arXiv research

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

We study tilting subweibull distributions and their tail behavior.

Paper studies second order tail probabilities in risk models.

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

Single gradient step finds adversarial examples in random neural networks.

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

Liouville theorems extended to graphs with bounded geometry.

Estimates change point in high dimensional time series models.

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.

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

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…

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

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…

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

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…

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…

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 …

New tools in nonlinear random matrices improve understanding of the Sum of Squares hierarchy.

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 + …

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

New algorithm learns halfspaces over hypercube with random bit flips.

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 $e^{(\frac{1}{2}+o(1))\sqrt{n}{\log n}}$.

Study on hyperbolic groups, focusing on separability and splittings.

For the tensor PCA (principal component analysis) problem, we propose a new hierarchy of increasingly powerful algorithms with increasing runtime. Our hierarchy is analogous to the sum-of-squares (SOS) hierarchy but is instead inspired by statistical physics and related algorithms such as belief propagation and AMP (ap…

We introduce tensor network contraction algorithms for the evaluation of the Jones polynomial of arbitrary knots. The value of the Jones polynomial of a knot maps to the partition function of a $q$-state Potts model defined as a planar graph with weighted edges that corresponds to the knot. For any integer $q$, we cast…

Study of linear classifiers in infinite imbalance scenarios.

Sharp concentration results for sums of heavy-tailed random variables.

Paper extends stochastic dominance for compound binomial distributions.

New tree-structured Markov fields with Poisson marginals for counting variables.

New class of heavy-tailed distributions shows weighted averages dominate individual variables.

Consider an experiment involving a potentially small number of subjects. Some random variables are observed on each subject: a high-dimensional one called the "observed" random variable, and a one-dimensional one called the "outcome" random variable. We are interested in the dependencies between the observed random var…

Diversification improves profits for heavy-tailed investments.

The paper sets limits on the accuracy of macroeconomic forecasts based on statistical moments and trade volumes.

We investigate concentration inequalities for Dirichlet and Multinomial random variables.

This study compares machine learning methods for high-cardinality categorical variables.

This work improves bounds on Bayesian coreset quality.

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…

Random Forest variable importance is improved by class balancing techniques.

A note on extending Chernoff bound for unit interval random variables.

This paper examines from an experimental perspective random forests, the increasingly used statistical method for classification and regression problems introduced by Leo Breiman in 2001. It first aims at confirming, known but sparse, advice for using random forests and at proposing some complementary remarks for both …

AugBagg improves random forest accuracy with added noise variables.

Paper generalizes bipolar theorems for non-negative random variables.

New bounds on continuous random variables' right-tail probabilities.

Develops a new method for nonlinear dimension reduction using random features.

In the study of investment problem, aside from the investment risk the background risk appears. Both the investment risk and the background risk are probabilistically described by random variables. This paper starts from the hypothesis that the two types of risk can be represented both probabilistically (by random vari…

New algorithm combines Geostatistics and Quantile Random Forests for non-stationary spatial modelling.

Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input variables of the model. When the statistics of the output event are known, these input …