arXiv research

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

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…

Quantifies polynomial approximation rates for smooth functions under various distributions.

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

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

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

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…

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

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

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

Generative Adversarial Networks improve robust statistics for various distributions.

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

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.

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.

Thompson Sampling is a well established approach to bandit and reinforcement learning problems. However its use in continuum armed bandit problems has received relatively little attention. We provide the first bounds on the regret of Thompson Sampling for continuum armed bandits under weak conditions on the function cl…

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

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.

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

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

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

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

New bounds for kernel regression under non-Gaussian noise.

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

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…

New analysis improves SGD for robust and quantile regression with sub-quadratic convergence.

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

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

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

Paper improves confidence intervals and variance estimation for deep learning models.

We consider the problem of learning a mixture of linear regressions (MLRs). An MLR is specified by $k$ nonnegative mixing weights $p_1, \ldots, p_k$ summing to $1$, and $k$ unknown regressors $w_1,...,w_k\in\mathbb{R}^d$. A sample from the MLR is drawn by sampling $i$ with probability $p_i$, then outputting $(x, y)$ wh…

New findings on depth vs. width in neural networks, showing depth can improve learnability.

The recent success of generative adversarial networks and variational learning suggests training a classifier network may work well in addressing the classical two-sample problem. Network-based tests have the computational advantage that the algorithm scales to large samples. This paper proposes a two-sample statistic …

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

We improve bounds for stochastic processes, especially those with heavy tails.

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…

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…

The paper reviews and improves concentration inequalities for statistical inference.

Study robust linear regression without distributional assumptions for heavy-tailed responses.

Paper optimizes change-point detection using learned distributions from training sequences.

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…

New algorithm speeds up knot polynomial calculations.

High-dimensional diffusion models suffer from distorted samples due to CFG.

Langevin Dynamics fails to sample from mixture distributions efficiently.

Finite index constant mean curvature hypersurfaces are minimal or hyperplanes.

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

Algorithm learns mixtures of Gaussians efficiently using diffusion models.