Related papers: Bayesian Coreset Construction via Greedy Iterative…
We consider structure learning of linear Gaussian structural equation models with weak edges. Since the presence of weak edges can lead to a loss of edge orientations in the true underlying CPDAG, we define a new graphical object that can…
We study the convergence rate of the proximal incremental aggregated gradient (PIAG) method for minimizing the sum of a large number of smooth component functions (where the sum is strongly convex) and a non-smooth convex function. At each…
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…
Leveraging the wealth of unlabeled data produced in recent years provides great potential for improving supervised models. When the cost of acquiring labels is high, probabilistic active learning methods can be used to greedily select the…
Local Bayesian optimization is a promising practical approach to solve the high dimensional black-box function optimization problem. Among them is the approximated gradient class of methods, which implements a strategy similar to gradient…
We prove some results on the rate of convergence of greedy algorithms, which provide expansions. We consider both the case of Hilbert spaces and the more general case of Banach spaces. The new ingredient of the paper is that we bound the…
Variable selection in ultra-high dimensional linear regression is often preceded by a screening step to significantly reduce the dimension. Here we develop a Bayesian variable screening method (BITS) guided by the posterior model…
Numerical integration and emulation are fundamental topics across scientific fields. We propose novel adaptive quadrature schemes based on an active learning procedure. We consider an interpolative approach for building a surrogate…
We develop a novel hybrid method for Bayesian network structure learning called partitioned hybrid greedy search (pHGS), composed of three distinct yet compatible new algorithms: Partitioned PC (pPC) accelerates skeleton learning via a…
Bayesian optimization is a data-efficient technique that has been shown to be extremely powerful to optimize expensive, black-box, and possibly noisy objective functions. Many applications involve optimizing probabilities and mixtures which…
Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…
The paper presents a priori error analysis of the shallow neural network approximation to the solution to the indefinite elliptic equation and and cutting-edge implementation of the Orthogonal Greedy Algorithm (OGA) tailored to overcome the…
With a greedy strategy to construct control index set of coordinates firstly and then choosing the corresponding column submatrix in each iteration, we present a greedy block Gauss-Seidel (GBGS) method for solving large linear least squares…
We present geometric Bayesian active learning by disagreements (GBALD), a framework that performs BALD on its core-set construction interacting with model uncertainty estimation. Technically, GBALD constructs core-set on ellipsoid, not…
Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…
Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…
Bayesian optimization is a class of global optimization techniques. In Bayesian optimization, the underlying objective function is modeled as a realization of a Gaussian process. Although the Gaussian process assumption implies a random…
Loss-based clustering methods, such as k-means and its variants, are standard tools for finding groups in data. However, the lack of quantification of uncertainty in the estimated clusters is a disadvantage. Model-based clustering based on…
We introduce a novel edge tracing algorithm using Gaussian process regression. Our edge-based segmentation algorithm models an edge of interest using Gaussian process regression and iteratively searches the image for edge pixels in a…
Preconditioned gradient iterations for very large eigenvalue problems are efficient solvers with growing popularity. However, only for the simplest preconditioned eigensolver, namely the preconditioned gradient iteration (or preconditioned…