arXiv research

Enhances SDR via Hellinger correlation for better data dependency understanding.

Study nearest-neighbor radii under dependent sampling, finding they remain informative.

Paper introduces new bounds linking data compressibility to generalization error.

Many nonparametric regressors were recently shown to converge at rates that depend only on the intrinsic dimension of data. These regressors thus escape the curse of dimension when high-dimensional data has low intrinsic dimension (e.g. a manifold). We show that k-NN regression is also adaptive to intrinsic dimension. …

Gromov's universal filling inequalities relate the filling radius and the filling volume of a Riemannian manifold to its volume. The main result of the present article is that in dimensions at least three the optimal constants in the filling inequalities depend only on dimension and orientability, not on the manifold i…

Upper bounds for volume spectrum depend on volume, dimension, and a conformal invariant.

Gradient methods struggle with high dimensions in convex optimization.

BBVI converges nearly dimensionally independent for log-concave targets.

The purpose of sufficient dimension reduction (SDR) is to find the low-dimensional subspace of input features that is sufficient for predicting output values. In this paper, we propose a novel distribution-free SDR method called sufficient component analysis (SCA), which is computationally more efficient than existing …

Any closed, connected Riemannian manifold $M$ can be smoothly embedded by its Laplacian eigenfunction maps into $\mathbb{R}^m$ for some $m$. We call the smallest such $m$ the maximal embedding dimension of $M$. We show that the maximal embedding dimension of $M$ is bounded from above by a constant depending only on the…

To model high dimensional data, Gaussian methods are widely used since they remain tractable and yield parsimonious models by imposing strong assumptions on the data. Vine copulas are more flexible by combining arbitrary marginal distributions and (conditional) bivariate copulas. Yet, this adaptability is accompanied b…

Sentinel improves time series forecasting by modeling both temporal and channel dependencies.

New bounds for adaptive control in high dimensions without fixed state space.

New stability analysis improves generalization of multipass SGD.

Many 0/1 datasets have a very large number of variables; on the other hand, they are sparse and the dependency structure of the variables is simpler than the number of variables would suggest. Defining the effective dimensionality of such a dataset is a nontrivial problem. We consider the problem of defining a robust m…

New algorithms reduce regret in neural logistic bandits.

Improved Frank-Wolfe algorithm for polytopes converges linearly with dimension dependence on optimal face.

This study quantifies the scalability of k-Sliced Mutual Information (k-SMI) with dimension.

Paper extends learning theory to dependent data with uniform risk bounds.

Paper provides GOT convergence guarantees for sub-gamma distributions and dependent samples.

This paper analyzes the bias of inexact MCMC methods in high dimensions.

Novel model captures high-dimensional copulas with spectral dynamics and regularization.

The paper analyzes why Gaussianization slows down with higher dimensions and proposes a solution.

Abstract reviews recent Lagrangian analysis on immersions into higher dimensions.

Classifies maximal symmetry models of CR dimension 1.

New algorithm converges to equilibrium in nonconvex-nonconcave optimization problems without dimension dependence.

Over the past few years, neural networks were proven vulnerable to adversarial images: targeted but imperceptible image perturbations lead to drastically different predictions. We show that adversarial vulnerability increases with the gradients of the training objective when viewed as a function of the inputs. Surprisi…

Infinite-dimensional contact geometry explored.

Paper studies estimating asset correlations across sectors.

New Sauer inequality improves multiclass hypothesis class bounds.

Generative model captures complex dependence in financial data.

We present the first tree-based regressor whose convergence rate depends only on the intrinsic dimension of the data, namely its Assouad dimension. The regressor uses the RPtree partitioning procedure, a simple randomized variant of k-d trees.

We investigate the second Dirac eigenvalue on Riemannian manifolds admitting a Killing spinor. In small dimensions the whole Dirac spectrum depends on special eigenvalues on functions and 1-forms. We compute and discuss the formulas in dimension $n = 7$.

A simple and computationally efficient scheme for tree-structured vector quantization is presented. Unlike previous methods, its quantization error depends only on the intrinsic dimension of the data distribution, rather than the apparent dimension of the space in which the data happen to lie.

Study provides bounds for estimating intrinsic dimension using Gaussian kernels.

We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even when the dimens…

PAC-Bayesian theory applied to data-dependent hypothesis sets yields uniform generalization bounds.

We break dimension dependence in sparse distribution estimation with communication constraints.

We study the topology of smectic defects in two and three dimensions. We give a topological classification of smectic point defects and disclination lines in three dimensions. In addition we describe the combination rules for smectic point defects in two and three dimensions, showing how the broken translational symmet…

Estimates intrinsic dimension of data for GANs.

The paper analyzes high-dimensional kernel regression, showing different risk curves based on data and regularization.

SGD generalizes well in high dimensions without regularization.

A typical goal of supervised dimension reduction is to find a low-dimensional subspace of the input space such that the projected input variables preserve maximal information about the output variables. The dependence maximization approach solves the supervised dimension reduction problem through maximizing a statistic…

This work proves generalization bounds for neural networks without Lipschitz assumptions.

New RL method reduces sample complexity for large policy spaces.

Study on learning properties of scale-dependent kernels controlling stability and error.

Multi-period measures of risk account for the path that the value of an investment portfolio takes. In the context of probabilistic risk measures, the focus has traditionally been on the magnitude of investment loss and not on the dimension associated with the passage of time. In this paper, the concept of temporal pat…

eDCF estimates intrinsic dimension using local connectivity.