Related papers: Bayesian Renormalization
Bayesian methods have proved powerful in many applications for the inference of model parameters from data. These methods are based on Bayes' theorem, which itself is deceptively simple. However, in practice the computations required are…
Boosting methods are widely used in statistical learning to deal with high-dimensional data due to their variable selection feature. However, those methods lack straightforward ways to construct estimators for the precision of the…
An increasing number of applications require real-time reasoning under uncertainty with streaming input. The temporal (dynamic) Bayes net formalism provides a powerful representational framework for such applications. However, existing…
A new empirical Bayes approach to variable selection in the context of generalized linear models is developed. The proposed algorithm scales to situations in which the number of putative explanatory variables is very large, possibly much…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
We consider the Bayesian approach to the linear Gaussian inference problem of inferring the initial condition of a linear dynamical system from noisy output measurements taken after the initial time. In practical applications, the large…
The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…
Score based learning (SBL) is a promising approach for learning Bayesian networks in the discrete domain. However, when employing SBL in the continuous domain, one is either forced to move the problem to the discrete domain or use metrics…
This paper introduces Bayesian supervised and unsupervised segmentation algorithms aimed at oceanic segmentation of SAR images. The data term, \emph{i.e}., the density of the observed backscattered signal given the region, is modeled by a…
The estimation of Bayesian networks given high-dimensional data, in particular gene expression data, has been the focus of much recent research. Whilst there are several methods available for the estimation of such networks, these typically…
In this paper, a feature extraction approach for the deformable linear object is presented, which uses a Bezier curve to represent the original geometric shape. The proposed extraction strategy is combined with a parameterization technique,…
Information Bottlenecks (IBs) learn representations that generalize to unseen data by information compression. However, existing IBs are practically unable to guarantee generalization in real-world scenarios due to the vacuous…
Parameter estimation is a foundational step in statistical modeling, enabling us to extract knowledge from data and apply it effectively. Bayesian estimation of parameters incorporates prior beliefs with observed data to infer distribution…
Bayesian optimization is an effective methodology for the global optimization of functions with expensive evaluations. It relies on querying a distribution over functions defined by a relatively cheap surrogate model. An accurate model for…
I show how a renormalization group (RG) method can be used to incrementally integrate the information in cosmological large-scale structure data sets (including CMB, galaxy redshift surveys, etc.). I show numerical tests for Gaussian…
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…
Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…
The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
The standard approach to renormalization relies, technically, on the asymptotic perturbation of Gaussian measures embodied in Feynman diagram theory. From a mathematical standpoint this is not good enough, because thereby solving the…