A linear memory algorithm for Baum-Welch training

Background: Baum-Welch training is an expectation-maximisation algorithm for training the emission and transition probabilities of hidden Markov models in a fully automated way. Methods and results: We introduce a linear space algorithm for Baum-Welch training. For a hidden Markov model with M states, T free transition and E free emission parameters, and an input sequence of length L, our new algorithm requires O(M) memory and O(L M T_max (T + E)) time for one Baum-Welch iteration, where T_max is the maximum number of states that any state is connected to. The most memory efficient algorithm until now was the checkpointing algorithm with O(log(L) M) memory and O(log(L) L M T_max) time requirement. Our novel algorithm thus renders the memory requirement completely independent of the length of the training sequences. More generally, for an n-hidden Markov model and n input sequences of length L, the memory requirement of O(log(L) L^(n-1) M) is reduced to O(L^(n-1) M) memory while the running time is changed from O(log(L) L^n M T_max + L^n (T + E)) to O(L^n M T_max (T + E)). Conclusions: For the large class of hidden Markov models used for example in gene prediction, whose number of states does not scale with the length of the input sequence, our novel algorithm can thus be both faster and more memory-efficient than any of the existing algorithms.Comment: 14 pages, 1 figure version 2: fixed some errors, final version of pape

Unsupervised Neural Hidden Markov Models

In this work, we present the first results for neuralizing an Unsupervised Hidden Markov Model. We evaluate our approach on tag in- duction. Our approach outperforms existing generative models and is competitive with the state-of-the-art though with a simpler model easily extended to include additional context.Comment: accepted at EMNLP 2016, Workshop on Structured Prediction for NLP. Oral presentatio

Duration modeling with expanded HMM applied to speech recognition

The occupancy of the HMM states is modeled by means of a Markov chain. A linear estimator is introduced to compute the probabilities of the Markov chain. The distribution function (DF) represents accurately the observed data. Representing the DF as a Markov chain allows the use of standard HMM recognizers. The increase of complexity is negligible in training and strongly limited during recognition. Experiments performed on acoustic-phonetic decoding shows how the phone recognition rate increases from 60.6 to 61.1. Furthermore, on a task of database inquires, where phones are used as subword units, the correct word rate increases from 88.2 to 88.4.Peer ReviewedPostprint (published version

Information matrix for hidden Markov models with covariates

For a general class of hidden Markov models that may include time-varying covariates, we illustrate how to compute the observed information matrix, which may be used to obtain standard errors for the parameter estimates and check model identifiability. The proposed method is based on the Oakes’ identity and, as such, it allows for the exact computation of the information matrix on the basis of the output of the expectation-maximization (EM) algorithm for maximum likelihood estimation. In addition to this output, the method requires the first derivative of the posterior probabilities computed by the forward-backward recursions introduced by Baum and Welch. Alternative methods for computing exactly the observed information matrix require, instead, to differentiate twice the forward recursion used to compute the model likelihood, with a greater additional effort with respect to the EM algorithm. The proposed method is illustrated by a series of simulations and an application based on a longitudinal dataset in Health Economics

Regime switching volatility calibration by the Baum-Welch method

Regime switching volatility models provide a tractable method of modelling stochastic volatility. Currently the most popular method of regime switching calibration is the Hamilton filter. We propose using the Baum-Welch algorithm, an established technique from Engineering, to calibrate regime switching models instead. We demonstrate the Baum-Welch algorithm and discuss the significant advantages that it provides compared to the Hamilton filter. We provide computational results of calibrating and comparing the performance of the Baum-Welch and the Hamilton filter to S&P 500 and Nikkei 225 data, examining their performance in and out of sample