## AbstractWe propose a set of Bayesian methods that help us toward the goal of autonomous learning systems. Systems that can react autonomously, with minimal human supervision, have the potential for significant impact, especially in applications with considerable uncertainty in the environment. In current algorithms, parameter values are set using heuristic techniques, statistical cross-validation or other search procedures to find the "right'' values. We rely on Bayesian inference as a principled way to eliminate open parameters, resulting in a black-box-like approach. We are interested in scenarios where the input data is high-dimensional (and many input dimensions may be redundant or irrelevant) and where real-time, incremental learning may be needed. Such data sets are common in the domain of robotics and brain-machine interfaces, which are the main areas of evaluation in this dissertation. We start by examining the problem of regression since classification can be performed by interpreting regression outputs in a binary way. This dissertation first introduces a set of autonomous Bayesian methods that learn from data with the following properties: a high number of input dimensions, noise in input data, and outliers. All these methods can be leveraged together to develop a local Bayesian kernel shaping framework for nonlinear regression. The Bayesian kernel shaping algorithm we propose is the first step towards realizing real-time autonomous learning systems. Even though the version described in this thesis is in batch form, it is computationally efficient and can be used in not only local methods, but also global nonlinear methods such as Gaussian processes for non-stationary function approximation.
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