Duration and Interval Hidden Markov Model for Sequential Data Analysis

Analysis of sequential event data has been recognized as one of the essential tools in data modeling and analysis field. In this paper, after the examination of its technical requirements and issues to model complex but practical situation, we propose a new sequential data model, dubbed Duration and Interval Hidden Markov Model (DI-HMM), that efficiently represents "state duration" and "state interval" of data events. This has significant implications to play an important role in representing practical time-series sequential data. This eventually provides an efficient and flexible sequential data retrieval. Numerical experiments on synthetic and real data demonstrate the efficiency and accuracy of the proposed DI-HMM

Statistical identification with hidden Markov models of large order splitting strategies in an equity market

Large trades in a financial market are usually split into smaller parts and traded incrementally over extended periods of time. We address these large trades as hidden orders. In order to identify and characterize hidden orders we fit hidden Markov models to the time series of the sign of the tick by tick inventory variation of market members of the Spanish Stock Exchange. Our methodology probabilistically detects trading sequences, which are characterized by a net majority of buy or sell transactions. We interpret these patches of sequential buying or selling transactions as proxies of the traded hidden orders. We find that the time, volume and number of transactions size distributions of these patches are fat tailed. Long patches are characterized by a high fraction of market orders and a low participation rate, while short patches have a large fraction of limit orders and a high participation rate. We observe the existence of a buy-sell asymmetry in the number, average length, average fraction of market orders and average participation rate of the detected patches. The detected asymmetry is clearly depending on the local market trend. We also compare the hidden Markov models patches with those obtained with the segmentation method used in Vaglica {\it et al.} (2008) and we conclude that the former ones can be interpreted as a partition of the latter ones.Comment: 26 pages, 12 figure

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

Implementation of hidden semi-Markov models

One of the most frequently used concepts applied to a variety of engineering and scientific studies over the recent years is that of a Hidden Markov Model (HMM). The Hidden semi-Markov model (HsMM) is contrived in such a way that it does not make any premise of constant or geometric distributions of a state duration. In other words, it allows the stochastic process to be a semi-Markov chain. Each state can have a collection of observations and the duration of each state is a variable. This allows the HsMM to be used extensively over a range of applications. Some of the most prominent work is done in speech recognition, gene prediction, and character recognition. This thesis deals with the general structure and modeling of Hidden semi-Markov models and their implementations. It will further show the details of evaluation, decoding, and training with a running example

A Unified Multilingual Handwriting Recognition System using multigrams sub-lexical units

We address the design of a unified multilingual system for handwriting recognition. Most of multi- lingual systems rests on specialized models that are trained on a single language and one of them is selected at test time. While some recognition systems are based on a unified optical model, dealing with a unified language model remains a major issue, as traditional language models are generally trained on corpora composed of large word lexicons per language. Here, we bring a solution by con- sidering language models based on sub-lexical units, called multigrams. Dealing with multigrams strongly reduces the lexicon size and thus decreases the language model complexity. This makes pos- sible the design of an end-to-end unified multilingual recognition system where both a single optical model and a single language model are trained on all the languages. We discuss the impact of the language unification on each model and show that our system reaches state-of-the-art methods perfor- mance with a strong reduction of the complexity.Comment: preprin