Baum-Welch Research Articles

Parameter estimation for robust HMM analysis of ChIP-chip data

BackgroundTiling arrays are an important tool for the study of transcriptional activity, protein-DNA interactions and chromatin structure on a genome-wide scale at high resolution. Although hidden Markov models have been used successfully to analyse tiling array data, parameter estimation for these models is typically ad hoc. Especially in the context of ChIP-chip experiments, no standard procedures exist to obtain parameter estimates from the data. Common methods for the calculation of maximum likelihood estimates such as the Baum-Welch algorithm or Viterbi training are rarely applied in the context of tiling array analysis.ResultsHere we develop a hidden Markov model for the analysis of chromatin structure ChIP-chip tiling array data, using t emission distributions to increase robustness towards outliers. Maximum likelihood estimates are used for all model parameters. Two different approaches to parameter estimation are investigated and combined into an efficient procedure.ConclusionWe illustrate an efficient parameter estimation procedure that can be used for HMM based methods in general and leads to a clear increase in performance when compared to the use of ad hoc estimates. The resulting hidden Markov model outperforms established methods like TileMap in the context of histone modification studies.

Modelling pronunciation variation with single-path and multi-path syllable models: Issues to consider

In this paper, we construct context-independent single-path and multi-path syllable models aimed at improved pronunciation variation modelling. We use phonetic transcriptions to define the topologies of the syllable models and to initialise the model parameters, and the Baum–Welch algorithm for the re-estimation of the model parameters. We hypothesise that the richer topology of multi-path syllable models would be better at accounting for pronunciation variation than context-dependent phone models that can only account for the effects of the left and right neighbours, or single-path syllable models whose power of modelling segmental variation would seem to be limited. However, both context-dependent phone models and single-path syllable models outperform multi-path syllable models on a large-vocabulary continuous speech recognition task. Careful analyses of the errors made by the recognisers with single-path and multi-path syllable models show that the most important factors affecting the speech recognition performance are syllable context and lexical confusability. In addition, the speech recognition results suggest that the benefits of the greater acoustic modelling accuracy of the multi-path syllable models can only be reaped if the information about the syllable-level pronunciation variation can be linked with the word-level information in the language model.

Off-line recognition of realistic Chinese handwriting using segmentation-free strategy

Great challenges are faced in the off-line recognition of realistic Chinese handwriting. This paper presents a segmentation-free strategy based on Hidden Markov Model (HMM) to handle this problem, where character segmentation stage is avoided prior to recognition. Handwritten textlines are first converted to observation sequence by sliding windows. Then embedded Baum–Welch algorithm is adopted to train character HMMs. Finally, best character string maximizing the a posteriori is located through Viterbi algorithm. Experiments are conducted on the HIT-MW database written by more than 780 writers. The results show the feasibility of such systems and reveal apparent complementary capacities between the segmentation-free systems and the segmentation-based ones.

Implementing EM and Viterbi algorithms for Hidden Markov Model in linear memory

BackgroundThe Baum-Welch learning procedure for Hidden Markov Models (HMMs) provides a powerful tool for tailoring HMM topologies to data for use in knowledge discovery and clustering. A linear memory procedure recently proposed by Miklós, I. and Meyer, I.M. describes a memory sparse version of the Baum-Welch algorithm with modifications to the original probabilistic table topologies to make memory use independent of sequence length (and linearly dependent on state number). The original description of the technique has some errors that we amend. We then compare the corrected implementation on a variety of data sets with conventional and checkpointing implementations.ResultsWe provide a correct recurrence relation for the emission parameter estimate and extend it to parameter estimates of the Normal distribution. To accelerate estimation of the prior state probabilities, and decrease memory use, we reverse the originally proposed forward sweep. We describe different scaling strategies necessary in all real implementations of the algorithm to prevent underflow. In this paper we also describe our approach to a linear memory implementation of the Viterbi decoding algorithm (with linearity in the sequence length, while memory use is approximately independent of state number). We demonstrate the use of the linear memory implementation on an extended Duration Hidden Markov Model (DHMM) and on an HMM with a spike detection topology. Comparing the various implementations of the Baum-Welch procedure we find that the checkpointing algorithm produces the best overall tradeoff between memory use and speed. In cases where sequence length is very large (for Baum-Welch), or state number is very large (for Viterbi), the linear memory methods outlined may offer some utility.ConclusionOur performance-optimized Java implementations of Baum-Welch algorithm are available at . The described method and implementations will aid sequence alignment, gene structure prediction, HMM profile training, nanopore ionic flow blockades analysis and many other domains that require efficient HMM training with EM.

Using target-language information to train part-of-speech taggers for machine translation

Although corpus-based approaches to machine translation (MT) are growing in interest, they are not applicable when the translation involves less-resourced language pairs for which there are no parallel corpora available; in those cases, the rule-based approach is the only applicable solution. Most rule-based MT systems make use of part-of-speech (PoS) taggers to solve the PoS ambiguities in the source-language texts to translate; those MT systems require accurate PoS taggers to produce reliable translations in the target language (TL). The standard statistical approach to PoS ambiguity resolution (or tagging) uses hidden Markov models (HMM) trained in a supervised way from hand-tagged corpora, an expensive resource not always available, or in an unsupervised way through the Baum-Welch expectation-maximization algorithm; both methods use information only from the language being tagged. However, when tagging is considered as an intermediate task for the translation procedure, that is, when the PoS tagger is to be embedded as a module within an MT system, information from the TL can be (unsupervisedly) used in the training phase to increase the translation quality of the whole MT system. This paper presents a method to train HMM-based PoS taggers to be used in MT; the new method uses not only information from the source language (SL), as general-purpose methods do, but also information from the TL and from the remaining modules of the MT system in which the PoS tagger is to be embedded. We find that the translation quality of the MT system embedding a PoS tagger trained in an unsupervised manner through this new method is clearly better than that of the same MT system embedding a PoS tagger trained through the Baum-Welch algorithm, and comparable to that obtained by embedding a PoS tagger trained in a supervised way from hand-tagged corpora.

은닉 마르코프 모델의 다목적함수 최적화를 통한 자동 독순의 성능 향상

This paper proposes a new multiobjective optimization method for discriminative training of hidden Markov models (HMMs) used as the recognizer for automatic lipreading. While the conventional Baum-Welch algorithm for training HMMs aims at maximizing the probability of the data of a class from the corresponding HMM, we define a new training criterion composed of two minimization objectives and develop a global optimization method of the criterion based on simulated annealing. The result of a speaker-dependent recognition experiment shows that the proposed method improves performance by the relative error reduction rate of about 8% in comparison to the Baum-Welch algorithm.

Activity Classification for Interactive Game Interfaces

We present a technique for modeling and recognising human activity from moving light displays using hidden Markov models. We extract a small number of joint angles at each frame to form a feature vector. Continuous hidden Markov models are then trained with the resulting time series, one for each of a variety of human activity, using the Baum-Welch algorithm. Motion classification is then attempted by evaluation of the forward variable for each model using previously unseen test data. Experimental results based on real-world human motion capture data demonstrate the performance of the algorithm and some degree of robustness to data noise and human motion irregularity. This technique has potential applications in activity classification for gesture-based game interfaces and character animation.

Speeding Up HMM Decoding and Training by Exploiting Sequence Repetitions

We present a method to speed up the dynamic program algorithms used for solving the HMM decoding and training problems for discrete time-independent HMMs. We discuss the application of our method to Viterbi’s decoding and training algorithms (IEEE Trans. Inform. Theory IT-13:260–269, 1967), as well as to the forward-backward and Baum-Welch (Inequalities 3:1–8, 1972) algorithms. Our approach is based on identifying repeated substrings in the observed input sequence. Initially, we show how to exploit repetitions of all sufficiently small substrings (this is similar to the Four Russians method). Then, we describe four algorithms based alternatively on run length encoding (RLE), Lempel-Ziv (LZ78) parsing, grammar-based compression (SLP), and byte pair encoding (BPE). Compared to Viterbi’s algorithm, we achieve speedups of Θ(log n) using the Four Russians method, \(\Omega(\frac{r}{\log r})\) using RLE, \(\Omega(\frac{\log n}{k})\) using LZ78, \(\Omega(\frac{r}{k})\) using SLP, and Ω(r) using BPE, where k is the number of hidden states, n is the length of the observed sequence and r is its compression ratio (under each compression scheme). Our experimental results demonstrate that our new algorithms are indeed faster in practice. We also discuss a parallel implementation of our algorithms.

An evolutionary method for learning HMM structure: prediction of protein secondary structure.

BackgroundThe prediction of the secondary structure of proteins is one of the most studied problems in bioinformatics. Despite their success in many problems of biological sequence analysis, Hidden Markov Models (HMMs) have not been used much for this problem, as the complexity of the task makes manual design of HMMs difficult. Therefore, we have developed a method for evolving the structure of HMMs automatically, using Genetic Algorithms (GAs).ResultsIn the GA procedure, populations of HMMs are assembled from biologically meaningful building blocks. Mutation and crossover operators were designed to explore the space of such Block-HMMs. After each step of the GA, the standard HMM estimation algorithm (the Baum-Welch algorithm) was used to update model parameters. The final HMM captures several features of protein sequence and structure, with its own HMM grammar. In contrast to neural network based predictors, the evolved HMM also calculates the probabilities associated with the predictions. We carefully examined the performance of the HMM based predictor, both under the multiple- and single-sequence condition.ConclusionWe have shown that the proposed evolutionary method can automatically design the topology of HMMs. The method reads the grammar of protein sequences and converts it into the grammar of an HMM. It improved previously suggested evolutionary methods and increased the prediction quality. Especially, it shows good performance under the single-sequence condition and provides probabilistic information on the prediction result. The protein secondary structure predictor using HMMs (P.S.HMM) is on-line available http://www.binf.ku.dk/~won/pshmm.htm. It runs under the single-sequence condition.

Joint Channel Estimation and Symbol Detection for Orthogonal Space-Time Block-Coding Systems in Frequency-Selective Channels

Orthogonal space-time block coding (OSTBC) in multiple-antenna wireless systems has recently emerged as one of the most promising reliability-enhancing technologies for high-speed, high-quality data services. In this paper, we propose a technique to achieve joint channel estimation and symbol detection for OSTBC in frequency-selective fading channels. The key observation is that a multiple-input-single-output system, which is using OSTBC, can be transformed into an equivalent single-input-multiple-output system using the implicit redundancy in OSTBC. This allows a probabilistic method, known as the Baum-Welch algorithm, to be applied at each output branch. As each output branch is a function of the same input, redundant information may be exchanged between the multiple branches to improve detection performance. The proposed technique does not require multiple antennas at the receiver and only has moderate computational complexity. Furthermore, the Cramer-Rao lower bound (CRB) is also developed to facilitate performance analysis. Simulation results are provided to demonstrate the performance of the proposed algorithm.

Linear Spectral Transformation for Robust Speech Recognition Using Maximum Mutual Information

This paper presents a transformation-based rapid adaptation technique for robust speech recognition using a linear spectral transformation (LST) and a maximum mutual information (MMI) criterion. Previously, a maximum likelihood linear spectral transformation (ML-LST) algorithm was proposed for fast adaptation in unknown environments. Since the MMI estimation method does not require evenly distributed training data and increases the a posteriori probability of the word sequences of the training data, we combine the linear spectral transformation method and the MMI estimation technique in order to achieve extremely rapid adaptation using only one word of adaptation data. The proposed algorithm, called MMI-LST, was implemented using the extended Baum-Welch algorithm and phonetic lattices, and evaluated on the TIMIT and FFMTIMIT corpora. It provides a relative reduction in the speech recognition error rate of 11.1% using only 0.25 s of adaptation data.

A new look at discriminative training for hidden Markov models

Discriminative training for hidden Markov models (HMMs) has been a central theme in speech recognition research for many years. One most popular technique is minimum classification error (MCE) training, with the objective function closely related to the empirical error rate and with the optimization method based traditionally on gradient descent. In this paper, we provide a new look at the MCE technique in two ways. First, we develop a non-trivial framework in which the MCE objective function is re-formulated as a rational function for multiple sentence-level training tokens. Second, using this novel re-formulation, we develop a new optimization method for discriminatively estimating HMM parameters based on growth transformation or extended Baum–Welch algorithm. Technical details are given for the use of lattices as a rich representation of competing candidates for the MCE training.

On Adjusted Viterbi Training

The EM algorithm is a principal tool for parameter estimation in the hidden Markov models, where its efficient implementation is known as the Baum–Welch algorithm. This paper is however motivated by applications where EM is replaced by Viterbi training, or extraction (VT), also known as the Baum–Viterbi algorithm. VT is computationally less intensive and more stable, and has more of an intuitive appeal. However, VT estimators are also biased and inconsistent. Recently, we have proposed elsewhere the adjusted Viterbi training (VA), a new method to alleviate the above imprecision of the VT estimators while preserving the computational advantages of the baseline VT algorithm. The key difference between VA and VT is that asymptotically, the true parameter values are a fixed point of VA (and EM), but not of VT. We have previously studied VA for a special case of Gaussian mixtures, including simulations to illustrate its improved performance. The present work proves the asymptotic fixed point property of VA for general hidden Markov models.

Channel-parameter estimation for turbo trellis coded modulation in OFDM systems

In this paper, a blind maximum-likelihood channel-parameter estimation algorithm is developed for turbo trellis coded modulation (TTCM) in orthogonal frequency division multiplexing (OFDM) systems. We modify the Baum-Welch (BW) parameter estimation algorithm to provide a computationally efficient solution for error performance. The bit-error performance of the TTCM-OFDM scheme has been investigated in AWGN, Rayleigh, Rician channels with and without channel-state information (CSI) for different Doppler shifts, signal-to-noise ratios (SNR), iteration numbers, number of subcarriers, and frame sizes.

Rain attenuation time series synthesis with combined Markov models for microwave terrestrial links

This contribution provides a method to synthesise rain attenuation time series for microwave terrestrial radio links. The time series generator is based on the combination of a two-state Markov chain to model the long-term attenuation behaviour of the link, and a Hidden Markov Model (HMM) which generates the fine structure of the attenuation. This combined method is required due to the non-stationary behaviour of the attenuation process. The parameters of the two-state model are determined from the fade duration statistics of the link. The HMM will be parameterised with the Baum-Welch Algorithm (BWA) applying a measurement database containing attenuation time series of a 38 GHz terrestrial radio link. The combination of the long-term model with the HMM can be applied to synthesise time series for any duration by taking into account that the model parameters may vary depending on the local climatic variations.

Real Time Monitoring of Cutting Chatter Based on Fuzzy Hidden Markov Models

The full automation of machine tools has gained substantial importance in manufacturing industries in recent years, as machining technology has progressed from manually operated production machines to highly advanced and sophisticated CNC machine tool. Whereas manufacturing technology has moved to the stage of automation, there is still an unsolved problem in metal cutting processes: cutting chatter. Due to its complexity, thus cutting chatter is still the primary problem in metal cutting processes. According to the characteristic of cutting chatter, a real time monitoring technique of cutting chatter based on fuzzy hidden Markov model (FHMM) was presented. Hidden Markov model (HMM) is a state-of-the-art technique for speech recognition because of its elegant mathematical structure and the availability of computer implementation of these models. In this paper, the fuzzy EM algorithm was used to the Baum-Welch algorithm in the HMM method, and the strategy of time frequency feature extraction to non-stability signal was described. The experimental results show that the proposed method is feasible and effective for the monitoring of cutting chatter in the metal cutting processes.

Blind equalization of multilevel turbo coded‐continuous phase frequency shift keying over MIMO channels

AbstractIn this paper, multilevel turbo coded‐continuous phase frequency shift keying (MLTC‐CPFSK) is introduced and its bit error performance in multiple input multiple output (MIMO) fading channels are investigated considering a blind maximum likelihood channel estimation. Multilevel turbo coded signals with continuous phase modulation (CPM) provides low spectral occupancy and is suitable for power and bandwidth‐limited channels. Besides, antenna diversity is one of the best method to combat with multipath fading effects. The performance of 2LTC for 4‐ary CPFSK over AWGN, Rician (for Rician channel parameter K=10 dB) and Rayleigh channels are given for 1Tx–1Rx, 2Tx–1Rx and 2Tx–2Rx antenna configurations. Channel capacities of 2LTC‐4CPFSK signals are obtained as −5.26, −7.65 and −7.14 dB for 1Tx–1Rx, 2Tx–1Rx and 2Tx–2Rx antenna configurations, respectively. Baum–Welch (BW) algorithm is used to estimate the channel parameters. Bit error probabilities of 2 level turbo coded 4 CPFSK (2LTC‐4CPFSK) are drawn in the cases of no channel state information (CSI), BW estimation, and perfect CSI. Approximately 0.1 and 0.75 dB gains in Es/N0 are obtained using BW channel estimator for Rician and Rayleigh channels, respectively. Therefore, MLTC‐CPFSK with BW channel estimator has excellent performance in MIMO fading channels. Copyright © 2006 John Wiley & Sons, Ltd.

Extraction of timing error parameters from readback waveforms

In this paper, we consider the problem of modeling the timing error process in magnetic recording systems. We propose a discrete-valued Markov model for the timing error process, and design two methods (data-aided and nondata-aided), based on the Baum-Welch algorithm, to extract the model parameters from the readback waveforms. The channel model we consider is an intersymbol interference (ISI) channel with additive Gaussian noise. The continuous-time readback signal at the output of the channel is sampled at baud-rate. Simulation results show that the estimated parameters are close to the actual values and the convergence is attained in a few iterations of the Baum-Welch algorithm. We also demonstrate the usefulness of the accurate model extraction by comparing a fine-tuned Markov timing recovery loop to the standard Mueller and Muller detector with a tuned second-order loop filter.

Evolving the structure of hidden Markov models

A genetic algorithm (GA) is proposed for finding the structure of hidden Markov Models (HMMs) used for biological sequence analysis. The GA is designed to preserve biologically meaningful building blocks. The search through the space of HMM structures is combined with optimization of the emission and transition probabilities using the classic Baum-Welch algorithm. The system is tested on the problem of finding the promoter and coding region of C. jejuni. The resulting HMM has a superior discrimination ability to a handcrafted model that has been published in the literature.

FAULT DIAGNOSIS TECHNIQUE OF ROTATING MACHINE BASED ON CHMM

Hidden Markov model(HMM) as a tool for disposing signal pattern which has great ability of building time sequence, has widely been used in speech recognition. It is especially fit for signal which is nonlinear, non-stationary, bad in repeating to analysis. Based on the comparability between vibration signal and sound signal, CHMM is introduced to fault diagnosis for rotating machine. CHMM is built by using 12 rank LPC cep-strum coefficient to extract feature vectors, scaled for-wards-backwards algorithm is introduced to calculate log-likelihood avoiding the data to underflow and k-means algorithm is also used to initialize the parameter. In the given observation sequence, optimizing every model with Viterbi algorithm, with baum-welch algorithm to re-estimate parameter, and the re-estimation formula is also provided. Last, four kinds of fault experiment have been simulated on the rotor test-bed, and four kinds of fault CHMM model are built. Machine's operating state is determined by calculating the maximal log-likelihood, and the results of experiment proves that this kind of method is effective.