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We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…
We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…
Numerical simulations are crucial for modeling complex systems, but calibrating them becomes challenging when data are noisy or incomplete and likelihood evaluations are computationally expensive. Bayesian calibration offers an interesting…
In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…
This paper presents a novel stochastic optimisation methodology to perform empirical Bayesian inference in semi-blind image deconvolution problems. Given a blurred image and a parametric class of possible operators, the proposed…
Implicit models, which allow for the generation of samples but not for point-wise evaluation of probabilities, are omnipresent in real-world problems tackled by machine learning and a hot topic of current research. Some examples include…
Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…
We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…
The ability to accurately predict human behavior is central to the safety and efficiency of robot autonomy in interactive settings. Unfortunately, robots often lack access to key information on which these predictions may hinge, such as…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
We introduce a class of interatomic potential models that can be automatically generated from data consisting of the energies and forces experienced by atoms, derived from quantum mechanical calculations. The resulting model does not have a…
We present a novel method for drawing samples from Gibbs distributions with densities of the form $\pi(x) \propto \exp(-U(x))$. The method accelerates the unadjusted Langevin algorithm by introducing an inertia term similar to Polyak's…
A recent novel extension of multi-output Gaussian processes handles heterogeneous outputs assuming that each output has its own likelihood function. It uses a vector-valued Gaussian process prior to jointly model all likelihoods' parameters…
We consider stochastic convex optimization problems where the objective is an expectation over smooth functions. For this setting we suggest a novel gradient estimate that combines two recent mechanism that are related to notion of…
We establish a systematic framework of unbiased quantum sampling and estimation protocols for the classical Gibbs expectation. This framework generalizes existing approaches to the partition function estimation and has broader applications…
We introduce two quantum algorithms for solving structured prediction problems. We first show that a stochastic gradient descent that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the…
We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…