Probabilistic structure discovery in time series data

Existing methods for structure discovery in time series data construct interpretable, compositional kernels for Gaussian process regression models. While the learned Gaussian process model provides posterior mean and variance estimates, typically the structure is learned via a greedy optimization procedure. This restricts the space of possible solutions and leads to over-confident uncertainty estimates. We introduce a fully Bayesian approach, inferring a full posterior over structures, which more reliably captures the uncertainty of the model.

[1]  Guigang Zhang,et al.  Deep Learning , 2016, Int. J. Semantic Comput..

[2]  Leo Breiman,et al.  Random Forests , 2001, Machine Learning.

[3]  Kostas Stathis,et al.  Probabilistic Programming with Gaussian Process Memoization , 2015, ArXiv.

[4]  W. Gilks,et al.  Following a moving target—Monte Carlo inference for dynamic Bayesian models , 2001 .

[5]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[6]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[7]  J. Marin,et al.  Population Monte Carlo , 2004 .

[8]  Joshua B. Tenenbaum,et al.  Structure Discovery in Nonparametric Regression through Compositional Kernel Search , 2013, ICML.

[9]  Roger Baker Grosse,et al.  Model selection in compositional spaces , 2014 .

[10]  Frank D. Wood,et al.  A New Approach to Probabilistic Programming Inference , 2014, AISTATS.

[11]  Yee Whye Teh,et al.  Top-down particle filtering for Bayesian decision trees , 2013, ICML.

[12]  Aaron Klein,et al.  Efficient and Robust Automated Machine Learning , 2015, NIPS.

[13]  P. Moral,et al.  Sequential Monte Carlo samplers , 2002, cond-mat/0212648.

[14]  Frank D. Wood,et al.  Canonical Correlation Forests , 2015, ArXiv.

[15]  Corinna Cortes,et al.  Support-Vector Networks , 1995, Machine Learning.

[16]  Joshua B. Tenenbaum,et al.  Automatic Construction and Natural-Language Description of Nonparametric Regression Models , 2014, AAAI.

[17]  H. Chipman,et al.  Bayesian CART Model Search , 1998 .

[18]  Hinrich Schütze,et al.  Book Reviews: Foundations of Statistical Natural Language Processing , 1999, CL.

[19]  Senén Barro,et al.  Do we need hundreds of classifiers to solve real world classification problems? , 2014, J. Mach. Learn. Res..