Hidden state models for time series

Amongst all the objectives in the study of time series, uncovering the dynamic law of its generation is probably the most important. When the underlying dynamics are not available, time series modelling consists of developing a model which best explains a sequence of observations. In this thesis, we consider hidden space models for analysing and describing time series. We first provide an introduction to the principal concepts of hidden state models and draw an analogy between hidden Markov models and state space models. Central ideas such as hidden state inference or parameter estimation are reviewed in detail. A key part of multivariate time series analysis is identifying the delay between different variables. We present a novel approach for time delay estimating in a non-stationary environment. The technique makes use of hidden Markov models and we demonstrate its application for estimating a crucial parameter in the oil industry. We then focus on hybrid models that we call dynamical local models. These models combine and generalise hidden Markov models and state space models. Probabilistic inference is unfortunately computationally intractable and we show how to make use of variational techniques for approximating the posterior distribution over the hidden state variables. Experimental simulations on synthetic and real-world data demonstrate the application of dynamical local models for segmenting a time series into regimes and providing predictive distributions.

Allosteric Control of Gating Mechanisms Revisited: The Large Conductance Ca(2+)-Activated K(+) Channel

Large-conductance Ca(2+)-activated K(+) channels (BK) play a fundamental role in modulating membrane potential in many cell types. The gating of BK channels and its modulation by Ca(2+) and voltage has been the subject of intensive research over almost three decades, yielding several of the most complicated kinetic mechanisms ever proposed. A large number of open and closed states disposed, respectively, in two planes, named tiers, characterize these mechanisms. Transitions between states in the same plane are cooperative and modulated by Ca(2+). Transitions across planes are highly concerted and voltage-dependent. Here we reexamine the validity of the two-tiered hypothesis by restricting attention to the modulation by Ca(2+). Large single channel data sets at five Ca(2+) concentrations were simultaneously analyzed from a Bayesian perspective by using hidden Markov models and Markov-chain Monte Carlo stochastic integration techniques. Our results support a dramatic reduction in model complexity, favoring a simple mechanism derived from the Monod-Wyman-Changeux allosteric model for homotetramers, able to explain the Ca(2+) modulation of the gating process. This model differs from the standard Monod-Wyman-Changeux scheme in that one distinguishes when two Ca(2+) ions are bound to adjacent or diagonal subunits of the tetramer.

Musical genres: beating to the rhythms of different drums

Online music databases have increased significantly as a consequence of the rapid growth of the Internet and digital audio, requiring the development of faster and more efficient tools for music content analysis. Musical genres are widely used to organize music collections. In this paper, the problem of automatic single and multi-label music genre classification is addressed by exploring rhythm-based features obtained from a respective complex network representation. A Markov model is built in order to analyse the temporal sequence of rhythmic notation events. Feature analysis is performed by using two multi-variate statistical approaches: principal components analysis (unsupervised) and linear discriminant analysis (supervised). Similarly, two classifiers are applied in order to identify the category of rhythms: parametric Bayesian classifier under the Gaussian hypothesis (supervised) and agglomerative hierarchical clustering (unsupervised). Qualitative results obtained by using the kappa coefficient and the obtained clusters corroborated the effectiveness of the proposed method.

Computational methods for prediction of T-cell epitopes - a framework for modelling, testing, and applications

Computational models complement laboratory experimentation for efficient identification of MHC-binding peptides and T-cell epitopes. Methods for prediction of MHC-binding peptides include binding motifs, quantitative matrices, artificial neural networks, hidden Markov models, and molecular modelling. Models derived by these methods have been successfully used for prediction of T-cell epitopes in cancer, autoimmunity, infectious disease, and allergy. For maximum benefit, the use of computer models must be treated as experiments analogous to standard laboratory procedures and performed according to strict standards. This requires careful selection of data for model building, and adequate testing and validation. A range of web-based databases and MHC-binding prediction programs are available. Although some available prediction programs for particular MHC alleles have reasonable accuracy, there is no guarantee that all models produce good quality predictions. In this article, we present and discuss a framework for modelling, testing, and applications of computational methods used in predictions of T-cell epitopes. (C) 2004 Elsevier Inc. All rights reserved.

Tradutor da língua gestual portuguesa modelo de tradução bidireccional

O projeto tem como objetivo desenvolver e avaliar um modelo que facilita o acesso para pessoas surdas ou com deficiência auditiva, o acesso ao conteúdo digital - em particular o conteúdo educacional e objetos de aprendizagem – a criação de condições para uma maior inclusão social de surdos e deficientes auditivos. Pretende-se criar um modelo bidirecional, em que permite a pessoas com deficiências auditivas, possam se comunicar com outras pessoas, com a tradução da Língua Gestual Portuguesa (LGP) para a Língua Portuguesa (LP) e que outras pessoas não portadoras de qualquer deficiência auditiva possam por sua vez comunicar com os surdos ou deficientes auditivos através da tradução da LP para a LGP. Há um conjunto de técnicas que poderíamos nos apoiar para desenvolver o modelo e implementar a API de tradução da LGP em LP. Muitos estudos são feitos com base nos modelos escondidos de Markov (HMM) para efetuar o reconhecimento. Recentemente os estudos estão a caminhar para o uso de técnicas como o “Dynamic Time Warping” (DTW), que tem tido mais sucesso do que outras técnicas em termos de performance e de precisão. Neste projeto optamos por desenvolver a API e o Modelo, com base na técnica de aprendizagem Support Vector Machines (SVM) por ser uma técnica simples de implementar e com bons resultados demonstrados em reconhecimento de padrões. Os resultados obtidos utilizando esta técnica de aprendizagem foram bastante ótimos, como iremos descrever no decorrer do capítulo 4, mesmo sabendo que utilizamos dois dispositivos para capturar dados de descrição de cada gesto. Toda esta tese integra-se no âmbito do projeto científico/ investigação a decorrer no grupo de investigação GILT, sob a coordenação da professora Paula Escudeiro e suportado pela Fundação para Ciência e Tecnologia (FCT).

Sound Texture Modelling

In the PhD thesis “Sound Texture Modeling” we deal with statistical modelling or textural sounds like water, wind, rain, etc. For synthesis and classification. Our initial model is based on a wavelet tree signal decomposition and the modeling of the resulting sequence by means of a parametric probabilistic model, that can be situated within the family of models trainable via expectation maximization (hidden Markov tree model ). Our model is able to capture key characteristics of the source textures (water, rain, fire, applause, crowd chatter ), and faithfully reproduces some of the sound classes. In terms of a more general taxonomy of natural events proposed by Graver, we worked on models for natural event classification and segmentation. While the event labels comprise physical interactions between materials that do not have textural propierties in their enterity, those segmentation models can help in identifying textural portions of an audio recording useful for analysis and resynthesis. Following our work on concatenative synthesis of musical instruments, we have developed a pattern-based synthesis system, that allows to sonically explore a database of units by means of their representation in a perceptual feature space. Concatenative syntyhesis with “molecules” built from sparse atomic representations also allows capture low-level correlations in perceptual audio features, while facilitating the manipulation of textural sounds based on their physical and perceptual properties. We have approached the problem of sound texture modelling for synthesis from different directions, namely a low-level signal-theoretic point of view through a wavelet transform, and a more high-level point of view driven by perceptual audio features in the concatenative synthesis setting. The developed framework provides unified approach to the high-quality resynthesis of natural texture sounds. Our research is embedded within the Metaverse 1 European project (2008-2011), where our models are contributting as low level building blocks within a semi-automated soundscape generation system.

A generalized mechanistic codon model.

Models of codon evolution have attracted particular interest because of their unique capabilities to detect selection forces and their high fit when applied to sequence evolution. We described here a novel approach for modeling codon evolution, which is based on Kronecker product of matrices. The 61 × 61 codon substitution rate matrix is created using Kronecker product of three 4 × 4 nucleotide substitution matrices, the equilibrium frequency of codons, and the selection rate parameter. The entities of the nucleotide substitution matrices and selection rate are considered as parameters of the model, which are optimized by maximum likelihood. Our fully mechanistic model allows the instantaneous substitution matrix between codons to be fully estimated with only 19 parameters instead of 3,721, by using the biological interdependence existing between positions within codons. We illustrate the properties of our models using computer simulations and assessed its relevance by comparing the AICc measures of our model and other models of codon evolution on simulations and a large range of empirical data sets. We show that our model fits most biological data better compared with the current codon models. Furthermore, the parameters in our model can be interpreted in a similar way as the exchangeability rates found in empirical codon models.

GeneID in "Drosophila"

GeneID is a program to predict genes in anonymous genomic sequences designed with a hierarchical structure. In the first step, splice sites, and start and stop codons are predicted and scored along the sequence using position weight matrices (PWMs). In the second step, exons are built from the sites. Exons are scored as the sum of the scores of the defining sites, plus the log-likelihood ratio of a Markov model for coding DNA. In the last step, from the set of predicted exons, the gene structure is assembled, maximizing the sum of the scores of the assembled exons. In this paper we describe the obtention of PWMs for sites, and the Markov model of coding DNA in Drosophila melanogaster. We also compare other models of coding DNA with the Markov model. Finally, we present and discuss the results obtained when GeneID is used to predict genes in the Adh region. These results show that the accuracy of GeneID predictions compares currently with that of other existing tools but that GeneID is likely to be more efficient in terms of speed and memory usage.

The Effect of Four-Lane to Three-Lane Conversion on the Number of Crashes and Crash Rates in Iowa Roads, June 2005

We analyze crash data collected by the Iowa Department of Transportation using Bayesian methods. The data set includes monthly crash numbers, estimated monthly traffic volumes, site length and other information collected at 30 paired sites in Iowa over more than 20 years during which an intervention experiment was set up. The intervention consisted in transforming 15 undivided road segments from four-lane to three lanes, while an additional 15 segments, thought to be comparable in terms of traffic safety-related characteristics were not converted. The main objective of this work is to find out whether the intervention reduces the number of crashes and the crash rates at the treated sites. We fitted a hierarchical Poisson regression model with a change-point to the number of monthly crashes per mile at each of the sites. Explanatory variables in the model included estimated monthly traffic volume, time, an indicator for intervention reflecting whether the site was a “treatment” or a “control” site, and various interactions. We accounted for seasonal effects in the number of crashes at a site by including smooth trigonometric functions with three different periods to reflect the four seasons of the year. A change-point at the month and year in which the intervention was completed for treated sites was also included. The number of crashes at a site can be thought to follow a Poisson distribution. To estimate the association between crashes and the explanatory variables, we used a log link function and added a random effect to account for overdispersion and for autocorrelation among observations obtained at the same site. We used proper but non-informative priors for all parameters in the model, and carried out all calculations using Markov chain Monte Carlo methods implemented in WinBUGS. We evaluated the effect of the four to three-lane conversion by comparing the expected number of crashes per year per mile during the years preceding the conversion and following the conversion for treatment and control sites. We estimated this difference using the observed traffic volumes at each site and also on a per 100,000,000 vehicles. We also conducted a prospective analysis to forecast the expected number of crashes per mile at each site in the study one year, three years and five years following the four to three-lane conversion. Posterior predictive distributions of the number of crashes, the crash rate and the percent reduction in crashes per mile were obtained for each site for the months of January and June one, three and five years after completion of the intervention. The model appears to fit the data well. We found that in most sites, the intervention was effective and reduced the number of crashes. Overall, and for the observed traffic volumes, the reduction in the expected number of crashes per year and mile at converted sites was 32.3% (31.4% to 33.5% with 95% probability) while at the control sites, the reduction was estimated to be 7.1% (5.7% to 8.2% with 95% probability). When the reduction in the expected number of crashes per year, mile and 100,000,000 AADT was computed, the estimates were 44.3% (43.9% to 44.6%) and 25.5% (24.6% to 26.0%) for converted and control sites, respectively. In both cases, the difference in the percent reduction in the expected number of crashes during the years following the conversion was significantly larger at converted sites than at control sites, even though the number of crashes appears to decline over time at all sites. Results indicate that the reduction in the expected number of sites per mile has a steeper negative slope at converted than at control sites. Consistent with this, the forecasted reduction in the number of crashes per year and mile during the years after completion of the conversion at converted sites is more pronounced than at control sites. Seasonal effects on the number of crashes have been well-documented. In this dataset, we found that, as expected, the expected number of monthly crashes per mile tends to be higher during winter months than during the rest of the year. Perhaps more interestingly, we found that there is an interaction between the four to three-lane conversion and season; the reduction in the number of crashes appears to be more pronounced during months, when the weather is nice than during other times of the year, even though a reduction was estimated for the entire year. Thus, it appears that the four to three-lane conversion, while effective year-round, is particularly effective in reducing the expected number of crashes in nice weather.

A behavioral ecology of shermen: hidden stories from trajectory data in the Northern Humboldt Current System

This work proposes an original contribution to the understanding of shermen spatial behavior, based on the behavioral ecology and movement ecology paradigms. Through the analysis of Vessel Monitoring System (VMS) data, we characterized the spatial behavior of Peruvian anchovy shermen at di erent scales: (1) the behavioral modes within shing trips (i.e., searching, shing and cruising); (2) the behavioral patterns among shing trips; (3) the behavioral patterns by shing season conditioned by ecosystem scenarios; and (4) the computation of maps of anchovy presence proxy from the spatial patterns of behavioral mode positions. At the rst scale considered, we compared several Markovian (hidden Markov and semi-Markov models) and discriminative models (random forests, support vector machines and arti cial neural networks) for inferring the behavioral modes associated with VMS tracks. The models were trained under a supervised setting and validated using tracks for which behavioral modes were known (from on-board observers records). Hidden semi-Markov models performed better, and were retained for inferring the behavioral modes on the entire VMS dataset. At the second scale considered, each shing trip was characterized by several features, including the time spent within each behavioral mode. Using a clustering analysis, shing trip patterns were classi ed into groups associated to management zones, eet segments and skippers' personalities. At the third scale considered, we analyzed how ecological conditions shaped shermen behavior. By means of co-inertia analyses, we found signi cant associations between shermen, anchovy and environmental spatial dynamics, and shermen behavioral responses were characterized according to contrasted environmental scenarios. At the fourth scale considered, we investigated whether the spatial behavior of shermen re ected to some extent the spatial distribution of anchovy. Finally, this work provides a wider view of shermen behavior: shermen are not only economic agents, but they are also foragers, constrained by ecosystem variability. To conclude, we discuss how these ndings may be of importance for sheries management, collective behavior analyses and end-to-end models.

MBIS: multivariate Bayesian image segmentation tool.

We present MBIS (Multivariate Bayesian Image Segmentation tool), a clustering tool based on the mixture of multivariate normal distributions model. MBIS supports multichannel bias field correction based on a B-spline model. A second methodological novelty is the inclusion of graph-cuts optimization for the stationary anisotropic hidden Markov random field model. Along with MBIS, we release an evaluation framework that contains three different experiments on multi-site data. We first validate the accuracy of segmentation and the estimated bias field for each channel. MBIS outperforms a widely used segmentation tool in a cross-comparison evaluation. The second experiment demonstrates the robustness of results on atlas-free segmentation of two image sets from scan-rescan protocols on 21 healthy subjects. Multivariate segmentation is more replicable than the monospectral counterpart on T1-weighted images. Finally, we provide a third experiment to illustrate how MBIS can be used in a large-scale study of tissue volume change with increasing age in 584 healthy subjects. This last result is meaningful as multivariate segmentation performs robustly without the need for prior knowledge.

Validation of tissue modelization and classification techniques in T1-weighted MR brain images

We propose a deep study on tissue modelization andclassification Techniques on T1-weighted MR images. Threeapproaches have been taken into account to perform thisvalidation study. Two of them are based on FiniteGaussian Mixture (FGM) model. The first one consists onlyin pure gaussian distributions (FGM-EM). The second oneuses a different model for partial volume (PV) (FGM-GA).The third one is based on a Hidden Markov Random Field(HMRF) model. All methods have been tested on a DigitalBrain Phantom image considered as the ground truth. Noiseand intensity non-uniformities have been added tosimulate real image conditions. Also the effect of ananisotropic filter is considered. Results demonstratethat methods relying in both intensity and spatialinformation are in general more robust to noise andinhomogeneities. However, in some cases there is nosignificant differences between all presented methods.

Risk Aversion, Intertemporal Substitution, and Option Pricing

This paper develops a general stochastic framework and an equilibrium asset pricing model that make clear how attitudes towards intertemporal substitution and risk matter for option pricing. In particular, we show under which statistical conditions option pricing formulas are not preference-free, in other words, when preferences are not hidden in the stock and bond prices as they are in the standard Black and Scholes (BS) or Hull and White (HW) pricing formulas. The dependence of option prices on preference parameters comes from several instantaneous causality effects such as the so-called leverage effect. We also emphasize that the most standard asset pricing models (CAPM for the stock and BS or HW preference-free option pricing) are valid under the same stochastic setting (typically the absence of leverage effect), regardless of preference parameter values. Even though we propose a general non-preference-free option pricing formula, we always keep in mind that the BS formula is dominant both as a theoretical reference model and as a tool for practitioners. Another contribution of the paper is to characterize why the BS formula is such a benchmark. We show that, as soon as we are ready to accept a basic property of option prices, namely their homogeneity of degree one with respect to the pair formed by the underlying stock price and the strike price, the necessary statistical hypotheses for homogeneity provide BS-shaped option prices in equilibrium. This BS-shaped option-pricing formula allows us to derive interesting characterizations of the volatility smile, that is, the pattern of BS implicit volatilities as a function of the option moneyness. First, the asymmetry of the smile is shown to be equivalent to a particular form of asymmetry of the equivalent martingale measure. Second, this asymmetry appears precisely when there is either a premium on an instantaneous interest rate risk or on a generalized leverage effect or both, in other words, whenever the option pricing formula is not preference-free. Therefore, the main conclusion of our analysis for practitioners should be that an asymmetric smile is indicative of the relevance of preference parameters to price options.

Time Reversibility of Stationary Regular Finite State Markov Chains

We propose an alternate parameterization of stationary regular finite-state Markov chains, and a decomposition of the parameter into time reversible and time irreversible parts. We demonstrate some useful properties of the decomposition, and propose an index for a certain type of time irreversibility. Two empirical examples illustrate the use of the proposed parameter, decomposition and index. One involves observed states; the other, latent states.

Investigations On The Development Of An Ann Model & Visual Manipulation Approach For 2-D Dft Computation In Image Processing

This thesis is an outcome of the investigations carried out on the development of an Artificial Neural Network (ANN) model to implement 2-D DFT at high speed. A new definition of 2-D DFT relation is presented. This new definition enables DFT computation organized in stages involving only real addition except at the final stage of computation. The number of stages is always fixed at 4. Two different strategies are proposed. 1) A visual representation of 2-D DFT coefficients. 2) A neural network approach. The visual representation scheme can be used to compute, analyze and manipulate 2D signals such as images in the frequency domain in terms of symbols derived from 2x2 DFT. This, in turn, can be represented in terms of real data. This approach can help analyze signals in the frequency domain even without computing the DFT coefficients. A hierarchical neural network model is developed to implement 2-D DFT. Presently, this model is capable of implementing 2-D DFT for a particular order N such that ((N))4 = 2. The model can be developed into one that can implement the 2-D DFT for any order N upto a set maximum limited by the hardware constraints. The reported method shows a potential in implementing the 2-D DF T in hardware as a VLSI / ASIC