arXiv research

Develops a deep learning framework for various data types.

Study resolves polynomial germs, proving no mixed critical points and strict transform properties.

The paper tackles deep learning from dependent data, achieving optimal performance.

Paper proposes deep neural networks for nonparametric regression from dependent data.

Study on singularities of specific polynomial functions.

New method for conformal prediction under Markovian data reduces coverage gap.

Fewer data weight updates lead to faster convergence in machine learning models.

In this note we consider sampling from (non-homogeneous) strongly Rayleigh probability measures. As an important corollary, we obtain a fast mixing Markov Chain sampler for Determinantal Point Processes.

We first show that every quasisimple sporadic group possesses an unmixed strongly real Beauville structure aside from the Mathieu groups M11 and M23 (and possibly 2B and M). We go on to show that no almost simple sporadic group possesses a mixed Beauville structure. We then go on to use the exceptional nature of the al…

We study probability measures induced by set functions with constraints. Such measures arise in a variety of real-world settings, where prior knowledge, resource limitations, or other pragmatic considerations impose constraints. We consider the task of rapidly sampling from such constrained measures, and develop fast M…

Research on mixed polynomials, extending non-degeneracy concepts to complex variables.

The paper analyzes convergence rates of Langevin dynamics and Proximal Sampler using $Φ$-divergence.

The paper studies convergence of kernel autocovariance operators for stationary processes.

Study on counting orbits and Poincaré series for specific hyperbolic metrics.

MALA mixes efficiently under smoothness and isoperimetry assumptions.

Gibbs sampler contracts entropy under strong log-concavity, improving mixing time.

Gradient EM converges exponentially to optimal solution in agnostic mixtures.

We show that the gradient norm $\|\nabla f(x)\|$ for $x \sim \exp(-f(x))$, where $f$ is strongly convex and smooth, concentrates tightly around its mean. This removes a barrier in the prior state-of-the-art analysis for the well-studied Metropolized Hamiltonian Monte Carlo (HMC) algorithm for sampling from a strongly l…

This article provides the first procedure for computing a fully data-dependent interval that traps the mixing time $t_{\text{mix}}$ of a finite reversible ergodic Markov chain at a prescribed confidence level. The interval is computed from a single finite-length sample path from the Markov chain, and does not require t…

MALA mixes optimally in κ√d steps for log-concave sampling.

New measure of maximal entropy found for a class of geometrically finite groups.

Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. They are strictly more general than strongly Rayleigh (SR) distributions such as the well-known determinantal point process. While SR distributions offer elegant models of diversity, they lac…

The paper extends geometric results from negatively-curved spaces to strictly convex Hilbert geometry.

LMC achieves sqrt(d) dependence in sampling error, improving previous bounds.

Paper tackles robust deep learning from weakly dependent data with unbounded loss and input.

A new framework uses an Incremental Transformer to design geopolymer mixtures efficiently.

The spectral gap $γ$ of a finite, ergodic, and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix $P$ may be unknown, yet one sample of the chain up to a fixed time $n$ may be observed. We consider here the problem of estimating $γ$ fro…

Learning non-linear systems from noisy, limited, and/or dependent data is an important task across various scientific fields including statistics, engineering, computer science, mathematics, and many more. In general, this learning task is ill-posed; however, additional information about the data's structure or on the …

Graph Beta Diffusion (GBD) generates graphs with mixed discrete and continuous components.

We extend Teichmueller dynamics to a flow on the total space of a flat bundle of deformation spaces of representations of the fundamental group of a fixed surface S in a Lie group G. The resulting dynamical system is a continuous version of the action of the mapping class group of S on the deformation space. We observe…

We prove new fast learning rates for the one-vs-all multiclass plug-in classifiers trained either from exponentially strongly mixing data or from data generated by a converging drifting distribution. These are two typical scenarios where training data are not iid. The learning rates are obtained under a multiclass vers…

Uniform counting formulas for orthogeodesics in Kleinian groups converge.

U-turn chains improve sampling from complex distributions.

We study the generalization performance of online learning algorithms trained on samples coming from a dependent source of data. We show that the generalization error of any stable online algorithm concentrates around its regret--an easily computable statistic of the online performance of the algorithm--when the underl…

This paper resolves the Langevin Algorithm's mixing time for log-concave distributions.

Gibbs sampler mixes quickly for certain smooth distributions.

A fundamental result in differential privacy states that the privacy guarantees of a mechanism are preserved by any post-processing of its output. In this paper we investigate under what conditions stochastic post-processing can amplify the privacy of a mechanism. By interpreting post-processing as the application of a…

New bounds for mixing time and privacy in projected Langevin algorithm and noisy SGD.

New MIP methods improve training of integer-valued neural networks.

We study the problem of controlling linear time-invariant systems with known noisy dynamics and adversarially chosen quadratic losses. We present the first efficient online learning algorithms in this setting that guarantee $O(\sqrt{T})$ regret under mild assumptions, where $T$ is the time horizon. Our algorithms rely …

We consider the problem of sampling from a density of the form $p(x) \propto \exp(-f(x)- g(x))$, where $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is a smooth and strongly convex function and $g: \mathbb{R}^d \rightarrow \mathbb{R}$ is a convex and Lipschitz function. We propose a new algorithm based on the Metropolis-Has…

Independent component analysis (ICA) is a cornerstone of modern data analysis. Its goal is to recover a latent random vector S with independent components from samples of X=AS where A is an unknown mixing matrix. Critically, all existing methods for ICA rely on and exploit strongly the assumption that S is not Gaussian…

We consider the problem of sampling from a strongly log-concave density in $\mathbb{R}^d$, and prove a non-asymptotic upper bound on the mixing time of the Metropolis-adjusted Langevin algorithm (MALA). The method draws samples by simulating a Markov chain obtained from the discretization of an appropriate Langevin dif…

New algorithm reduces communication in federated learning.

Unified approach for first-order methods with Markovian noise in stochastic optimization and variational inequalities.

The literature on statistical learning for time series assumes the asymptotic independence or ``mixing' of the data-generating process. These mixing assumptions are never tested, nor are there methods for estimating mixing rates from data. We give an estimator for the $β$-mixing rate based on a single stationary sample…

Library learns Bayesian networks from mixed data without discretization.

Study on Lane-Emden equation on curved spaces, revealing new existence and non-existence phenomena.