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157
Dynamic Bayesian Networks: Representation, Inference and Learning
, 2002
"... 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 biosequence analysis, and KFMs have bee ..."
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Cited by 564 (3 self)
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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 biosequence 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) linearGaussian. 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 3), 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 RaoBlackwellised 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.
Measuring Business Cycles: A Modern Perspective
 The Review of Economics and Statistics
, 1996
"... Abstract: In the first half of this century, special attention was given to two features of the business cycle: the comovement of many individual economic series and the different behavior of the economy during expansions and contractions. Recent theoretical and empirical research has revived intere ..."
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Cited by 90 (11 self)
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Abstract: In the first half of this century, special attention was given to two features of the business cycle: the comovement of many individual economic series and the different behavior of the economy during expansions and contractions. Recent theoretical and empirical research has revived interest in each attribute separately, and we survey this work. Notable empirical contributions are dynamic factor models that have a single common macroeconomic factor and nonlinear regimeswitching models of a macroeconomic aggregate. We conduct an empirical synthesis that incorporates both of these features. It is desirable to know the facts before attempting to explain them; hence, the attractiveness of organizing businesscycle regularities within a modelfree framework. During the first half of this century, much research was devoted to obtaining just such an empirical characterization of the business cycle. The most prominent example of this work
Bayesian Methods for Hidden Markov Models  Recursive Computing in the 21st Century
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2002
"... Markov chain Monte Carlo (MCMC) sampling strategies can be used to simulate hidden Markov model (HMM) parameters from their posterior distribution given observed data. Some MCMC methods (for computing likelihood, conditional probabilities of hidden states, and the most likely sequence of states) use ..."
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Cited by 86 (8 self)
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Markov chain Monte Carlo (MCMC) sampling strategies can be used to simulate hidden Markov model (HMM) parameters from their posterior distribution given observed data. Some MCMC methods (for computing likelihood, conditional probabilities of hidden states, and the most likely sequence of states) used in practice can be improved by incorporating established recursive algorithms. The most important is a set of forwardbackward recursions calculating conditional distributions of the hidden states given observed data and model parameters. We show how to use the recursive algorithms in an MCMC context and demonstrate mathematical and empirical results showing a Gibbs sampler using the forwardbackward recursions mixes more rapidly than another sampler often used for HMM's. We introduce an augmented variables technique for obtaining unique state labels in HMM's and finite mixture models. We show how recursive computing allows statistically efficient use of MCMC output when estimating the hidden states. We directly calculate the posterior distribution of the hidden chain's state space size by MCMC, circumventing asymptotic arguments underlying the Bayesian information criterion, which is shown to be inappropriate for a frequently analyzed data set in the HMM literature. The use of loglikelihood for assessing MCMC convergence is illustrated, and posterior predictive checks are used to investigate application specific questions of model adequacy.
Markovian Models for Sequential Data
, 1996
"... Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many machine learning applications, especially for speech recognition. Furthermore, in the last few years, many new and promising probabilistic models related to HMMs have been proposed. We firs ..."
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Cited by 84 (2 self)
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Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many machine learning applications, especially for speech recognition. Furthermore, in the last few years, many new and promising probabilistic models related to HMMs have been proposed. We first summarize the basics of HMMs, and then review several recent related learning algorithms and extensions of HMMs, including in particular hybrids of HMMs with artificial neural networks, InputOutput HMMs (which are conditional HMMs using neural networks to compute probabilities), weighted transducers, variablelength Markov models and Markov switching statespace models. Finally, we discuss some of the challenges of future research in this very active area. 1 Introduction Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many applications in artificial intelligence, pattern recognition, speech recognition, and modeling of biological ...
Nonlinear Gated Experts for Time Series: Discovering Regimes and Avoiding Overfitting
, 1995
"... this paper: ftp://ftp.cs.colorado.edu/pub/TimeSeries/MyPapers/experts.ps.Z, ..."
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Cited by 81 (5 self)
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this paper: ftp://ftp.cs.colorado.edu/pub/TimeSeries/MyPapers/experts.ps.Z,
An Econometric Model of Serial Correlation and Illiquidity in Hedge Fund Returns
 Journal of Financial Economics
, 2004
"... The returns to hedge funds and other alternative investments are often highly serially correlated, in sharp contrast to the returns of more traditional investment vehicles such as longonly equity portfolios and mutual funds. In this paper, we explore several sources of such serial correlation and s ..."
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Cited by 80 (4 self)
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The returns to hedge funds and other alternative investments are often highly serially correlated, in sharp contrast to the returns of more traditional investment vehicles such as longonly equity portfolios and mutual funds. In this paper, we explore several sources of such serial correlation and show that the most likely explanation is illiquidity exposure, i.e., investments in securities that are not actively traded and for which market prices are not always readily available. For portfolios of illiquid securities, reported returns will tend to be smoother than true economic returns, which will understate volatility and increase riskadjusted performance measures such as the Sharpe ratio. We propose an econometric model of illiquidity exposure and develop estimators for the smoothing profile as well as a smoothingadjusted Sharpe ratio. For a sample of 908 hedge funds drawn from the TASS database, we show that our estimated smoothing coefficients vary considerably across hedgefund style categories and may be a useful proxy for quantifying illiquidity exposure.
Term Structure of Interest Rates with Regime Shifts
 Journal of Finance
, 2002
"... We develop a term structure model where the short interest rate and the market price of risks are subject to discrete regime shifts. Empirical evidence from efficient method of moments estimation provides considerable support for the regime shifts model. Standard models, which include affine specifi ..."
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Cited by 79 (1 self)
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We develop a term structure model where the short interest rate and the market price of risks are subject to discrete regime shifts. Empirical evidence from efficient method of moments estimation provides considerable support for the regime shifts model. Standard models, which include affine specifications with up to three factors, are sharply rejected in the data. Our diagnostics show that only the regime shifts model can account for the welldocumented violations of the expectations hypothesis, the observed conditional volatility, and the conditional correlation across yields. We find that regimes are intimately related to business cycles. MANY PAPERS DOCUMENT THAT THE UNIVARIATE short interest rate process can be reasonably well modeled in the time series as a regime switching process ~see Hamilton ~1988!, Garcia and Perron ~1996!!. In addition to this statistical evidence, there are economic reasons as well to believe that regime shifts are important to understanding the behavior of the entire yield curve. For example, business cycle expansion and contraction “regimes ” potentially
Switching Kalman Filters
, 1998
"... We show how many different variants of Switching Kalman Filter models can be represented in a unified way, leading to a single, generalpurpose inference algorithm. We then show how to find approximate Maximum Likelihood Estimates of the parameters using the EM algorithm, extending previous results ..."
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Cited by 58 (3 self)
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We show how many different variants of Switching Kalman Filter models can be represented in a unified way, leading to a single, generalpurpose inference algorithm. We then show how to find approximate Maximum Likelihood Estimates of the parameters using the EM algorithm, extending previous results on learning using EM in the nonswitching case [DRO93, GH96a] and in the switching, but fully observed, case [Ham90]. 1 Introduction Dynamical systems are often assumed to be linear and subject to Gaussian noise. This model, called the Linear Dynamical System (LDS) model, can be defined as x t = A t x t\Gamma1 + v t y t = C t x t +w t where x t is the hidden state variable at time t, y t is the observation at time t, and v t ¸ N(0; Q t ) and w t ¸ N(0; R t ) are independent Gaussian noise sources. Typically the parameters of the model \Theta = f(A t ; C t ; Q t ; R t )g are assumed to be timeinvariant, so that they can be estimated from data using e.g., EM [GH96a]. One of the main adva...
Robustness and Pricing with Uncertain Growth
 REV. FINANC. STUD
, 2000
"... We study how decision makers' concerns about robustness affect prices and quantities in a stochastic growth model. In the model economy, growth rates in technology are altered by infrequent large shocks and continuous small shocks. An investor observes movements in the technology level but cannot pe ..."
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Cited by 40 (6 self)
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We study how decision makers' concerns about robustness affect prices and quantities in a stochastic growth model. In the model economy, growth rates in technology are altered by infrequent large shocks and continuous small shocks. An investor observes movements in the technology level but cannot perfectly distinguish their sources. Instead the investor solves a signal extraction problem. We depart from most of the macroeconomics and finance literature by presuming that the investor treats the specification of technology evolution as an approximation. To promote a decision rule that is robust to model misspecification, an investor acts as if a malevolent player threatens to perturb the actual data generating process relative to his approximating model. We study how a concern about robustness alters asset prices. We show that the dynamic evolution of the riskreturn tradeoff is dominated by movements in the growthstate probabilities and that the evolution of the dividendprice ratio is driven primarily by the capitaltechnology ratio.
CCP estimation of dynamic discrete choice models with unobserved heterogeneity
, 2010
"... We adapt the ExpectationMaximization (EM) algorithm to incorporate unobserved heterogeneity into conditional choice probability (CCP) estimators of dynamic discrete choice problems. The unobserved heterogeneity can be timeinvariant or follow a Markov chain. By developing a class of problems where ..."
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Cited by 37 (1 self)
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We adapt the ExpectationMaximization (EM) algorithm to incorporate unobserved heterogeneity into conditional choice probability (CCP) estimators of dynamic discrete choice problems. The unobserved heterogeneity can be timeinvariant or follow a Markov chain. By developing a class of problems where difference in future value terms depend on few conditional choice probabilities, we extend the class of dynamic optimization problems where CCP estimators provide a computationally cheap alternative to full solution methods. For this class of problems, we establish partial identification results for cases where the environment is nonstationary and the sample period falls short of the decisionmaker’s time horizon. Monte Carlo results confirm that our algorithms perform quite well, both in terms of computational time and in the precision of the parameter estimates.