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Predictive State Representations (PSRs) are powerful techniques for modellingdynamical systems, which represent a state as a vector of predictions aboutfuture observable events (tests). In PSRs, one of the fundamental problems isthe learning of the PSR model of the underlying system. Recently, spectralmethods have been successfully used to address this issue by treating thelearning problem as the task of computing an singular value decomposition (SVD)over a submatrix of a special type of matrix called the Hankel matrix. Underthe assumptions that the rows and columns of the submatrix of the Hankel Matrixare sufficient~(which usually means a very large number of rows and columns,and almost fails in practice) and the entries of the matrix can be estimatedaccurately, it has been proven that the spectral approach for learning PSRs isstatistically consistent and the learned parameters can converge to the trueparameters. However, in practice, due to the limit of the computation ability,only a finite set of rows or columns can be chosen to be used for the spectrallearning. While different sets of columns usually lead to variant accuracy ofthe learned model, in this paper, we propose an approach for selecting the setof columns, namely basis selection, by adopting a concept of model entropy tomeasure the accuracy of the learned model. Experimental results are shown todemonstrate the effectiveness of the proposed approach.

Selecting Bases in Spectral learning of Predictive State Representations via Model Entropy