相关论文: Riemannian Stein Variational Gradient Descent for …

We study the properties of stochastic approximation applied to a tame nondifferentiable function subject to constraints defined by a Riemannian manifold. The objective landscape of tame functions, arising in o-minimal topology extended to a…

We propose a Riemannian version of Nesterov's Accelerated Gradient algorithm (RAGD), and show that for geodesically smooth and strongly convex problems, within a neighborhood of the minimizer whose radius depends on the condition number as…

We present a new particle filtering algorithm for nonlinear systems in the discrete-time setting. Our algorithm is based on the Stein variational gradient descent (SVGD) framework, which is a general approach to sample from a target…

We propose a fast and scalable variational method for Bayesian inference in high-dimensional parameter space, which we call projected Stein variational Newton (pSVN) method. We exploit the intrinsic low-dimensional geometric structure of…

Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…

We introduce novel estimators for computing the curvature, tangent spaces, and dimension of data from manifolds, using tools from diffusion geometry. Although classical Riemannian geometry is a rich source of inspiration for geometric data…

Statistical inference for spatial processes from partially realized or scattered data has seen voluminous developments in diverse areas ranging from environmental sciences to business and economics. Inference on the associated rates of…

We present Re-weighted Gradient Descent (RGD), a novel optimization technique that improves the performance of deep neural networks through dynamic sample re-weighting. Leveraging insights from distributionally robust optimization (DRO)…

Magnetoencephalography and electroencephalography (M/EEG) can reveal neuronal dynamics non-invasively in real-time and are therefore appreciated methods in medicine and neuroscience. Recent advances in modeling brain-behavior relationships…

This paper studies large-scale optimization problems on Riemannian manifolds whose objective function is a finite sum of negative log-probability losses. Such problems arise in various machine learning and signal processing applications. By…

Efficiently accessing the information contained in non-linear and high dimensional probability distributions remains a core challenge in modern statistics. Traditionally, estimators that go beyond point estimates are either categorized as…

Over the last decade, a single algorithm has changed many facets of our lives - Stochastic Gradient Descent (SGD). In the era of ever decreasing loss functions, SGD and its various offspring have become the go-to optimization tool in…

We discover a fundamental exterior differential system of Riemannian geometry; indeed, an intrinsic and invariant global system of differential forms of degree $n$ associated to any given oriented Riemannian manifold $M$ of dimension $n+1$.…

Generalized Bayesian Inference (GBI) provides a flexible framework for updating prior distributions using various loss functions instead of the traditional likelihoods, thereby enhancing the model robustness to model misspecification.…

Diffusion models are recent state-of-the-art methods for image generation and likelihood estimation. In this work, we generalize continuous-time diffusion models to arbitrary Riemannian manifolds and derive a variational framework for…

Full waveform inversion is an ill-posed inverse problem whose solution non-uniqueness -- i.e., arising from band-limited, finite-aperture, noisy data -- calls for uncertainty quantification to avoid overconfident geological interpretations.…

We propose a projected Wasserstein gradient descent method (pWGD) for high-dimensional Bayesian inference problems. The underlying density function of a particle system of WGD is approximated by kernel density estimation (KDE), which faces…

Riemannian geometry provides the fundamental framework for optimization on nonlinear spaces such as matrix manifolds, which arise in machine learning, signal processing, and robotics. While the underlying theory is classical, existing…

Bayesian inference plays an important role in advancing machine learning, but faces computational challenges when applied to complex models such as deep neural networks. Variational inference circumvents these challenges by formulating…

In this paper, we present an adaptive gradient descent method for geodesically convex optimization on a Riemannian manifold with nonnegative sectional curvature. The method automatically adapts to the local geometry of the function and does…