-the-art results on segmentation and depth regression benchmarks.

What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision

This paper develops variational continual learning (VCL), a simple but general framework for continual learning that fuses online variational inference (VI) and recent advances in Monte Carlo VI for neural networks. The framework can successfully train both deep discriminative models and deep generative models in complex continual learning settings where existing tasks evolve over time and entirely new tasks emerge. Experimental results show that VCL outperforms state-of-the-art continual learning methods on a variety of tasks, avoiding catastrophic forgetting in a fully automatic way.

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Variational continual learning

Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward networks with more than one hidden layer and Gaussian processes with a recursive kernel definition. We show that, under broad conditions, as we make the architecture increasingly wide, the implied random function converges in distribution to a Gaussian process, formalising and extending existing results by Neal (1996) to deep networks. To evaluate convergence rates empirically, we use maximum mean discrepancy. We then compare finite Bayesian deep networks from the literature to Gaussian processes in terms of the key predictive quantities of interest, finding that in some cases the agreement can be very close. We discuss the desirability of Gaussian process behaviour and review non-Gaussian alternative models from the literature.

Gaussian Process Behaviour in Wide Deep Neural Networks

Model-free deep reinforcement learning (RL) methods have been successful in a wide variety of simulated domains. However, a major obstacle facing deep RL in the real world is their high sample complexity. Batch policy gradient methods offer stable learning, but at the cost of high variance, which often requires large batches. TD-style methods, such as off-policy actor-critic and Q-learning, are more sample-efficient but biased, and often require costly hyperparameter sweeps to stabilize. In this work, we aim to develop methods that combine the stability of policy gradients with the efficiency of off-policy RL. We present Q-Prop, a policy gradient method that uses a Taylor expansion of the off-policy critic as a control variate. Q-Prop is both sample efficient and stable, and effectively combines the benefits of on-policy and off-policy methods. We analyze the connection between Q-Prop and existing model-free algorithms, and use control variate theory to derive two variants of Q-Prop with conservative and aggressive adaptation. We show that conservative Q-Prop provides substantial gains in sample efficiency over trust region policy optimization (TRPO) with generalized advantage estimation (GAE), and improves stability over deep deterministic policy gradient (DDPG), the state-of-the-art on-policy and off-policy methods, on OpenAI Gym's MuJoCo continuous control environments.

Q-PrOP: Sample-efficient policy gradient with an off-policy critic

There is information in speech sounds about the length of the vocal tract; specifically, as a child grows, the resonators in the vocal tract grow and the formant frequencies of the vowels decrease. It has been hypothesized that the auditory system applies a scale transform to all sounds to segregate size information from resonator shape information, and thereby enhance both size perception and speech recognition [Irino and Patterson, Speech Commun. 36, 181-203 (2002)]. This paper describes size discrimination experiments and vowel recognition experiments designed to provide evidence for an auditory scaling mechanism. Vowels were scaled to represent people with vocal tracts much longer and shorter than normal, and with pitches much higher and lower than normal. The results of the discrimination experiments show that listeners can make fine judgments about the relative size of speakers, and they can do so for vowels scaled well beyond the normal range. Similarly, the recognition experiments show good performance for vowels in the normal range, and for vowels scaled well beyond the normal range of experience. Together, the experiments support the hypothesis that the auditory system automatically normalizes for the size information in communication sounds.

The processing and perception of size information in speech sounds

Introduction Variational methods are a key component of the approximate inference and learning toolbox. These methods fill an important middle ground, retaining distributional information about uncertainty in latent variables, unlike maximum a posteriori methods, and yet generally requiring less computational time than Markov chain Monte Carlo methods. In particular the variational expectation maximisation (vEM) and variational Bayes algorithms, both involving variational optimisation of a free-energy, are widely used in time series modelling. Here, we investigate the success of vEM in simple probabilistic time series models. First we consider the inference step of vEM, and show that a consequence of the well-known compactness property of variational inference is a failure to propagate uncertainty in time, thus limiting the usefulness of the retained distributional information. In particular, the uncertainty may appear to be smallest precisely when the approximation is poorest. Second, we consider parameter learning and analytically reveal systematic biases in the parameters found by vEM. Surprisingly, simpler variational approximations (such as mean-field) can lead to less bias than more complicated structured approximations. The variational approach We begin this chapter with a brief theoretical review of the variational expectation maximisation algorithm, before illustrating the important concepts with a simple example in the next section. The vEM algorithm is an approximate version of the expectation maximisation (EM) algorithm [4]. Expectation maximisation is a standard approach to finding maximum likelihood (ML) parameters for latent variable models, including hidden Markov models and linear or non-linear state space models (SSMs) for time series.

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Richard E. Turner

Papers

Variational continual learning

Gaussian Process Behaviour in Wide Deep Neural Networks

Q-PrOP: Sample-efficient policy gradient with an off-policy critic

The processing and perception of size information in speech sounds

Two problems with variational expectation maximisation for time-series models