In a probabilistic set covering problem the right hand side is a random binary vector and the covering constraint has to be satisfied with some prescribed probability. We analyse the structure of the set of probabilistically efficient points of binary random vectors, develop methods

We consider a probabilistic set covering problem where there is uncertainty regarding whether a selected set can cover an item, and the objective is to determine a minimum-cost combination of sets so that each item is covered with a pre-specified probability. To date, literature on this problem has

Using topos theory I prove that reasoning about probabilities can be formalized with only one simple assumption: given two sets of measures A, B, if B A, then B is less imprecise than A.

Abstract — Evaluating similarity between sets is a fundamental task in computer science. However, there are many applications in which elements in a set may be uncertain due to various reasons. Existing work on modeling such probabilistic sets and computing their similarities suffers from huge

Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum-likelihood estimation

of the relational structure present in our database. This paper builds on the recent work on probabilistic relational models (PRMs), and describes how to learn them from databases. PRMs allow the properties of an object to depend probabilistically both on other properties of that object and on properties of related

Probabilistic Latent Semantic Indexing is a novel approach to automated document indexing which is based on a statistical latent class model for factor analysis of count data. Fitted from a training corpus of text documents by a generalization of the Expectation Maximization algorithm, the utilized

Probabilistic Latent Semantic Analysis is a novel statistical technique for the analysis of two--mode and co-occurrence data, which has applications in information retrieval and filtering, natural language processing, machine learning from text, and in related areas. Compared to standard Latent

The knowledge-based rational decision model (KBR-model), developed in [1], offers an approach to rational decision making in a non-probabilistic setting, e.g., in perfect information games with deterministic payoffs. The KBR-model is an epistemically explicit form of standard game

maximum-likelihood framework, based on a specific form of Gaussian latent variable model. This leads to a well-defined mixture model for probabilistic principal component analysers, whose parameters can be determined using an EM algorithm. We discuss the advantages of this model in the context