arXiv research

Study improves error bounds for sparse regression with heavy-tailed covariates.

New insights into natural exponential families improve regret bounds for bandit problems.

Paper studies second order tail probabilities in risk models.

We study tilting subweibull distributions and their tail behavior.

The paper proposes a new method to measure risk with fine-grained tail sensitivity.

In this paper, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for risk processes with claims of subexponential tails for non-stationary arrival processes that satisfy a large deviation principle. As a result, the arrival process can be dependent, non-stationary and non-renewal. We give t…

New PAC-Bayes bounds for heavy-tailed losses using supermartingales.

Ridge regression performs optimally in noisy environments with heavy-tailed distributions.

Liouville theorems extended to graphs with bounded geometry.

Study of linear classifiers in infinite imbalance scenarios.

We present the notion of asymptotically large depth for a metric space which is (a priory) weaker than having subexponential asymptotic dimension growth and (a priory) stronger than property A.

We present a new, more elementary proof of the Freedman-Teichner result that the geometric classification techniques (surgery, s-cobordism, and pseudoisotopy) hold for topological 4-manifolds with groups of subexponential growth. In an appendix Freedman and Teichner give a correction to their original proof, and reform…

We introduce a new quasi-isometry invariant $\subcorank X$ of a metric space $X$ called {\it subexponential corank}. A metric space $X$ has subexponential corank $k$ if roughly speaking there exists a continuous map $g:X\to T$ such that for each $t\in T$ the set $g^{-1}(t)$ has subexponential growth rate in $X$ and the…

This work improves bounds on Bayesian coreset quality.

Proposes a new sampling policy for ranking and selection problems.

Study shows torsion grows subexponentially in book of I-bundles but can grow exponentially in non-regular covers.

Study finds the minimum number of finite Gaussian mixtures for best approximation.

We prove several cases of Zimmer's conjecture for actions of higher-rank cocompact lattices on low dimensional manifolds. For example, if $Γ$ is a cocompact lattice in $\mathrm{Sl}(n, \mathbb R)$, $M$ is a compact manifold, and $ω$ a volume form on $M$ we show that any homomorphism $ρ\colon Γ\rightarrow \mathrm{Diff}(M…

Single gradient step finds adversarial examples in random neural networks.

The article shows how to count small eigenvalues without assuming Morse functions.

Graphs with bounded degrees and non-negative Ollivier-Ricci curvature have subexponential growth and diffusive random walk.

We address a long-standing and long-investigated problem in combinatorial topology, and break the exponential barrier for triangulations of real projective space, constructing a trianglation of $\mathbb{RP}^n$ of size $e^{(\frac{1}{2}+o(1))\sqrt{n}{\log n}}$.

Estimates change point in high dimensional time series models.

Study on hyperbolic groups, focusing on separability and splittings.

The paper proves concentration inequalities for diffusion processes.

Trace norm regularization is a popular method of multitask learning. We give excess risk bounds with explicit dependence on the number of tasks, the number of examples per task and properties of the data distribution. The bounds are independent of the dimension of the input space, which may be infinite as in the case o…

The quantification of diversification benefits due to risk aggregation plays a prominent role in the (regulatory) capital management of large firms within the financial industry. However, the complexity of today's risk landscape makes a quantifiable reduction of risk concentration a challenging task. In the present pap…

This is a sequel to the paper [Cas]. Here, we extend the methods of Farb-Wolfson using the theory of FI_G-modules to obtain stability of equivariant Galois representations of the etale cohomology of orbit configuration spaces. We establish subexponential bounds on the growth of unstable cohomology, and then use the Gro…

This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many loss functions besides the squared loss, and scales only with the sub-Gaussian or …

We study the crossing number of links that are formed by edges of a triangulation T of the 3-sphere with n tetrahedra. We show that the crossing number is bounded from above by an exponential function of n^2. In general, this bound can not be replaced by a subexponential bound. However, if T is polytopal (resp. shellab…

We investigate the average-case complexity of decision problems for finitely generated groups, in particular the word and membership problems. Using our recent results on ``generic-case complexity'' we show that if a finitely generated group $G$ has the word problem solvable in subexponential time and has a subgroup of…

We study the computational cost of recovering a unit-norm sparse principal component $x \in \mathbb{R}^n$ planted in a random matrix, in either the Wigner or Wishart spiked model (observing either $W + λxx^\top$ with $W$ drawn from the Gaussian orthogonal ensemble, or $N$ independent samples from $\mathcal{N}(0, I_n + …

Optimal data-driven formulations are found for learning and decision-making with historical data.

We continue the study of a general class of spaces of 0-cycles on a manifold defined and begun by Farb-Wolfson-Wood. Using work of Gadish on linear subspace arrangements, we obtain representation stability for the cohomology of the ordered version of these spaces. We establish subexponential bounds on the growth of uns…

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

New method models fat-tailed distributions with anisotropic tail-adaptive flows.

New measures capture tail dependence and non-exchangeability in financial data.

We contribute to the arithmetic/topology dictionary by relating asymptotic point counts and arithmetic statistics over finite fields to homological stability and representation stability over $\Cb$ in the example of configuration spaces of $n$ points in smooth varieties. To do this, we import the method of homological …

The paper examines how heavy-tailed risks behave under Gaussian copula models.

New tail dependence measures for stock indices.

Study tail behavior of sum of heavy-tailed risks with copulas.

Paper provides tail bounds for stochastic mirror descent in heavy-tailed noise.

A simple log-transform fixes heavy-tailed data for generative models.

SS-GEN simulates rare events in heavy and light-tailed data.

This work extends diffusion models to handle heavy-tailed targets, improving score estimation and sampling guarantees.

This paper investigates the average-case time complexity of certifying RIP matrices.

The literature of heavy tails (typically) starts with a random walk and finds mechanisms that lead to fat tails under aggregation. We follow the inverse route and show how starting with fat tails we get to thin-tails when deriving the probability distribution of the response to a random variable. We introduce a general…

This paper improves tail dependence analysis by introducing a path-based approach.