Related papers: On numerical approximation schemes for expectation…

Efficient feature selection from high-dimensional datasets is a very important challenge in many data-driven fields of science and engineering. We introduce a statistical mechanics inspired strategy that addresses the problem of sparse…

Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by…

We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…

We propose a Gaussian variational inference framework for the motion planning problem. In this framework, motion planning is formulated as an optimization over the distribution of the trajectories to approximate the desired trajectory…

Practitioners building classifiers often start with a smaller pilot dataset and plan to grow to larger data in the near future. Such projects need a toolkit for extrapolating how much classifier accuracy may improve from a 2x, 10x, or 50x…

In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of…

We consider a general class of binary packing problems with a convex quadratic knapsack constraint. We prove that these problems are APX-hard to approximate and present constant-factor approximation algorithms based upon three different…

Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be…

This paper is concerned with sample size determination methodology for prediction models. We propose combining the individual calculations via a learning-type curve. We suggest two distinct ways of doing so, a deterministic skeleton of a…

The parareal algorithm represents an important class of parallel-in-time algorithms for solving evolution equations and has been widely applied in practice. To achieve effective speedup, the choice of the coarse propagator in the algorithm…

The generalized Laplace (GL) distribution, which falls in the larger family of generalized hyperbolic distributions, provides a versatile model to deal with a variety of applications thanks to its shape parameters. The elliptically…

Making good predictions of a physical system using a computer code requires the inputs to be carefully specified. Some of these inputs called control variables have to reproduce physical conditions whereas other inputs, called parameters,…

In this article, we propose the use of partitioning and clustering methods as an alternative to Gaussian quadrature for stochastic collocation. The key idea is to use cluster centers as the nodes for collocation. In this way, we can extend…

We consider the problem of learning high-dimensional Gaussian graphical models. The graphical lasso is one of the most popular methods for estimating Gaussian graphical models. However, it does not achieve the oracle rate of convergence. In…

A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the general inverse…

It is common practice to use Laplace approximations to compute marginal likelihoods in Bayesian versions of generalised linear models (GLM). Marginal likelihoods combined with model priors are then used in different search algorithms to…

Robust statistical estimators offer resilience against outliers but are often computationally challenging, particularly in high-dimensional sparse settings. Modern optimization techniques are utilized for robust sparse association…

Grid search and random search are widely used techniques for hyperparameter tuning in machine learning, especially when gradient information is unavailable. In these methods, a finite set of candidate configurations is evaluated, and the…

Using a hierarchical construction, we develop methods for a wide and flexible class of models by taking a fully parametric approach to generalized linear mixed models with complex covariance dependence. The Laplace approximation is used to…

Many popular learning algorithms (E.g. Regression, Fourier-Transform based algorithms, Kernel SVM and Kernel ridge regression) operate by reducing the problem to a convex optimization problem over a vector space of functions. These methods…