Hidden Markov Models With Set-Valued Parameters

Hidden Markov models (HMMs) are widely used probabilistic models of sequential data. As with other probabilistic models, they require the specification of local conditional probability distributions, whose assessment can be too difficult and error-prone, especially when data are scarce or costly to acquire. The imprecise HMM (iHMM) generalizes HMMs by allowing the quantification to be done by sets of, instead of single, probability distributions. iHMMs have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. In this paper, we consider iHMMs under the strong independence interpretation, for which we develop efficient inference algorithms to address standard HMM usage such as the computation of likelihoods and most probable explanations, as well as performing filtering and predictive inference. Experiments with real data show that iHMMs produce more reliable inferences without compromising the computational efficiency.

Semiring induced valuation algebras: Exact and approximate local computation algorithms

Local computation in join trees or acyclic hypertrees has been shown to be linked to a particular algebraic structure, called valuation algebra.There are many models of this algebraic structure ranging from probability theory to numerical analysis, relational databases and various classical and non-classical logics. It turns out that many interesting models of valuation algebras may be derived from semiring valued mappings. In this paper we study how valuation algebras are induced by semirings and how the structure of the valuation algebra is related to the algebraic structure of the semiring. In particular, c-semirings with idempotent multiplication induce idempotent valuation algebras and therefore permit particularly efficient architectures for local computation. Also important are semirings whose multiplicative semigroup is embedded in a union of groups. They induce valuation algebras with a partially defined division. For these valuation algebras, the well-known architectures for Bayesian networks apply. We also extend the general computational framework to allow derivation of bounds and approximations, for when exact computation is not feasible.

The Inferential Complexity of Bayesian and Credal Networks

This paper presents new results on the complexity of graph-theoretical models that represent probabilities (Bayesian networks) and that represent interval and set valued probabilities (credal networks). We define a new class of networks with bounded width, and introduce a new decision problem for Bayesian networks, the maximin a posteriori. We present new links between the Bayesian and credal networks, and present new results both for Bayesian networks (most probable explanation with observations, maximin a posteriori) and for credal networks (bounds on probabilities a posteriori, most probable explanation with and without observations, maximum a posteriori).

Belief Updating and Learning in Semi-Qualitative Probabilistic Networks

This paper explores semi-qualitative probabilistic networks (SQPNs) that combine numeric and qualitative information. We first show that exact inferences with SQPNs are NPPP-Complete. We then show that existing qualitative relations in SQPNs (plus probabilistic logic and imprecise assessments) can be dealt effectively through multilinear programming. We then discuss learning: we consider a maximum likelihood method that generates point estimates given a SQPN and empirical data, and we describe a Bayesian-minded method that employs the Imprecise Dirichlet Model to generate set-valued estimates.

Multilinear and Integer Programming for Markov Decision Processes with Imprecise Probabilities

Markov Decision Processes (MDPs) are extensively used to encode sequences of decisions with probabilistic effects. Markov Decision Processes with Imprecise Probabilities (MDPIPs) encode sequences of decisions whose effects are modeled using sets of probability distributions. In this paper we examine the computation of Γ-maximin policies for MDPIPs using multilinear and integer programming. We discuss the application of our algorithms to “factored” models and to a recent proposal, Markov Decision Processes with Set-valued Transitions (MDPSTs), that unifies the fields of probabilistic and “nondeterministic” planning in artificial intelligence research. 

Rapid tryptophan depletion improves decision-making cognition in healthy humans without affecting reversal learning or set shifting

Rapid tryptophan (Trp) depletion (RTD) has been reported to cause deterioration in the quality of decision making and impaired reversal learning, while leaving attentional set shifting relatively unimpaired. These findings have been attributed to a more powerful neuromodulatory effect of reduced 5-HT on ventral prefrontal cortex (PFC) than on dorsolateral PFC. In view of the limited number of reports, the aim of this study was to independently replicate these findings using the same test paradigms. Healthy human subjects without a personal or family history of affective disorder were assessed using a computerized decision making/gambling task and the CANTAB ID/ED attentional set-shifting task under Trp-depleted (n=17; nine males and eight females) or control (n=15; seven males and eight females) conditions, in a double-blind, randomized, parallel-group design. There was no significant effect of RTD on set shifting, reversal learning, risk taking, impulsivity, or subjective mood. However, RTD significantly altered decision making such that depleted subjects chose the more likely of two possible outcomes significantly more often than controls. This is in direct contrast to the previous report that subjects chose the more likely outcome significantly less often following RTD. In the terminology of that report, our result may be interpreted as improvement in the quality of decision making following RTD. This contrast between studies highlights the variability in the cognitive effects of RTD between apparently similar groups of healthy subjects, and suggests the need for future RTD studies to control for a range of personality, family history, and genetic factors that may be associated with 5-HT function.

Application-Specific Instruction Set Processor for SoC implementation of Modern Signal Processing Algorithms

A novel application-specific instruction set processor (ASIP) for use in the construction of modern signal processing systems is presented. This is a flexible device that can be used in the construction of array processor systems for the real-time implementation of functions such as singular-value decomposition (SVD) and QR decomposition (QRD), as well as other important matrix computations. It uses a coordinate rotation digital computer (CORDIC) module to perform arithmetic operations and several approaches are adopted to achieve high performance including pipelining of the micro-rotations, the use of parallel instructions and a dual-bus architecture. In addition, a novel method for scale factor correction is presented which only needs to be applied once at the end of the computation. This also reduces computation time and enhances performance. Methods are described which allow this processor to be used in reduced dimension (i.e., folded) array processor structures that allow tradeoffs between hardware and performance. The net result is a flexible matrix computational processing element (PE) whose functionality can be changed under program control for use in a wider range of scenarios than previous work. Details are presented of the results of a design study, which considers the application of this decomposition PE architecture in a combined SVD/QRD system and demonstrates that a combination of high performance and efficient silicon implementation are achievable. © 2005 IEEE.

CORDIC based application-specific instruction set processor for QRD/SVD

An application specific programmable processor (ASIP) suitable for the real-time implementation of matrix computations such as Singular Value and QR Decomposition is presented. The processor incorporates facilities for the issue of parallel instructions and a dual-bus architecture that are designed to achieve high performance. Internally, it uses a CORDIC module to perform arithmetic operations, with pipelining of the internal recursive loop exploited to multiplex the two independent micro-rotations onto a single piece of hardware. The net result is a flexible processing element whose functionality can be changed under program control, which combines high performance with efficient silicon implementation. This is illustrated through the results of a detailed silicon design study and the applications of the techniques to a combined SVD/QRD system.