Related papers: Expectation Propagation
Bayes' rule describes how to infer posterior beliefs about latent variables given observations, and inference is a critical step in learning algorithms for latent variable models (LVMs). Although there are exact algorithms for inference and…
Calibration$\unicode{x2014}$the problem of ensuring that predicted probabilities align with observed class frequencies$\unicode{x2014}$is a basic desideratum for reliable prediction with machine learning systems. Calibration error is…
Advances in variational inference enable parameterisation of probabilistic models by deep neural networks. This combines the statistical transparency of the probabilistic modelling framework with the representational power of deep learning.…
Dempster/Shafer (D/S) theory has been advocated as a way of representing incompleteness of evidence in a system's knowledge base. Methods now exist for propagating beliefs through chains of inference. This paper discusses how rules with…
Active inference is a state-of-the-art framework in neuroscience that offers a unified theory of brain function. It is also proposed as a framework for planning in AI. Unfortunately, the complex mathematics required to create new models --…
We define and study an inference algorithm based on "belief propagation" (BP) and the Bethe approximation. The idea is to encode into a graph an a priori information composed of correlations or marginal probabilities of variables, and to…
Despite the advances in the representational capacity of approximate distributions for variational inference, the optimization process can still limit the density that is ultimately learned. We demonstrate the drawbacks of biasing the true…
Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling…
We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting a given iterative method for the original system as an…
In the theory of programming languages, type inference is the process of inferring the type of an expression automatically, often making use of information from the context in which the expression appears. Such mechanisms turn out to be…
We propose a fair machine learning algorithm to model interpretable differences between observed and desired human decision-making, with the latter aimed at reducing disparity in a downstream outcome impacted by the human decision. Prior…
Bayesian inference is a popular method to build learning algorithms but it is hampered by the fact that its key object, the posterior probability distribution, is often uncomputable. Expectation Propagation (EP) (Minka (2001)) is a popular…
In this paper, we define the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
Topic models are Bayesian models that are frequently used to capture the latent structure of certain corpora of documents or images. Each data element in such a corpus (for instance each item in a collection of scientific articles) is…
Influence propagation has been the subject of extensive study due to its important role in social networks, epidemiology, and many other areas. Understanding propagation mechanisms is critical to control the spread of fake news or…
Computing expected predictions of discriminative models is a fundamental task in machine learning that appears in many interesting applications such as fairness, handling missing values, and data analysis. Unfortunately, computing…
Probabilistic programs provide an expressive representation language for generative models. Given a probabilistic program, we are interested in the task of posterior inference: estimating a latent variable given a set of observed variables.…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
Negation operation is important in intelligent information processing. Different with existing arithmetic negation, an exponential negation is presented in this paper. The new negation can be seen as a kind of geometry negation. Some basic…