arXiv research

Efficiently estimates binary product distributions with privacy.

Parallel sampling for smooth distributions with fast convergence.

Robust Bayesian inference improves model performance on discrete data.

New sampling method improves efficiency for diffusion models.

Paper learns dictionaries for sparse signal recovery using automatic differentiation.

Algorithm learns affine transformations robustly from corrupted samples.

Ideas from the image processing literature have recently motivated a new set of clustering algorithms that rely on the concept of total variation. While these algorithms perform well for bi-partitioning tasks, their recursive extensions yield unimpressive results for multiclass clustering tasks. This paper presents a g…

The paper studies curves in Riemannian manifolds using total variation flow.

Optimal pre-processing reduces disparate impact by minimizing total variation distance.

We show a very simple and general total second variation formula for Perelman's $\mathcal{W}$-functional at arbitrary points in the space of Riemannian metrics. Moreover we perform a study of the properties of the variations of Kähler structures. We deduce a quite simple and general total second variation formula for P…

Two new deterministic offspring selection methods reduce statistical distance in SMC and pMCMC.

We present a graph-based variational algorithm for classification of high-dimensional data, generalizing the binary diffuse interface model to the case of multiple classes. Motivated by total variation techniques, the method involves minimizing an energy functional made up of three terms. The first two terms promote a …

We derive variational formulas for the total Q-prime curvature under the deformation of strictly pseudoconvex domains in a complex manifold. We also show that the total Q-prime curvature agrees with the renormalized volume of such domains with respect to the complete Einstein-Kähler metric. In the appendix, by Rod Gove…

Advances smooth over-parameterization for solving non-smooth optimization problems.

New bounds use IPMs to improve generalization in machine learning.

We consider the problem of estimating a function defined over $n$ locations on a $d$-dimensional grid (having all side lengths equal to $n^{1/d}$). When the function is constrained to have discrete total variation bounded by $C_n$, we derive the minimax optimal (squared) $\ell_2$ estimation error rate, parametrized by …

We study convergence rates of variational posterior distributions for nonparametric and high-dimensional inference. We formulate general conditions on prior, likelihood, and variational class that characterize the convergence rates. Under similar "prior mass and testing" conditions considered in the literature, the rat…

Statistical shape models enhance machine learning algorithms providing prior information about deformation. A Point Distribution Model (PDM) is a popular landmark-based statistical shape model for segmentation. It requires choosing a model order, which determines how much of the variation seen in the training data is a…

We study the theoretical properties of image denoising via total variation penalized least-squares. We define the total vatiation in terms of the two-dimensional total discrete derivative of the image and show that it gives rise to denoised images that are piecewise constant on rectangular sets. We prove that, if the t…

We extend the Deep Image Prior (DIP) framework to one-dimensional signals. DIP is using a randomly initialized convolutional neural network (CNN) to solve linear inverse problems by optimizing over weights to fit the observed measurements. Our main finding is that properly tuned one-dimensional convolutional architectu…

Efficiently estimates Gaussian distributions privately and robustly.

New algorithm samples from log-concave distributions with high accuracy in polynomial time.

The total variation distance is a core statistical distance between probability measures that satisfies the metric axioms, with value always falling in $[0,1]$. This distance plays a fundamental role in machine learning and signal processing: It is a member of the broader class of $f$-divergences, and it is related to …

Through the direct study of the analysis estimator we derive oracle inequalities with fast and slow rates by adapting the arguments involving projections by Dalalyan, Hebiri and Lederer (2017). We then extend the theory to the square root analysis estimator. Finally, we focus on (square root) total variation regularize…

New theory improves diffusion model convergence for generating data.

SaR-SVM-STV improves hyperspectral image classification with shape-adaptive reconstruction and denoising.

Study variational properties of curves in half-plane with area constraints.

Improves latent space structure for better data representation.

Study variations of Riemannian submersions to maintain geodesic fibers and positive curvatures.

The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex, non-smooth and highly non-linear, the first-order optimal condition of which ar…

Optimal testing of discrete distributions with high probability, achieving sample complexity bounds.

We examine the total mixed scalar curvature of a fixed distribution as a functional of a pseudo-Riemannian metric. We develop variational formulas for quantities of extrinsic geometry of the distribution to find the critical points of this action. Together with the arbitrary variations of the metric, we consider also v…

Estimates parameters of interconnected linear systems using total variation penalization.

C-VAE improves VAE by resolving prior issues and generating better samples.

Improves transparency and incorporates prior knowledge in Gaussian Process models.

Empirical Bayes rates via variational approximations and prior decomposition.

A new meta-learning method using shared variational inference.

Sharp inequality between TV and Hellinger distances for Gaussian mixtures.

Paper proposes a method to estimate total variation distance for synthetic data fidelity.

We extend the existing framework of semi-implicit variational inference (SIVI) and introduce doubly semi-implicit variational inference (DSIVI), a way to perform variational inference and learning when both the approximate posterior and the prior distribution are semi-implicit. In other words, DSIVI performs inference …

The paper analyzes uncertainty quantification in sparse Gaussian process regression with a Brownian motion prior.

Bayesian algorithms perform well even with misspecified priors, especially in meta-learning.

Paper addresses variational inference issues in Bayesian neural networks.

Robustly clusters mixtures of Gaussians even with outliers.

tvGP-VAE models tensor-valued latent variables with Gaussian processes for better data structure representation.

Stochastic variational inference for Bayesian deep neural network (DNN) requires specifying priors and approximate posterior distributions over neural network weights. Specifying meaningful weight priors is a challenging problem, particularly for scaling variational inference to deeper architectures involving high dime…

Study improves convergence rates for GVI under prior misspecification.

Paper introduces a new method to model epidemic dynamics with varying parameters.