Efficient Learning and Feature Selection in High-Dimensional Regression

• Published in: Neural computation Vol. 22; no. 4; pp. 831 - 886
• Main Authors: Ting, Jo-Anne, D'Souza, Aaron, Vijayakumar, Sethu, Schaal, Stefan
• Format: Journal Article
• Language: English
• Published: One Rogers Street, Cambridge, MA 02142-1209, USA MIT Press 01.04.2010; MIT Press Journals, The
• Subjects: Algorithms; Applied sciences; Approximation; Artificial intelligence; Bayesian analysis; Biological and medical sciences; Computer science; control theory; systems; Exact sciences and technology; Fundamental and applied biological sciences. Psychology; General aspects; Humans; Learning; Learning - physiology; Learning and adaptive systems; Letters; Linear Models; Mathematics; Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects); Miscellaneous; Neural Networks (Computer); Neurobiology; Parametric inference; Pattern Recognition, Automated; Probability and statistics; Regression analysis; Sciences and techniques of general use; Statistics; Brain; Neural computation; Estimator robustness; Iterative method; Approximation algorithm; Linear model; Robotics; Relevance; Least squares method; Classification; Learning algorithm; Bayes estimation; Maximization; Non linear regression; Linear regression; Benchmarks; Nonlinear problems; Neural network; Real time; Statistical method; Statistical regression; Selection problem; Regression model; Detection; Interface; Automatic
• ISSN: 0899-7667; 1530-888X
• DOI: 10.1162/neco.2009.02-08-702

We present a novel algorithm for efficient learning and feature selection in high-dimensional regression problems. We arrive at this model through a modification of the standard regression model, enabling us to derive a probabilistic version of the well-known statistical regression technique of backfitting. Using the expectation-maximization algorithm, along with variational approximation methods to overcome intractability, we extend our algorithm to include automatic relevance detection of the input features. This variational Bayesian least squares (VBLS) approach retains its simplicity as a linear model, but offers a novel statistically robust black-box approach to generalized linear regression with high-dimensional inputs. It can be easily extended to nonlinear regression and classification problems. In particular, we derive the framework of sparse Bayesian learning, the relevance vector machine, with VBLS at its core, offering significant computational and robustness advantages for this class of methods. The iterative nature of VBLS makes it most suitable for real-time incremental learning, which is crucial especially in the application domain of robotics, brain-machine interfaces, and neural prosthetics, where real-time learning of models for control is needed. We evaluate our algorithm on synthetic and neurophysiological data sets, as well as on standard regression and classification benchmark data sets, comparing it with other competitive statistical approaches and demonstrating its suitability as a drop-in replacement for other generalized linear regression techniques.