Kuznetsov independence for interval-valued expectations and sets of probability distributions: Properties and algorithms

Kuznetsov independence of variables X and Y means that, for any pair of bounded functions f(X) and g(Y), E[f(X)g(Y)]=E[f(X)] *times* E[g(Y)], where E[.] denotes interval-valued expectation and *times* denotes interval multiplication. We present properties of Kuznetsov independence for several variables, and connect it with other concepts of independence in the literature; in particular we show that strong extensions are always included in sets of probability distributions whose lower and upper expectations satisfy Kuznetsov independence. We introduce an algorithm that computes lower expectations subject to judgments of Kuznetsov independence by mixing column generation techniques with nonlinear programming. Finally, we define a concept of conditional Kuznetsov independence, and study its graphoid properties.

Complexity of Inferences in Polytree-shaped Semi-Qualitative Probabilistic Networks

Semi-qualitative probabilistic networks (SQPNs) merge two important graphical model formalisms: Bayesian networks and qualitative probabilistic networks. They provide a very general modeling framework by allowing the combination of numeric and qualitative assessments over a discrete domain, and can be compactly encoded by exploiting the same factorization of joint probability distributions that are behind the Bayesian networks. This paper explores the computational complexity of semi-qualitative probabilistic networks, and takes the polytree-shaped networks as its main target. We show that the inference problem is coNP-Complete for binary polytrees with multiple observed nodes. We also show that inferences can be performed in linear time if there is a single observed node, which is a relevant practical case. Because our proof is constructive, we obtain an efficient linear time algorithm for SQPNs under such assumptions. To the best of our knowledge, this is the first exact polynomial-time algorithm for SQPNs. Together these results provide a clear picture of the inferential complexity in polytree-shaped SQPNs.

Semi-Qualitative Probabilistic Networks in Computer Vision Problems

This paper explores the application of semi-qualitative probabilistic networks (SQPNs) that combine numeric and qualitative information to computer vision problems. Our version of SQPN allows qualitative influences and imprecise probability measures using intervals. We describe an Imprecise Dirichlet model for parameter learning and an iterative algorithm for evaluating posterior probabilities, maximum a posteriori and most probable explanations. Experiments on facial expression recognition and image segmentation problems are performed using real data.

Assembling a consistent set of sentences in relational probabilistic logic with stochastic independence

We examine the representation of judgements of stochastic independence in probabilistic logics. We focus on a relational logic where (i) judgements of stochastic independence are encoded by directed acyclic graphs, and (ii) probabilistic assessments are flexible in the sense that they are not required to specify a single probability measure. We discuss issues of knowledge representation and inference that arise from our particular combination of graphs, stochastic independence, logical formulas and probabilistic assessments.

Computing lower and upper expectations under epistemic independence

This paper investigates the computation of lower/upper expectations that must cohere with a collection of probabilistic assessments and a collection of judgements of epistemic independence. New algorithms, based on multilinear programming, are presented, both for independence among events and among random variables. Separation properties of graphical models are also investigated.

Integração de evidências em redes credais e a regra de Jeffrey

Credal networks provide a scheme for dealing with imprecise probabilistic models. The inference algorithms often used in credal networks compute the interval of the posterior probability of an event of interest given evidence of the specific kind -- evidence that describe the current state of a set of variables. These algorithms do not perform evidential reasoning in case of the evidence must be processed according to the conditioning rule proposed by RC Jeffrey. This paper describes a procedure to integrate evidence with Jeffrey's rule when performing inferences with credal nets.

Decision Making by Credal Nets

Credal nets are probabilistic graphical models which extend Bayesian nets to cope with sets of distributions. This feature makes the model particularly suited for the implementation of classifiers and knowledge-based systems. When working with sets of (instead of single) probability distributions, the identification of the optimal option can be based on different criteria, some of them eventually leading to multiple choices. Yet, most of the inference algorithms for credal nets are designed to compute only the bounds of the posterior probabilities. This prevents some of the existing criteria from being used. To overcome this limitation, we present two simple transformations for credal nets which make it possible to compute decisions based on the maximality and E-admissibility criteria without any modification in the inference algorithms. We also prove that these decision problems have the same complexity of standard inference, being NP^PP-hard for general credal nets and NP-hard for polytrees.

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.

Plan Selection for Probabilistic BDI Agents

When an agent wants to fulfill its desires about the world, the agent usually has multiple plans to choose from and these plans have different pre-conditions and additional effects in addition to achieving its goals. Therefore, for further reasoning and interaction with the world, a plan selection strategy (usually based on plan cost estimation) is mandatory for an autonomous agent. This demand becomes even more critical when uncertainty on the observation of the world is taken into account, since in this case, we consider not only the costs of different plans, but also their chances of success estimated according to the agent's beliefs. In addition, when multiple goals are considered together, different plans achieving the goals can be conflicting on their preconditions (contexts) or the required resources. Hence a plan selection strategy should be able to choose a subset of plans that fulfills the maximum number of goals while maintaining context consistency and resource-tolerance among the chosen plans. To address the above two issues, in this paper we first propose several principles that a plan selection strategy should satisfy, and then we present selection strategies that stem from the principles, depending on whether a plan cost is taken into account. In addition, we also show that our selection strategy can partially recover intention revision.

Hybrid probabilistic wind power forecasting using temporally local Gaussian process

The demand for sustainable development has resulted in a rapid growth in wind power worldwide. Despite various approaches have been proposed to improve the accuracy and to overcome the uncertainties associated with traditional methods, the stochastic and variable nature of wind still remains the most challenging issue in accurately forecasting wind power. This paper presents a hybrid deterministic-probabilistic method where a temporally local ‘moving window’ technique is used in Gaussian Process to examine estimated forecasting errors. This temporally local Gaussian Process employs less measurement data while faster and better predicts wind power at two wind farms, one in the USA and the other in Ireland. Statistical analysis on the results shows that the method can substantially reduce the forecasting error while more likely generate Gaussian-distributed residuals, particularly for short-term forecast horizons due to its capability to handle the time-varying characteristics of wind power.