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The Baum-Welsh algorithm together with its derivatives and variations has been the main technique for learning Hidden Markov Models (HMM) from observational data. We present an HMM learning algorithm based on the non-negative matrix factorization (NMF) of higher order Markovian statistics that is structurally different from the Baum-Welsh and its associated approaches. The described algorithm supports estimation of the number of recurrent states of an HMM and iterates the non-negative matrix factorization (NMF) algorithm to improve the learned HMM parameters. Numerical examples are provided as well.
Hidden Markov Models (HMMs) are one of the most fundamental and widely used statistical tools for modeling discrete time series. In general, learning HMMs from data is computationally hard (under cryptographic assumptions), and practitioners typicall
The California Innocence Project (CIP), a clinical law school program aiming to free wrongfully convicted prisoners, evaluates thousands of mails containing new requests for assistance and corresponding case files. Processing and interpreting this la
Airborne gamma-ray surveys are useful for many applications, ranging from geology and mining to public health and nuclear security. In all these contexts, the ability to decompose a measured spectrum into a linear combination of background source ter
Extracting genetic information from a full range of sequencing data is important for understanding diseases. We propose a novel method to effectively explore the landscape of genetic mutations and aggregate them to predict cancer type. We used multin
Linear models have shown great effectiveness and flexibility in many fields such as machine learning, signal processing and statistics. They can represent rich spaces of functions while preserving the convexity of the optimization problems where they