arXiv research

The study provides error bounds for the generalized Lasso with sub-exponential data.

Paper establishes universal lower bounds and optimal rates for clustering sub-exponential mixture models.

Proves new concentration inequalities for sub-gaussian and sub-exponential variables.

Characterizes uncertainty in low-rank matrix completion with noisy data.

Using a family of modified Weibull distributions, encompassing both sub-exponentials and super-exponentials, to parameterize the marginal distributions of asset returns and their multivariate generalizations with Gaussian copulas, we offer exact formulas for the tails of the distribution $P(S)$ of returns $S$ of a port…

Quadratic-time algorithm computes stretch factors and foliations for pseudo-Anosov mapping classes.

SGD converges to an invariant distribution with sub-Gaussian or sub-exponential properties.

New framework recovers sparse vectors via ReLU networks, achieving near-optimal statistical rate.

We consider the problem of unconstrained online convex optimization (OCO) with sub-exponential noise, a strictly more general problem than the standard OCO. In this setting, the learner receives a subgradient of the loss functions corrupted by sub-exponential noise and strives to achieve optimal regret guarantee, witho…

We show that the regulator, which is the difference between the homology torsion and the combinatorial Ray-Singer torsion, of fnite abelian coverings of a fixed complex has sub-exponential growth rate.

Quantifies polynomial approximation rates for smooth functions under various distributions.

Paper studies early-stopped mirror descent for noisy sparse phase retrieval.

We show that there is no bi-Lipschitz homeomorphism of $\mathbb{R}^2$ that maps a spiral with a sub-exponential decay of winding radii to an unwinded arc. This result is sharp as shows an example of a logarithmic spiral.

In several real-world applications involving decision making under uncertainty, the traditional expected value objective may not be suitable, as it may be necessary to control losses in the case of a rare but extreme event. Conditional Value-at-Risk (CVaR) is a popular risk measure for modeling the aforementioned objec…

New algorithms achieve high-probability parameter-free regret in online convex optimization with heavy-tailed data.

Kernel thinning compresses distributions more effectively than i.i.d. sampling or standard thinning.

The Langevin Algorithm's stationary distribution is shown to be sub-exponential or sub-Gaussian under certain conditions.

Study finds best linear model in high dimensions using PGD.

This paper presents a unified approach based on Wasserstein distance to derive concentration bounds for empirical estimates for two broad classes of risk measures defined in the paper. The classes of risk measures introduced include as special cases well known risk measures from the finance literature such as condition…

This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + ε_j$, $j=1, \ldots, m$, with independent sub-exponential noise $ε_j$. The goals are to understand the effect of the sparsity of $x$ on the estimation prec…

Analytic networks with bounded coefficients can't outperform polynomial approximations.

Improved Thompson Sampling for smoother functions with noise.

Annealed Entropic Allocation improves ranking and selection by mitigating hard switching and improving finite-budget discrimination.

Novel bounds for SGLD show generalization error decreases with more samples.

The paper explores how benign overfitting occurs in heavy-tailed input distributions.

Decision trees are consistent for regression and classification tasks even with many predictors.

Generative Adversarial Networks improve robust statistics for various distributions.

The paper introduces a new method for tail bounds of random vectors and matrices.

We introduce a new set of consistent measures of risks, in terms of the semi-invariants of pdf's, such that the centered moments and the cumulants of the portfolio distribution of returns that put more emphasis on the tail the distributions. We derive generalized efficient frontiers, based on these novel measures of ri…

Combining diffusion models with Langevin dynamics improves posterior sampling efficiency.

Many polynomial invariants of knots and links, including the Jones and HOMFLY-PT polynomials, are widely used in practice but #P-hard to compute. It was shown by Makowsky in 2001 that computing the Jones polynomial is fixed-parameter tractable in the treewidth of the link diagram, but the parameterised complexity of th…

Using a family of modified Weibull distributions, encompassing both sub-exponentials and super-exponentials, to parameterize the marginal distributions of asset returns and their natural multivariate generalizations, we give exact formulas for the tails and for the moments and cumulants of the distribution of returns o…

A novel algorithm minimizes regret in a multi-agent bandit problem with time-varying random graphs and heterogeneous rewards.

The paper reformulates regression in infinite dimensions as an inverse problem, showing it's equivalent to compact inverse problems.

New analysis of SGD with MCMC gradient estimator shows convergence rate and saddle point escape.

The study classifies translating and self-expanding solitons in 3D space.

Algorithm learns mixtures of linear regressions in subexponential time.

We investigate deep Bayesian neural networks with Gaussian weight priors and a class of ReLU-like nonlinearities. Bayesian neural networks with Gaussian priors are well known to induce an L2, "weight decay", regularization. Our results characterize a more intricate regularization effect at the level of the unit activat…

Minimizing a convex risk function is the main step in many basic learning algorithms. We study protocols for convex optimization which provably leak very little about the individual data points that constitute the loss function. Specifically, we consider differentially private algorithms that operate in the local model…

The paper reviews and improves concentration inequalities for statistical inference.

New algorithm speeds up knot polynomial calculations.

Sharp concentration inequalities for sub-Orlicz random variables with phase transition at α=2.

New framework controls generalization for heavy-tailed data in RLHF and SGLD.

Finite index constant mean curvature hypersurfaces are minimal or hyperplanes.

New bounds for kernel regression under non-Gaussian noise.

New method reduces inventory inaccuracies by 10x, saving retailers 4% annually.

Recurrent tasks such as pricing, calibration and risk assessment need to be executed accurately and in real-time. Simultaneously we observe an increase in model sophistication on the one hand and growing demands on the quality of risk management on the other. To address the resulting computational challenges, it is nat…

While considerable advances have been made in estimating high-dimensional structured models from independent data using Lasso-type models, limited progress has been made for settings when the samples are dependent. We consider estimating structured VAR (vector auto-regressive models), where the structure can be capture…