arXiv research

In this note, we derive concentration inequalities for random vectors with subGaussian norm (a generalization of both subGaussian random vectors and norm bounded random vectors), which are tight up to logarithmic factors.

Study improves self-normalized bounds for vector-valued processes beyond sub-Gaussianity.

The paper generalizes product inequalities for random vectors and their applications.

The paper provides concentration bounds for embeddings of generative models.

The paper establishes concentration bounds for embeddings of generative models.

Study robust covariance estimation in large data with concentrated vectors.

A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full conditional independence between these two variables given all the other variables. In…

Note on subgaussian bounds for sign-quantized linear maps.

Develops inequalities for high-dimensional linear processes with dependent innovations.

Tick-by-tick liquidity provision aims to maximize fees and reserves.

Study spectral properties of sparse random graphs to recover latent vectors.

The paper studies how norms of random vectors are preserved by random projections.

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

Sharp bounds on uniform generalization errors in binary linear classification.

Study on bending energy of surfaces with curvature concentration, deriving new lower bounds.

A new method for multiclass calibration using vector quantization.

This paper shows that deep learning (DL) representations of data produced by generative adversarial nets (GANs) are random vectors which fall within the class of so-called \textit{concentrated} random vectors. Further exploiting the fact that Gram matrices, of the type $G = X^T X$ with $X=[x_1,\ldots,x_n]\in \mathbb{R}…

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

The paper offers a framework to analyze machine learning problems using concentration of measure.

The paper analyzes sparse high-dimensional linear regression with random design and unknown error variance, providing adaptiveness and concentration rates.

Study on identifying most preferred policy in bandits with vector-valued rewards.

We prove several finiteness theorems for the normal bundles to souls in nonnegatively curved manifolds. More generally, we obtain finiteness results for open Riemannian manifolds whose topology is concentrated on compact domains of ``bounded geometry''.

New method improves feasibility of fitting Gaussian vectors to an ellipsoid.

Improved concentration inequalities for sub-Weibull variables enhance statistical and machine learning applications.

Repelling random walks improve graph-based sampling efficiency.

We show Vector Autoregressive Moving Average models with scalar Moving Average components could be estimated by generalized least square (GLS) for each fixed moving average polynomial. The conditional variance of the GLS model is the concentrated covariant matrix of the moving average process. Under GLS the likelihood …

The problem of estimating a high-dimensional sparse vector $\boldsymbolθ \in \mathbb{R}^n$ from an observation in i.i.d. Gaussian noise is considered. The performance is measured using squared-error loss. An empirical Bayes shrinkage estimator, derived using a Bernoulli-Gaussian prior, is analyzed and compared with the…

We study the concentration of random kernel matrices around their mean. We derive nonasymptotic exponential concentration inequalities for Lipschitz kernels assuming that the data points are independent draws from a class of multivariate distributions on $\mathbb R^d$, including the strongly log-concave distributions u…

High-dimensional time series data exist in numerous areas such as finance, genomics, healthcare, and neuroscience. An unavoidable aspect of all such datasets is missing data, and dealing with this issue has been an important focus in statistics, control, and machine learning. In this work, we consider a high-dimensiona…

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

We consider linear models where $d$ potential causes $X_1,...,X_d$ are correlated with one target quantity $Y$ and propose a method to infer whether the association is causal or whether it is an artifact caused by overfitting or hidden common causes. We employ the idea that in the former case the vector of regression c…

Improved bounds for Monte Carlo Rademacher Averages using self-bounding functions.

A new method reduces task interference in model merging.

A new method approximates the Sliced-Wasserstein distance without random projections.

Improved location estimation for high-dimensional data with finite sample size.

This research simplifies Riemannian LBFGS for SPD manifolds.

Let $π:E\to M$ be a vector bundle over a simply connected manifold and $\nabla$ a linear connection in $π$. Let $σ: U \rightarrow E$ be a $\nabla$-parallel section of $π$ defined on a connected open subset $U$ of $M$. We give sufficient conditions on $U$ in order to extend $σ$ to the whole $M$. We mainly concentrate to…

Prove non-asymptotic bounds for minimal risk in statistical learning

Model predicts political ideology using context vectors to mitigate bias and scarcity.

Lecture notes on kernel functions and Random Fourier Features.

Using geometric quantization, we represent curve operators in the TQFT of Witten-Reshetikhin-Turaev with jauge group SU_2 as Toeplitz operators with symbols corresponding to trace functions. As an application, we show that eigenvectors of these operators are concentrated near the level sets of these trace functions, an…

Theory for algebraic data on categories via concentration structures.

Novel bounds improve TD learning consistency in RL.

Paper analyzes error bounds for learning with vector-valued RF, improving existing analyses.

Paper addresses concentration of distances for fractional quasi p-norms, identifying conditions for concentration and anti-concentration.

We propose and study a multi-scale approach to vector quantization. We develop an algorithm, dubbed reconstruction trees, inspired by decision trees. Here the objective is parsimonious reconstruction of unsupervised data, rather than classification. Contrasted to more standard vector quantization methods, such as K-mea…

Study Finsler metric measure manifolds' concentration properties.

New method improves missing mass concentration bounds.