Related papers: Bayesian Fisher's Discriminant for Functional Data

We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that…

Building a recommendation system involves analyzing user data, which can potentially leak sensitive information about users. Anonymizing user data is often not sufficient for preserving user privacy. Motivated by this, we propose a…

We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to…

This study presents a Bayesian maximum \textit{a~posteriori} (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized Tikhonov regularization, providing a rational…

For many data-intensive tasks, feature selection is an important preprocessing step. However, most existing methods do not directly and intuitively explore the intrinsic discriminative information of features. We propose a novel feature…

We present an improved Bayesian framework for performing inference of affine transformations of constrained functions. We focus on quadrature with nonnegative functions, a common task in Bayesian inference. We consider constraints on the…

Substantial research on structured sparsity has contributed to analysis of many different applications. However, there have been few Bayesian procedures among this work. Here, we develop a Bayesian model for structured sparsity that uses a…

Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices…

In this paper we investigate the existence of a separation principle between model identification and control design in the context of model predictive control. First, we clarify that such a separation principle holds asymptotically in the…

Bayesian inference involves the specification of a statistical model by a statistician or practitioner, with careful thought about what each parameter represents. This results in particularly interpretable models which can be used to…

We propose a novel approach for estimating conditional or parametric expectations in the setting where obtaining samples or evaluating integrands is costly. Through the framework of probabilistic numerical methods (such as Bayesian…

The Fisher matrix approach (Fisher 1935) allows one to calculate in advance how well a given experiment will be able to estimate model parameters, and has been an invaluable tool in experimental design. In the same spirit, we present here a…

Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…

The composition of multiple Gaussian Processes as a Deep Gaussian Process (DGP) enables a deep probabilistic nonparametric approach to flexibly tackle complex machine learning problems with sound quantification of uncertainty. Existing…

Rich and complex time-series data, such as those generated from engineering systems, financial markets, videos or neural recordings, are now a common feature of modern data analysis. Explaining the phenomena underlying these diverse data…

A Bayesian approach is used to estimate the covariance matrix of Gaussian data. Ideas from Gaussian graphical models and model selection are used to construct a prior for the covariance matrix that is a mixture over all decomposable graphs.…

Many problems in robotics involve both continuous and discrete components, and modeling them together for estimation tasks has been a long standing and difficult problem. Hybrid Factor Graphs give us a mathematical framework to model these…

In Data Science, entities are typically represented by single valued measurements. Symbolic Data Analysis extends this framework to more complex structures, such as intervals and histograms, that express internal variability. We propose an…

We provide an introductory review of Bayesian data analytical methods, with a focus on applications for linguistics, psychology, psycholinguistics, and cognitive science. The empirically oriented researcher will benefit from making Bayesian…

The analytic inference, e.g. predictive distribution being in closed form, may be an appealing benefit for machine learning practitioners when they treat wide neural networks as Gaussian process in Bayesian setting. The realistic widths,…