A core problem of learning control is to determine optimal feedback controllers for (partially) unknown nonlinear systems from experimental data. Reinforcement learning (RL) [1], [2] is a promising framework for this, yet often requires performing many experiments on the physical system to even find suitable controllers, which limits the applicability of such techniques. Therefore, a lot of research effort has been invested into data efficiency of RL aiming at learning controllers from as few experiments as possible. Recently, Bayesian optimization (BO) has been proposed for RL as a promising approach in this direction. BO employs a probabilistic description of the latent objective function (typically a Gaussian process (GP)), which allows for selecting next control experiments in a principled manner, e.g., to maximize information gain [3] or perform safe exploration [4]. While BO provides a promising framework for learning controllers in fairly general settings, the full power of Bayesian learning is often not exploited. A key advantage of Bayesian methods is that they allow for combining prior problem knowledge with learning from data in a principled manner. In case of GP models, this concerns specifically the choice of the kernel, which captures the covariance between function values at different inputs and is thus the core component to model prior knowledge about the function shape. By choosing standard kernels, however, naive BO approaches do often not exploit this opportunity to improve learning performance.

This paper sets out to resolve how agents ought to act in the Sleeping Beauty problem and various related anthropic (self-locating belief) problems, not through the calculation of anthropic probabilities, but through finding the correct decision to make. It creates an anthropic decision theory (ADT) that decides these problems from a small set of principles. By doing so, it demonstrates that the attitude of agents with regards to each other (selfish or altruistic) changes the decisions they reach, and that it is very important to take this into account. To illustrate ADT, it is then applied to two major anthropic problems and paradoxes, the Presumptuous Philosopher and Doomsday problems, thus resolving some issues about the probability of human extinction.

We consider the estimation of Dirichlet Process Mixture Models (DPMMs) in distributed environments, where data are distributed across multiple computing nodes. A key advantage of Bayesian nonparametric models such as DPMMs is that they allow new components to be introduced on the fly as needed. This, however, posts an important challenge to distributed estimation -- how to handle new components efficiently and consistently. To tackle this problem, we propose a new estimation method, which allows new components to be created locally in individual computing nodes. Components corresponding to the same cluster will be identified and merged via a probabilistic consolidation scheme. In this way, we can maintain the consistency of estimation with very low communication cost. Experiments on large real-world data sets show that the proposed method can achieve high scalability in distributed and asynchronous environments without compromising the mixing performance.

We revisit the problem of estimating the parameters of a partially observed diffusion process, consisting of a hidden state process and an observed process, with a continuous time parameter. The estimation is to be done online, i.e. the parameter estimate should be updated recursively based on the observation filtration. Here, we use an old but under-exploited representation of the incomplete-data log-likelihood function in terms of the filter of the hidden state from the observations. By performing a stochastic gradient ascent, we obtain a fully recursive algorithm for the time evolution of the parameter estimate. We prove the convergence of the algorithm under suitable conditions regarding the ergodicity of the process consisting of state, filter, and tangent filter. Additionally, our parameter estimation is shown numerically to have the potential of improving suboptimal filters, and can be applied even when the system is not identifiable due to parameter redundancies. Online parameter estimation is a challenging problem that is ubiquitous in fields such as robotics, neuroscience, or finance in order to design adaptive filters and optimal controllers for unknown or changing systems.

Some of the most common examples of machine learning are Netflix's algorithms to make movie suggestions based on movies you have watched in the past or Amazon's algorithms that recommend books based on books you have bought before. The textbook that we used is one of the AI classics: Peter Norvig's Artificial Intelligence -- A Modern Approach, in which we covered major topics including intelligent agents, problem-solving by searching, adversarial search, probability theory, multi-agent systems, social AI, philosophy/ethics/future of AI. Machine learning algorithms can be divided into 3 broad categories -- supervised learning, unsupervised learning, and reinforcement learning.Supervised learning is useful in cases where a property (label) is available for a certain dataset (training set), but is missing and needs to be predicted for other instances. You can think of linear regression as the task of fitting a straight line through a set of points.

In this paper we introduce ZhuSuan, a python probabilistic programming library for Bayesian deep learning, which conjoins the complimentary advantages of Bayesian methods and deep learning. ZhuSuan is built upon Tensorflow. Unlike existing deep learning libraries, which are mainly designed for deterministic neural networks and supervised tasks, ZhuSuan is featured for its deep root into Bayesian inference, thus supporting various kinds of probabilistic models, including both the traditional hierarchical Bayesian models and recent deep generative models. We use running examples to illustrate the probabilistic programming on ZhuSuan, including Bayesian logistic regression, variational auto-encoders, deep sigmoid belief networks and Bayesian recurrent neural networks.

Semi-supervised and unsupervised systems provide operators with invaluable support and can tremendously reduce the operators load. In the light of the necessity to process large volumes of video data and provide autonomous decisions, this work proposes new learning algorithms for activity analysis in video. The activities and behaviours are described by a dynamic topic model. Two novel learning algorithms based on the expectation maximisation approach and variational Bayes inference are proposed. Theoretical derivations of the posterior of model parameters are given. The designed learning algorithms are compared with the Gibbs sampling inference scheme introduced earlier in the literature. A detailed comparison of the learning algorithms is presented on real video data. We also propose an anomaly localisation procedure, elegantly embedded in the topic modeling framework. The proposed framework can be applied to a number of areas, including transportation systems, security and surveillance.

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works have proposed a probabilistic approach able to infer the number of significant components. To this purpose, this paper introduces a Bayesian nonparametric principal component analysis (BNP-PCA). The proposed model projects observations onto a random orthogonal basis which is assigned a prior distribution defined on the Stiefel manifold. The prior on factor scores involves an Indian buffet process to model the uncertainty related to the number of components. The parameters of interest as well as the nuisance parameters are finally inferred within a fully Bayesian framework via Monte Carlo sampling. A study of the (in-)consistence of the marginal maximum a posteriori estimator of the latent dimension is carried out. A new estimator of the subspace dimension is proposed. Moreover, for sake of statistical significance, a Kolmogorov-Smirnov test based on the posterior distribution of the principal components is used to refine this estimate. The behaviour of the algorithm is first studied on various synthetic examples. Finally, the proposed BNP dimension reduction approach is shown to be easily yet efficiently coupled with clustering or latent factor models within a unique framework.

A common applied statistics task involves building regression models to characterize non-linear relationships between variables. When we write a function that takes continuous values as inputs, we are essentially implying an infinite vector that only returns values (indexed by the inputs) when the function is called upon to do so. To make this notion of a "distribution over functions" more concrete, let's quickly demonstrate how we obtain realizations from a Gaussian process, which result in an evaluation of a function over a set of points. We are going generate realizations sequentially, point by point, using the lovely conditioning property of mutlivariate Gaussian distributions.