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Hierarchical Bayesian models based on Gaussian processes are considered useful for describing complex nonlinear statistical dependencies among variables in real-world data. However, effective Monte Carlo algorithms for inference with these…
The stochastic variational inference (SVI) paradigm, which combines variational inference, natural gradients, and stochastic updates, was recently proposed for large-scale data analysis in conjugate Bayesian models and demonstrated to be…
Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption,…
Sampling logconcave functions arising in statistics and machine learning has been a subject of intensive study. Recent developments include analyses for Langevin dynamics and Hamiltonian Monte Carlo (HMC). While both approaches have…
This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average control problem are considered for a tracking type cost…
Control variates are a well-established tool to reduce the variance of Monte Carlo estimators. However, for large-scale problems including high-dimensional and large-sample settings, their advantages can be outweighed by a substantial…
Langevin algorithms are gradient descent methods with additive noise. They have been used for decades in Markov chain Monte Carlo (MCMC) sampling, optimization, and learning. Their convergence properties for unconstrained non-convex…
There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…
In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent…
We consider stochastic optimization when one only has access to biased stochastic oracles of the objective and the gradient, and obtaining stochastic gradients with low biases comes at high costs. This setting captures various optimization…
The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…
We study the problem of sampling from a distribution $\target$ using the Langevin Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein distance of order $2$. Our result holds as long as the…
Hamiltonian Monte Carlo (HMC) has been progressively incorporated within the statistician's toolbox as an alternative sampling method in settings when standard Metropolis-Hastings is inefficient. HMC generates a Markov chain on an augmented…
In this paper, we investigate a continuous time version of the Stochastic Langevin Monte Carlo method, introduced in [WT11], that incorporates a stochastic sampling step inside the traditional over-damped Langevin diffusion. This method is…
Hamiltonian Monte Carlo (HMC) and related algorithms have become routinely used in Bayesian computation. In this article, we present a simple and provably accurate method to improve the efficiency of HMC and related algorithms with…
In machine learning and statistics, probabilistic inference involving multimodal distributions is quite difficult. This is especially true in high dimensional problems, where most existing algorithms cannot easily move from one mode to…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
Recently, the Hamilton Monte Carlo (HMC) has become widespread as one of the more reliable approaches to efficient sample generation processes. However, HMC is difficult to sample in a multimodal posterior distribution because the HMC chain…
Quantitative long-time entropic convergence and short-time regularization are established for an idealized Hamiltonian Monte Carlo chain which alternatively follows an Hamiltonian dynamics for a fixed time and then partially or totally…
We consider the problem of sampling from posterior distributions for Bayesian models where some parameters are restricted to be orthogonal matrices. Such matrices are sometimes used in neural networks models for reasons of regularization…