相关论文: Stability of Mean-Field Variational Inference

Approximate inference in high-dimensional, discrete probabilistic models is a central problem in computational statistics and machine learning. This paper describes discrete particle variational inference (DPVI), a new approach that…

We study inference in stochastic block models (SBMs) through the lens of optimal transport (OT). We first establish that maximum likelihood variational inference (MLVI) can be interpreted as a semi-relaxed Gromov-Wasserstein (srGW)…

In Bayesian statistics, a continuity property of the posterior distribution with respect to the observable variable is crucial as it expresses well-posedness, i.e., stability with respect to errors in the measurement of data. Essentially,…

We present the first minimax risk bounds for estimators of the spectral measure in multivariate linear factor models, where observations are linear combinations of regularly varying latent factors. Non-asymptotic convergence rates are…

Variational inference is a scalable technique for approximate Bayesian inference. Deriving variational inference algorithms requires tedious model-specific calculations; this makes it difficult to automate. We propose an automatic…

Recent advances in convex optimization have led to new strides in the phase retrieval problem over finite-dimensional vector spaces. However, certain fundamental questions remain: What sorts of measurement vectors uniquely determine every…

While Variational Inequality (VI) is a well-established mathematical framework that subsumes Nash equilibrium and saddle-point problems, less is known about its extension, Quasi-Variational Inequalities (QVI). QVI allows for cases where the…

In seismic exploration, sources and measurements of seismic waves on the surface are used to determine model parameters representing geophysical properties of the earth. Full-waveform inversion (FWI) is a nonlinear seismic inverse technique…

Variational inference (VI) is a popular approach in Bayesian inference, that looks for the best approximation of the posterior distribution within a parametric family, minimizing a loss that is typically the (reverse) Kullback-Leibler (KL)…

In data-driven learning and inference tasks, the high cost of acquiring samples from the target distribution often limits performance. A common strategy to mitigate this challenge is to augment the limited target samples with data from a…

We study Langevin-type algorithms for sampling from Gibbs distributions such that the potentials are dissipative and their weak gradients have finite moduli of continuity not necessarily convergent to zero. Our main result is a…

Variable selection in linear regression has been a central topic in statistical research for decades. Bayesian variable selection methods, which account for uncertainty in both the regression coefficients and the noise variance, have…

Stein's method has been widely used for probability approximations. However, in the multi-dimensional setting, most of the results are for multivariate normal approximation or for test functions with bounded second- or higher-order…

This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…

Structural equation models (SEMs) are commonly used to study the structural relationship between observed variables and latent constructs. Recently, Bayesian fitting procedures for SEMs have received more attention thanks to their potential…

This paper proposes a geometric estimator of dependency between a pair of multivariate samples. The proposed estimator of dependency is based on a randomly permuted geometric graph (the minimal spanning tree) over the two multivariate…

Margin has played an important role on the design and analysis of learning algorithms during the past years, mostly working with the maximization of the minimum margin. Recent years have witnessed the increasing empirical studies on the…

We derive first-order (in the stepsize) bounds on the bias in Wasserstein distances of the invariant measure of stochastic gradient kinetic Langevin dynamics with minimal assumptions on the stochastic gradient noise. These bounds sharpen…

The performance of decision policies and prediction models often deteriorates when applied to environments different from the ones seen during training. To ensure reliable operation, we analyze the stability of a system under distribution…

For the task of sampling from a density $\pi \propto \exp(-V)$ on $\mathbb{R}^d$, where $V$ is possibly non-convex but $L$-gradient Lipschitz, we prove that averaged Langevin Monte Carlo outputs a sample with $\varepsilon$-relative Fisher…