Computer Science 분야 (03): Gaussian noise (electronic); Gaussian distribution; GP regression

How can a machine learn from experience? Probabilistic modelling provides a framework for understanding what learning is, and has therefore emerged as one of the principal theoretical and practical approaches for designing machines that learn from data acquired through experience. The probabilistic framework, which describes how to represent and manipulate uncertainty about models and predictions, has a central role in scientific data analysis, machine learning, robotics, cognitive science and artificial intelligence. This Review provides an introduction to this framework, and discusses some of the state-of-the-art advances in the field, namely, probabilistic programming, Bayesian optimization, data compression and automatic model discovery.

Autonomous learning has been a promising direction in control and robotics for more than a decade since data-driven learning allows to reduce the amount of engineering knowledge, which is otherwise required. However, autonomous reinforcement learning (RL) approaches typically require many interactions with the system to learn controllers, which is a practical limitation in real systems, such as robots, where many interactions can be impractical and time consuming. To address this problem, current learning approaches typically require task-specific knowledge in form of expert demonstrations, realistic simulators, pre-shaped policies, or specific knowledge about the underlying dynamics. In this paper, we follow a different approach and speed up learning by extracting more information from data. In particular, we learn a probabilistic, non-parametric Gaussian process transition model of the system. By explicitly incorporating model uncertainty into long-term planning and controller learning our approach reduces the effects of model errors, a key problem in model-based learning. Compared to state-of-the art RL our model-based policy search method achieves an unprecedented speed of learning. We demonstrate its applicability to autonomous learning in real robot and control tasks.

We introduce scalable deep kernels, which combine the structural properties of deep learning architectures with the nonparametric flexibility of kernel methods. Specifically, we transform the inputs of a spectral mixture base kernel with a deep architecture, using local kernel interpolation, inducing points, and structure exploiting (Kronecker and Toeplitz) algebra for a scalable kernel representation. These closed-form kernels can be used as drop-in replacements for standard kernels, with benefits in expressive power and scalability. We jointly learn the properties of these kernels through the marginal likelihood of a Gaussian process. Inference and learning cost O(n) for n training points, and predictions cost O(1) per test point. On a large and diverse collection of applications, including a dataset with 2 million examples, we show improved performance over scalable Gaussian processes with flexible kernel learning models, and stand-alone deep architectures. Copyright 2016 by the authors.

GPflow is a Gaussian process library that uses TensorFlow for its core computations and Python for its front end. The distinguishing features of GPflow are that it uses variational inference as the primary approximation method, provides concise code through the use of automatic differentiation, has been engineered with a particular emphasis on software testing and is able to exploit GPU hardware.

We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel interpolation. The SKI framework clarifies how the quality of an inducing point approach depends on the number of inducing (aka interpolation) points, interpolation strategy, and GP covariance kernel. SKI also provides a mechanism to create new scalable kernel methods, through choosing different kernel interpolation strategies. Using SKI, with local cubic kernel interpolation, we introduce KISS-GP, which is 1) more scalable than inducing point alternatives, 2) naturally enables Kronecker and Toeplitz algebra for substantial additional gains in scalability, without requiring any grid data, and 3) can be used for fast and expressive kernel learning. KISS-GP costs O(n) time and storage for GP inference. We evaluate KISS-GP for kernel matrix approximation, kernel learning, and natural sound modelling. © Copyright 2015 by International Machine Learning Society (IMLS). All rights reserved.