arXiv research

Paper estimates spectral risk measures for insurance data with truncated and censored data.

New complexes refine multicomplexes for subRiemannian geometry.

Kernel ridge regression (KRR) is a well-known and popular nonparametric regression approach with many desirable properties, including minimax rate-optimality in estimating functions that belong to common reproducing kernel Hilbert spaces (RKHS). The approach, however, is computationally intensive for large data sets, d…

New kernels capture both local and non-local interactions efficiently.

TKRR improves KRR performance by aligning target functions with kernels.

A large class of machine learning techniques requires the solution of optimization problems involving spectral functions of parametric matrices, e.g. log-determinant and nuclear norm. Unfortunately, computing the gradient of a spectral function is generally of cubic complexity, as such gradient descent methods are rath…

Continuing the previous work, we propose a further extension of the structure equation for a truncated CMC hierarchy by the non-commuting, truncated Virasoro algebra of non-local symmetries. Via a canonical dressing transformation, we first define a wave function for the CMC hierarchy. This leads to a pair of additiona…

We consider spectral clustering algorithms for community detection under a general bipartite stochastic block model (SBM). A modern spectral clustering algorithm consists of three steps: (1) regularization of an appropriate adjacency or Laplacian matrix (2) a form of spectral truncation and (3) a k-means type algorithm…

High-dimensional inference for sparse spectral precision matrices

Model structures on multicomplexes help study complex geometry.

Recent work has demonstrated the effectiveness of gradient descent for directly recovering the factors of low-rank matrices from random linear measurements in a globally convergent manner when initialized properly. However, the performance of existing algorithms is highly sensitive in the presence of outliers that may …

Overview of geometric analysis for manifold learning.

Floer homotopy theory applies to Lagrangians, overcoming curvature issues.

New spectral clustering method for graphs with uneven node degrees.

The paper improves alignment methods for deep neural networks using geometric and spectral analysis.

Estimates manifold distances using graph Laplacian, proving consistency.

Recursive training of generative models can lead to model collapse, and the recursion converges to a unique limiting distribution.

LASE improves local network structure visualization by targeting locally low-dimensional regions.

The development of global sensitivity analysis of numerical model outputs has recently raised new issues on 1-dimensional Poincaré inequalities. Typically two kind of sensitivity indices are linked by a Poincaré type inequality, which provide upper bounds of the most interpretable index by using the other one, cheaper …

Discrete Fourier transforms provide a significant speedup in the computation of convolutions in deep learning. In this work, we demonstrate that, beyond its advantages for efficient computation, the spectral domain also provides a powerful representation in which to model and train convolutional neural networks (CNNs).…

New methods recover best rank-r approximations from few entries.

Efficiently estimates covariance for sub-Weibull vectors with sub-Gaussian rate.

Interactive privacy mechanisms improve spectral density estimation under local differential privacy.

New method improves DAG learning by using large coefficients for higher-order terms.

This paper presents a new algorithm, termed \emph{truncated amplitude flow} (TAF), to recover an unknown vector $\bm{x}$ from a system of quadratic equations of the form $y_i=|\langle\bm{a}_i,\bm{x}\rangle|^2$, where $\bm{a}_i$'s are given random measurement vectors. This problem is known to be \emph{NP-hard} in genera…

The problem of an arbitrary truncated Levy flight description using the method of cumulant approach has been solved. The set of cumulants of the truncated Levy distribution given the assumption of arbitrary truncation has been found. The influence of truncation shape on the truncated Levy flight properties in the Gauss…

Constructs QFT on curved surfaces, proving axioms and calculating entropy.

Efficiently estimate Boolean product distribution parameters from truncated samples.

Paper analyzes spectral algorithms under covariate shift, providing convergence rates.

ParPIC clusters directed graphs using random walks and diffusion operators.

In the paper "On Truncated Variation of Brownian Motion with Drift" (Bull. Pol. Acad. Sci. Math. 56 (2008), no.4, 267 - 281) we defined truncated variation of Brownian motion with drift, $W_t = B_t + μt, t\geq 0,$ where $(B_t)$ is a standard Brownian motion. Truncated variation differs from regular variation by neglect…

Optimal algorithm learns Gaussian under halfspace truncation with minimal samples.

Bayesian framework for sphere regression using Gaussian fields.

Bayesian method uses data spectra to estimate non-sparse high-dimensional models.

Positive weights improve kernel quadrature's accuracy.

New method for constructing truncated vine copulas.

Non-negative matrix factorization (NMF) minimizes the Euclidean distance between the data matrix and its low rank approximation, and it fails when applied to corrupted data because the loss function is sensitive to outliers. In this paper, we propose a Truncated CauchyNMF loss that handle outliers by truncating large e…

Paper improves robust spectral clustering for noisy data.

Paper proposes approximate Stein classes for efficient truncated density estimation.

Paper defines new risk measures for elliptical distributions.

We prove an analogue of the de Rham theorem for the extended L^2-cohomology introduced by M. Farber. This is done by establishing that the de Rham complex over a compact closed manifold with coefficients in a flat Hilbert bundle E of A-modules over a finite von Neumann algebra A is chain-homotopy equivalent (with bound…

A new kernel test reduces noise in MMD by focusing on leading eigen-directions.

New DP framework using data truncation for efficient estimation.

We show that given an estimate $\widehat{A}$ that is close to a general high-rank positive semi-definite (PSD) matrix $A$ in spectral norm (i.e., $\|\widehat{A}-A\|_2 \leq δ$), the simple truncated SVD of $\widehat{A}$ produces a multiplicative approximation of $A$ in Frobenius norm. This observation leads to many inte…

Unified framework for mean testing under truncation bias.

On curved spaces, viscous fluids reach equilibrium quickly.

Score matching method improves density estimation for truncated data on manifolds.

Study uses random matrix theory to improve tensor approximation accuracy.