Related papers: Frank-Wolfe Bayesian Quadrature: Probabilistic Int…
We introduce BayeSQP, a novel algorithm for general black-box optimization that merges the structure of sequential quadratic programming with concepts from Bayesian optimization. BayeSQP employs second-order Gaussian process surrogates for…
Full waveform inversion (FWI) can be expressed in a Bayesian framework, where the associated uncertainties are captured by the posterior probability distribution (PPD). In practice, solving Bayesian FWI with sampling-based methods such as…
Quantum Bayesian Computation (QBC) is an emerging field that levers the computational gains available from quantum computers to provide an exponential speed-up in Bayesian computation. Our paper adds to the literature in two ways. First, we…
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…
Automatic cubatures approximate integrals to user-specified error tolerances. For high dimensional problems, it is difficult to adaptively change the sampling pattern to focus on peaks because peaks can hide more easily in high dimensional…
Bayesian inference is a powerful paradigm for quantum state tomography, treating uncertainty in meaningful and informative ways. Yet the numerical challenges associated with sampling from complex probability distributions hampers Bayesian…
Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a…
Clustering is essential in data analysis and machine learning, but traditional algorithms like $k$-means and Gaussian Mixture Models (GMM) often fail with nonconvex clusters. To address the challenge, we introduce the Flexible Bivariate…
Owing to their low-complexity iterations, Frank-Wolfe (FW) solvers are well suited for various large-scale learning tasks. When block-separable constraints are present, randomized block FW (RB-FW) has been shown to further reduce complexity…
Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…
Bayesian inference with empirical likelihood faces a challenge as the posterior domain is a proper subset of the original parameter space due to the convex hull constraint. We propose a regularized exponentially tilted empirical likelihood…
Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised…
Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised…
The paper introduces an estimation method for flexible Bayesian quantile regression in ordinal (FBQROR) models i.e., an ordinal quantile regression where the error follows a generalized asymmetric Laplace (GAL) distribution. The GAL…
Bayesian learning is ubiquitous for implementing classification and regression tasks, however, it is accompanied by computationally intractable limitations when the feature spaces become extremely large. Aiming to solve this problem, we…
Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…
The Frank-Wolfe method has become increasingly useful in statistical and machine learning applications, due to the structure-inducing properties of the iterates, and especially in settings where linear minimization over the feasible set is…
Bayesian inference plays a central role in scientific and engineering applications by enabling principled reasoning under uncertainty. However, sampling from generic probability distributions remains a computationally demanding task. This…
Variational inference (VI) seeks to approximate a target distribution $\pi$ by an element of a tractable family of distributions. Of key interest in statistics and machine learning is Gaussian VI, which approximates $\pi$ by minimizing the…
We develop a novel variant of the classical Frank-Wolfe algorithm, which we call spectral Frank-Wolfe, for convex optimization over a spectrahedron. The spectral Frank-Wolfe algorithm has a novel ingredient: it computes a few eigenvectors…