Tensor Train Spectral Method for Learning Hidden Markov Models

  • Maxim Kuznetsov (Skolkovo Institute of Science and Technology)
G3 10 (Lecture hall)


We propose a new algorithm for spectral learning of Hidden Markov Models (HMM). In contrast to the standard approach, we do not estimate the parameters of the HMM directly, but construct an estimate for the joint probability distribution. The idea is based on the representation of a joint probability distribution as an N-th-order tensor with low ranks represented in the tensor train (TT) format. Using TT-format, we get an approximation by minimizing the Frobenius distance between the empirical joint probability distribution and tensors with low TT-ranks with core tensors normalization constraints. We propose an algorithm for the solution of the optimization problem that is based on the alternating least squares (ALS) approach and develop its fast version for sparse tensors.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

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