arXiv research

Study provides bounds for estimating intrinsic dimension using Gaussian kernels.

Study on Dirichlet process mixtures for clustering consistency.

New theory for BNNs with Gaussian priors achieves optimal posterior concentration rates.

This study assesses risk concentration in MDB portfolios using Monte Carlo simulations.

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

Data assimilation for parameter and state estimation in subsurface transport problems remains a significant challenge due to the sparsity of measurements, the heterogeneity of porous media, and the high computational cost of forward numerical models. We present a physics-informed deep neural networks (DNNs) machine lea…

Information concentration of probability measures have important implications in learning theory. Recently, it is discovered that the information content of a log-concave distribution concentrates around their differential entropy, albeit with an unpleasant dependence on the ambient dimension. In this work, we prove th…

Quantitative modeling of post-transcriptional regulation process is a challenging problem in systems biology. A mechanical model of the regulatory process needs to be able to describe the available spatio-temporal protein concentration and mRNA expression data and recover the continuous spatio-temporal fields. Rigorous…

A new matrix concentration inequality for random products of matrices.

This work explores the characteristics of financial contagion in networks whose links distributions approaches a power law, using a model that defines banks balance sheets from information of network connectivity. By varying the parameters for the creation of the network, several interbank networks are built, in which …

We provide a brief tutorial on the use of concentration inequalities as they apply to system identification of state-space parameters of linear time invariant systems, with a focus on the fully observed setting. We draw upon tools from the theories of large-deviations and self-normalized martingales, and provide both d…

This work achieves exponential concentration in heavy-tailed data over CAT(κ) spaces using the Fréchet median.

We present a novel notion of outlier, called the Concentration Free Outlier Factor, or CFOF. As a main contribution, we formalize the notion of concentration of outlier scores and theoretically prove that CFOF does not concentrate in the Euclidean space for any arbitrary large dimensionality. To the best of our knowled…

New method tightens sub-Gaussian concentration inequalities.

Barren plateaus are not an average-case phenomenon, but a highly non-unique problem.

Measurement and management of credit concentration risk is critical for banks and relevant for micro-prudential requirements. While several methods exist for measuring credit concentration risk within institutions, the systemic effect of different institutions' exposures to the same counterparties has been less explore…

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

New method uses machine learning to estimate drug parameters in brain models.

In this paper, we study non-asymptotic deviation bounds of the least squares estimator in Gaussian AR($n$) processes. By relying on martingale concentration inequalities and a tail-bound for $χ^2$ distributed variables, we provide a concentration bound for the sample covariance matrix of the process output. With this, …

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

Quantum kernel methods can lead to trivial models due to exponential concentration of kernel values.

Study improves fractional posterior for 1-bit matrix completion.

We give a simple optimistic algorithm for which it is easy to derive regret bounds of $\tilde{O}(\sqrt{t_{\rm mix} SAT})$ after $T$ steps in uniformly ergodic Markov decision processes with $S$ states, $A$ actions, and mixing time parameter $t_{\rm mix}$. These bounds are the first regret bounds in the general, non-epi…

Prove non-asymptotic bounds for minimal risk in statistical learning

The paper analyzes SMOTE for imbalanced classification, providing theoretical bounds and guidelines.

Our work connects parameter magnitudes and Hessian eigenspaces in deep neural nets.

Proposes a new latent variable model for hyperspherical latent spaces.

We study the concentration of NTK for MLPs at EOC, proving finite-width approximation of gradient independence.

Reduced-order model improves LES for atmospheric pollutant dispersion.

Develops a parameter-free SGD algorithm with optimal convergence rate.

The paper proposes methods to identify and sample from mixtures of Mallows models for top-k rankings.

Paper tightens PAC-Bayes bounds using coin-betting for better estimates.

Theory for algebraic data on categories via concentration structures.

A new inference method using regression and batched discrepancies.

Let $(M,g)$ and $(K,κ)$ be two Riemannian manifolds of dimensions $m$ and $k ,$ respectively. Let $ω\in C^2(N),$ $ω> 0.$ The warped product $M\times _ωK$ is the $(m+k)$-dimensional product manifold $M\times K$ furnished with metric $g+ω^2 κ.$ We prove that the supercritical problem $$-Δ_{g+ω^2 κ}u+h u=u^{ {m+2\over …

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

Study Finsler metric measure manifolds' concentration properties.

Method detects effects of synthesis parameters on plutonium oxide microstructure.

New method estimates GGLM parameters, overcoming non-convexity.

We establish a new estimate for the Ginzburg-Landau energies $E_ε(u)=\int_M\frac{1}{2}|du|^2+\frac{1}{4ε^2}(1-|u|^2)^2$ of complex-valued maps $u$ on a compact, oriented manifold $M$ with $b_1(M)\neq 0$, obtained by decomposing the harmonic component $h_u$ of the one-form $ju:=u^1du^2-u^2du^1$ into an integral and frac…

We propose an input design method for a general class of parametric probabilistic models, including nonlinear dynamical systems with process noise. The goal of the procedure is to select inputs such that the parameter posterior distribution concentrates about the true value of the parameters; however, exact computation…

New method improves missing mass concentration bounds.

Private estimation with public data reduces sample complexity.

Surfaces in 3-manifolds concentrate at curvature critical points.

The study assesses sensitivity to prior choices in Bayesian nonparametric models.

Sharp concentration bounds for i.i.d. variables.

Study on network-valued processes with asynchronous updates, proving consistency in community and changepoint estimation.

We survey recent results related to the concentration of eigenfunctions. We also prove some new results concerning ball-concentration, as well as showing that eigenfunctions saturating lower bounds for $L^1$-norms must also, in a measure theoretical sense, have extreme concentration near a geodesic.