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.

Probabilistic methods for drug discovery

This thesis introduces a flexible visual data exploration framework which combines advanced projection algorithms from the machine learning domain with visual representation techniques developed in the information visualisation domain to help a user to explore and understand effectively large multi-dimensional datasets. The advantage of such a framework to other techniques currently available to the domain experts is that the user is directly involved in the data mining process and advanced machine learning algorithms are employed for better projection. A hierarchical visualisation model guided by a domain expert allows them to obtain an informed segmentation of the input space. Two other components of this thesis exploit properties of these principled probabilistic projection algorithms to develop a guided mixture of local experts algorithm which provides robust prediction and a model to estimate feature saliency simultaneously with the training of a projection algorithm.Local models are useful since a single global model cannot capture the full variability of a heterogeneous data space such as the chemical space. Probabilistic hierarchical visualisation techniques provide an effective soft segmentation of an input space by a visualisation hierarchy whose leaf nodes represent different regions of the input space. We use this soft segmentation to develop a guided mixture of local experts (GME) algorithm which is appropriate for the heterogeneous datasets found in chemoinformatics problems. Moreover, in this approach the domain experts are more involved in the model development process which is suitable for an intuition and domain knowledge driven task such as drug discovery. We also derive a generative topographic mapping (GTM) based data visualisation approach which estimates feature saliency simultaneously with the training of a visualisation model.

The choice of the model in inventory control and the cost of sophistication

This thesis is concerned with the inventory control of items that can be considered independent of one another. The decisions when to order and in what quantity, are the controllable or independent variables in cost expressions which are minimised. The four systems considered are referred to as (Q, R), (nQ,R,T), (M,T) and (M,R,T). Wiith ((Q,R) a fixed quantity Q is ordered each time the order cover (i.e. stock in hand plus on order ) equals or falls below R, the re-order level. With the other three systems reviews are made only at intervals of T. With (nQ,R,T) an order for nQ is placed if on review the inventory cover is less than or equal to R, where n, which is an integer, is chosen at the time so that the new order cover just exceeds R. In (M, T) each order increases the order cover to M. Fnally in (M, R, T) when on review, order cover does not exceed R, enough is ordered to increase it to M. The (Q, R) system is examined at several levels of complexity, so that the theoretical savings in inventory costs obtained with more exact models could be compared with the increases in computational costs. Since the exact model was preferable for the (Q,R) system only exact models were derived for theoretical systems for the other three. Several methods of optimization were tried, but most were found inappropriate for the exact models because of non-convergence. However one method did work for each of the exact models. Demand is considered continuous, and with one exception, the distribution assumed is the normal distribution truncated so that demand is never less than zero. Shortages are assumed to result in backorders, not lost sales. However, the shortage cost is a function of three items, one of which, the backorder cost, may be either a linear, quadratic or an exponential function of the length of time of a backorder, with or without period of grace. Lead times are assumed constant or gamma distributed. Lastly, the actual supply quantity is allowed to be distributed. All the sets of equations were programmed for a KDF 9 computer and the computed performances of the four inventory control procedures are compared under each assurnption.

A probabilistic model for trust and reputation

This paper concerns the problem of agent trust in an electronic market place. We maintain that agent trust involves making decisions under uncertainty and therefore the phenomenon should be modelled probabilistically. We therefore propose a probabilistic framework that models agent interactions as a Hidden Markov Model (HMM). The observations of the HMM are the interaction outcomes and the hidden state is the underlying probability of a good outcome. The task of deciding whether to interact with another agent reduces to probabilistic inference of the current state of that agent given all previous interaction outcomes. The model is extended to include a probabilistic reputation system which involves agents gathering opinions about other agents and fusing them with their own beliefs. Our system is fully probabilistic and hence delivers the following improvements with respect to previous work: (a) the model assumptions are faithfully translated into algorithms; our system is optimal under those assumptions, (b) It can account for agents whose behaviour is not static with time (c) it can estimate the rate with which an agent's behaviour changes. The system is shown to significantly outperform previous state-of-the-art methods in several numerical experiments. Copyright © 2010, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved.

The spatial distribution of self-employment in India:evidence from semi-parametric geoadditive models

The spatial distribution of self-employment in India: evidence from semiparametric geoadditive models, Regional Studies. The entrepreneurship literature has rarely considered spatial location as a micro-determinant of occupational choice. It has also ignored self-employment in developing countries. Using Bayesian semiparametric geoadditive techniques, this paper models spatial location as a micro-determinant of self-employment choice in India. The empirical results suggest the presence of spatial occupational neighbourhoods and a clear north–south divide in self-employment when the entire sample is considered; however, spatial variation in the non-agriculture sector disappears to a large extent when individual factors that influence self-employment choice are explicitly controlled. The results further suggest non-linear effects of age, education and wealth on self-employment.

Semisupervised learning of hierarchical latent trait models for data visualization

Recently, we have developed the hierarchical Generative Topographic Mapping (HGTM), an interactive method for visualization of large high-dimensional real-valued data sets. In this paper, we propose a more general visualization system by extending HGTM in three ways, which allows the user to visualize a wider range of data sets and better support the model development process. 1) We integrate HGTM with noise models from the exponential family of distributions. The basic building block is the Latent Trait Model (LTM). This enables us to visualize data of inherently discrete nature, e.g., collections of documents, in a hierarchical manner. 2) We give the user a choice of initializing the child plots of the current plot in either interactive, or automatic mode. In the interactive mode, the user selects "regions of interest," whereas in the automatic mode, an unsupervised minimum message length (MML)-inspired construction of a mixture of LTMs is employed. The unsupervised construction is particularly useful when high-level plots are covered with dense clusters of highly overlapping data projections, making it difficult to use the interactive mode. Such a situation often arises when visualizing large data sets. 3) We derive general formulas for magnification factors in latent trait models. Magnification factors are a useful tool to improve our understanding of the visualization plots, since they can highlight the boundaries between data clusters. We illustrate our approach on a toy example and evaluate it on three more complex real data sets. © 2005 IEEE.

Probabilistic synchronisation of pinning control

This paper is concerned with synchronization of complex stochastic dynamical networks in the presence of noise and functional uncertainty. A probabilistic control method for adaptive synchronization is presented. All required probabilistic models of the network are assumed to be unknown therefore estimated to be dependent on the connectivity strength, the state and control values. Robustness of the probabilistic controller is proved via the Liapunov method. Furthermore, based on the residual error of the network states we introduce the definition of stochastic pinning controllability. A coupled map lattice with spatiotemporal chaos is taken as an example to illustrate all theoretical developments. The theoretical derivation is complemented by its validation on two representative examples.

Fully probabilistic control for stochastic nonlinear control systems with input dependent noise

Robust controllers for nonlinear stochastic systems with functional uncertainties can be consistently designed using probabilistic control methods. In this paper a generalised probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented emphasising how the uncertainty can be systematically incorporated in the absence of reliable systems models. To achieve this objective all probabilistic models of the system are estimated from process data using mixture density networks (MDNs) where all the parameters of the estimated pdfs are taken to be state and control input dependent. Based on this dependency of the density parameters on the input values, explicit formulations to the construction of optimal generalised probabilistic controllers are obtained through the techniques of dynamic programming and adaptive critic methods. Using the proposed generalised probabilistic controller, the conditional joint pdfs can be made to follow the ideal ones. A simulation example is used to demonstrate the implementation of the algorithm and encouraging results are obtained.

Probabilistic control for uncertain systems

In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the probabilistic models of both the forward and inverse dynamics are estimated such that they are dependent on the state and the control input. The optimal control strategy is then derived which minimizes uncertainty of the closed loop system. In the absence of reliable plant models, the proposed control algorithm incorporates uncertainties in model parameters, observations, and latent processes. The local stability of the closed loop system has been established. The efficacy of the control algorithm is demonstrated on two nonlinear stochastic control examples with additive and multiplicative noise.

Conceptual Foundations of Construction of the Models and Procedures for Prediction of the Avalanche-dangerous Situations Initiation

The conceptual foundations of the models and procedures for prediction of the avalanche-dangerous situations initiation are considered. The interpretation model for analysis of the avalanche-dangerous situations initiation based on the definition of probabilities of correspondence of studied parameters to the probabilistic distributions of avalanche-dangerous or avalanche non-dangerous situations is offered. The possibility to apply such a model to the real data is considered. The main approaches to the use of multiple representations for the avalanche dangerous situations initiation analysis are generalized.

Modeling Optical Response of Thin Films: Choice of the Refractive Index Dispersion Law

Determination of the so-called optical constants (complex refractive index N, which is usually a function of the wavelength, and physical thickness D) of thin films from experimental data is a typical inverse non-linear problem. It is still a challenge to the scientific community because of the complexity of the problem and its basic and technological significance in optics. Usually, solutions are looked for models with 3-10 parameters. Best estimates of these parameters are obtained by minimization procedures. Herein, we discuss the choice of orthogonal polynomials for the dispersion law of the thin film refractive index. We show the advantage of their use, compared to the Selmeier, Lorentz or Cauchy models.

Models of Alternating Renewal Process at Discrete Time

We study a class of models used with success in the modelling of climatological sequences. These models are based on the notion of renewal. At first, we examine the probabilistic aspects of these models to afterwards study the estimation of their parameters and their asymptotical properties, in particular the consistence and the normality. We will discuss for applications, two particular classes of alternating renewal processes at discrete time. The first class is defined by laws of sojourn time that are translated negative binomial laws and the second class, suggested by Green is deduced from alternating renewal process in continuous time with sojourn time laws which are exponential laws with parameters α^0 and α^1 respectively.

Probabilistic multiple model neural network based leak detection system:experimental study

This paper presents an effective decision making system for leak detection based on multiple generalized linear models and clustering techniques. The training data for the proposed decision system is obtained by setting up an experimental pipeline fully operational distribution system. The system is also equipped with data logging for three variables; namely, inlet pressure, outlet pressure, and outlet flow. The experimental setup is designed such that multi-operational conditions of the distribution system, including multi pressure and multi flow can be obtained. We then statistically tested and showed that pressure and flow variables can be used as signature of leak under the designed multi-operational conditions. It is then shown that the detection of leakages based on the training and testing of the proposed multi model decision system with pre data clustering, under multi operational conditions produces better recognition rates in comparison to the training based on the single model approach. This decision system is then equipped with the estimation of confidence limits and a method is proposed for using these confidence limits for obtaining more robust leakage recognition results.

Parameterized Link Functions in Generalized Linear Random Effect Models: a Case Study on Breast Cancer Treatment

In non-linear random effects some attention has been very recently devoted to the analysis ofsuitable transformation of the response variables separately (Taylor 1996) or not (Oberg and Davidian 2000) from the transformations of the covariates and, as far as we know, no investigation has been carried out on the choice of link function in such models. In our study we consider the use of a random effect model when a parameterized family of links (Aranda-Ordaz 1981, Prentice 1996, Pregibon 1980, Stukel 1988 and Czado 1997) is introduced. We point out the advantages and the drawbacks associated with the choice of this data-driven kind of modeling. Difficulties in the interpretation of regression parameters, and therefore in understanding the influence of covariates, as well as problems related to loss of efficiency of estimates and overfitting, are discussed. A case study on radiotherapy usage in breast cancer treatment is discussed.

Probabilistic Approach to Design of Large Antenna Arrays

2000 Mathematics Subject Classification: 78A50