Related papers: Factored Probabilistic Belief Tracking
While belief functions may be seen formally as a generalization of probabilistic distributions, the question of the interactions between belief functions and probability is still an issue in practice. This question is difficult, since the…
This paper examines Bayesian belief network inference using simulation as a method for computing the posterior probabilities of network variables. Specifically, it examines the use of a method described by Henrion, called logic sampling,…
The notion of belief likelihood function of repeated trials is introduced, whenever the uncertainty for individual trials is encoded by a belief measure (a finite random set). This generalises the traditional likelihood function, and…
Belief functions are a powerful and popular framework for the mathematical characterisation of uncertainty, in particular in situations in which lack of data renders learning a probability distribution for the problem impractical. The first…
Possibilistic and qualitative POMDPs (pi-POMDPs) are counterparts of POMDPs used to model situations where the agent's initial belief or observation probabilities are imprecise due to lack of past experiences or insufficient data…
We consider inference problems for a class of continuous state collective hidden Markov models, where the data is recorded in aggregate (collective) form generated by a large population of individuals following the same dynamics. We propose…
Type systems usually characterize the shape of values but not their free variables. However, there are many desirable safety properties one could guarantee if one could track how references can escape. For example, one may implement…
A conceptual foundation for approximation of belief functions is proposed and investigated. It is based on the requirements of consistency and closeness. An optimal approximation is studied. Unfortunately, the computation of the optimal…
Factorization machines (FMs) are a powerful tool for regression and classification in the context of sparse observations, that has been successfully applied to collaborative filtering, especially when side information over users or items is…
The problem of induction has persisted since Hume exposed the logical gap between repeated observation and universal inference. Traditional attempts to resolve it have oscillated between two extremes: the probabilistic optimism of Laplace…
Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and Bayesian inference with default priors are attempts to…
This paper considers a restriction to non-negative matrix factorization in which at least one matrix factor is stochastic. That is, the elements of the matrix factors are non-negative and the columns of one matrix factor sum to 1. This…
Bayesian sparse factor models have proven useful for characterizing dependence in multivariate data, but scaling computation to large numbers of samples and dimensions is problematic. We propose expandable factor analysis for scalable…
A major benefit of graphical models is that most knowledge is captured in the model structure. Many models, however, produce inference problems with a lot of symmetries not reflected in the graphical structure and hence not exploitable by…
We consider the filtering of continuous-time finite-state hidden Markov models, where the rate and observation matrices depend on unknown time-dependent parameters, for which no prior or stochastic model is available. We quantify and…
Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…
The increasing ease of data capture and storage has led to a corresponding increase in the choice of data, the type of analysis performed on that data, and the complexity of the analysis performed. The main contribution of this paper is to…
Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…
The true process that generated data cannot be determined when multiple explanations are possible. Prediction requires a model of the probability that a process, chosen randomly from the set of candidate explanations, generates some future…
Bayesian Non-negative Matrix Factorization (NMF) is a promising approach for understanding uncertainty and structure in matrix data. However, a large volume of applied work optimizes traditional non-Bayesian NMF objectives that fail to…