The growing interest in data mining is motivated by a common problem across disciplines: how does one store, access, model, and ultimately describe and understand very large data sets? Historically, different aspects of data mining have been addressed independently by different disciplines. This is the first truly interdisciplinary text on data mining, blending the contributions of information science, computer science, and statistics. The book consists of three sections. The first, foundations, provides a tutorial overview of the principles underlying data mining algorithms and their application. The presentation emphasizes intuition rather than rigor. The second section, data mining algorithms, shows how algorithms are constructed to solve specific problems in a principled manner. The algorithms covered include trees and rules for classification and regression, association rules, belief networks, classical statistical models, nonlinear models such as neural networks, and local "memory-based" models. The third section shows how all of the preceding analysis fits together when applied to real-world data mining problems. Topics include the role of metadata, how to handle missing data, and data preprocessing.

Principles of data mining

Dynamic Bayesian Networks: Representation, Inference and Learning by Kevin Patrick Murphy Doctor of Philosophy in Computer Science University of California, Berkeley Professor Stuart Russell, Chair Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and bio-sequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linear-Gaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data. In particular, the main novel technical contributions of this thesis are as follows: a way of representing Hierarchical HMMs as DBNs, which enables inference to be done in O(T ) time instead of O(T ), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T ) space instead of O(T ); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of applying Rao-Blackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.

/pdf/dynamic-bayesian-networks-representation-inference-and-yy4fhfxdcj.pdf

Dynamic bayesian networks: representation, inference and learning

The book consists of three sections. The first, foundations, provides a tutorial overview of the principles underlying data mining algorithms and their application. The presentation emphasizes intuition rather than rigor. The second section, data mining algorithms, shows how algorithms are constructed to solve specific problems in a principled manner. The algorithms covered include trees and rules for classification and regression, association rules, belief networks, classical statistical models, nonlinear models such as neural networks, and local "memory-based" models. The third section shows how all of the preceding analysis fits together when applied to real-world data mining problems. Topics include the role of metadata, how to handle missing data, and data preprocessing.

Principles of Data Mining

An overview of statistical and information-theoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discrete-time finite-state homogeneous Markov chain observed through a discrete-time memoryless invariant channel. In recent years, the work of Baum and Petrie (1966) on finite-state finite-alphabet HMPs was expanded to HMPs with finite as well as continuous state spaces and a general alphabet. In particular, statistical properties and ergodic theorems for relative entropy densities of HMPs were developed. Consistency and asymptotic normality of the maximum-likelihood (ML) parameter estimator were proved under some mild conditions. Similar results were established for switching autoregressive processes. These processes generalize HMPs. New algorithms were developed for estimating the state, parameter, and order of an HMP, for universal coding and classification of HMPs, and for universal decoding of hidden Markov channels. These and other related topics are reviewed.

http://www.isib.cnr.it/control/finesso/Ephraim_hmm.pdf

Hidden Markov processes

MODEL STRUCTURE, PROPERTIES, AND METHODS Mixture Distributions and Markov Chains Introduction Independent mixture models Markov chains Hidden Markov Models: Definition and Properties A simple hidden Markov model The basics The likelihood Estimation by Direct Maximization of the Likelihood Introduction Scaling the likelihood computation Maximization subject to constraints Other problems Example: earthquakes Standard errors and confidence intervals Example: parametric bootstrap Estimation by the EM Algorithm Forward and backward probabilities The EM algorithm Examples of EM applied to Poisson HMMs Discussion Forecasting, Decoding, and State Prediction Conditional distributions Forecast distributions Decoding State prediction Model Selection and Checking Model selection by AIC and BIC Model checking with pseudo-residuals Examples Discussion Bayesian Inference for Poisson HMMs Applying the Gibbs sampler to Poisson HMMs Bayesian estimation of the number of states Example: earthquakes Discussion Extensions of the Basic Hidden Markov Model Introduction HMMs with general univariate state-dependent distribution HMMs based on a second-order Markov chain HMMs for multivariate series Series which depend on covariates Models with additional dependencies APPLICATIONS Epileptic Seizures Introduction Models fitted Model checking by pseudo-residuals Eruptions of the Old Faithful Geyser Introduction Binary time series of short and long eruptions Normal HMMs for durations and waiting times Bivariate model for durations and waiting times Drosophila Speed and Change of Direction Introduction Von Mises distributions Von Mises HMMs for the two subjects Circular autocorrelation functions Bivariate model Wind Direction at Koeberg Introduction Wind direction as classified into 16 categories Wind direction as a circular variable Models for Financial Series Thinly traded shares Multivariate HMM for returns on four shares Stochastic volatility models Births at Edendale Hospital Introduction Models for the proportion Caesarean Models for the total number of deliveries Conclusion Cape Town Homicides and Suicides Introduction Firearm homicides as a proportion of all homicides, suicides, and legal intervention homicides The number of firearm homicides Firearm homicide and suicide proportions Proportion in each of the five categories Animal-Behavior Model with Feedback Introduction The model Likelihood evaluation Parameter estimation by maximum likelihood Model checking Inferring the underlying state Models for a heterogeneous group of subjects Other modifications or extensions Application to caterpillar feeding behavior Discussion Appendix A: Examples of R code Stationary Poisson HMM, numerical maximization More on Poisson HMMs, including EM Bivariate normal state-dependent distributions Categorical HMM, constrained optimization Appendix B: Some Proofs Factorization needed for forward probabilities Two results for backward probabilities Conditional independence of Xt1 and XTt+1 References Author Index Subject Index Exercises appear at the end of most chapters.

https://www.jstatsoft.org/article/view/v043b04/v43b04.pdf

I. L. MacDonald

Papers

Hidden Markov and Other Models for Discrete- valued Time Series