arXiv research

The Steklov problem is an eigenvalue problem with the spectral parameter in the boundary conditions, which has various applications. Its spectrum coincides with that of the Dirichlet-to-Neumann operator. Over the past years, there has been a growing interest in the Steklov problem from the viewpoint of spectral geometr…

The paper compares spectral geometry in hyperbolic and spherical manifolds.

We present Spectral Inference Networks, a framework for learning eigenfunctions of linear operators by stochastic optimization. Spectral Inference Networks generalize Slow Feature Analysis to generic symmetric operators, and are closely related to Variational Monte Carlo methods from computational physics. As such, the…

Study spectral properties of sub-Laplacians in Carnot groups.

Study on spectral asymptotics in elasticity on smooth manifolds.

Study shows stability of Schrödinger operator spectral data on a manifold.

Paper provides a performance guarantee for spectral clustering.

We study a spectral generalization of classical combinatorial graph spanners to the spectral setting. Given a set of vectors $V\subseteq \Re^d$, we say a set $U\subseteq V$ is an $α$-spectral spanner if for all $v\in V$ there is a probability distribution $μ_v$ supported on $U$ such that $$vv^\intercal \preceq α\cdot\m…

In this work a spectral theory for 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation is developed. Spectral data for such solutions are defined (following Hitchin and Bobenko) and the space of spectral data is described by an asymptotic characterization. Using methods of asymptotic …

Paper proposes a new method for sparse spectral clustering on Stiefel manifold.

Study uses spectral risk for learning with heavy-tailed data.

Despite excellent progress in recent years, mode collapse remains a major unsolved problem in generative adversarial networks (GANs).In this paper, we present spectral regularization for GANs (SR-GANs), a new and robust method for combating the mode collapse problem in GANs. Theoretical analysis shows that the optimal …

Spectral risk measures (SRMs) are risk measures that take account of user riskaversion, but to date there has been little guidance on the choice of utility function underlying them. This paper addresses this issue by examining alternative approaches based on exponential and power utility functions. A number of problems…

Bayesian parametric matrix models provide uncertainty quantification for spectral learning.

Paper solves long neck problem on odd-dimensional spin manifolds.

New methods rank players using covariates and comparisons, outperforming existing algorithms.

Clustering is the problem of separating a set of objects into groups (called clusters) so that objects within the same cluster are more similar to each other than to those in different clusters. Spectral clustering is a now well-known method for clustering which utilizes the spectrum of the data similarity matrix to pe…

Sharp spectral gap estimates for higher-order operators on hyperbolic spaces.

We propose an iterative gradient-based algorithm to efficiently solve the portfolio selection problem with multiple spectral risk constraints. Since the conditional value at risk (CVaR) is a special case of the spectral risk measure, our algorithm solves portfolio selection problems with multiple CVaR constraints. In e…

Study minimizes risk in MDPs with spectral measures.

We study Spectral Measures of Risk from the perspective of portfolio optimization. We derive exact results which extend to general Spectral Measures M_phi the Pflug--Rockafellar--Uryasev methodology for the minimization of alpha--Expected Shortfall. The minimization problem of a spectral measure is shown to be equivale…

Spectral algorithms solve optimal community detection and related problems.

Paper shows stability of metric reconstruction for orbifolds from spectral data.

The paper studies magnetic field effects on surface eigenvalues and spectral properties.

We study topological recursion on the irregular spectral curve $xy^2-xy+1=0$, which produces a weighted count of dessins d'enfant. This analysis is then applied to topological recursion on the spectral curve $xy^2=1$, which takes the place of the Airy curve $x=y^2$ to describe asymptotic behaviour of enumerative proble…

Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity measure used for graph sparsification. This choice is motivated by the observation…

Introduces Spectral Graph Network combining spatial and spectral message passing.

This note summarizes results that were obtained by the author in his habilitation thesis (arXiv:1607.08792) concerning the development of a spectral theory for simply periodic, 2-dimensional, complex-valued solutions of the sinh-Gordon equation. Spectral data for such solutions are defined for periodic Cauchy data on a…

In this paper we propose the notion of continuous-time dynamic spectral risk-measure (DSR). Adopting a Poisson random measure setting, we define this class of dynamic coherent risk-measures in terms of certain backward stochastic differential equations. By establishing a functional limit theorem, we show that DSRs may …

Spectral feature learning improves IV regression for causal effect estimation.

Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to quantify the acceptable risk, often in the objective. For this purpose it is important to have an adjusted, adapted and eff…

Detects graph topology changes from noisy signals using prior spectral information.

New method controls linear systems with partial info and disturbances.

Muon optimizer simplifies matrix optimization with spectral orthogonalization.

The goal of this paper is to show that there exists a simple, yet universal statistical logic of spectral graph analysis by recasting it into a nonparametric function estimation problem. The prescribed viewpoint appears to be good enough to accommodate most of the existing spectral graph techniques as a consequence of …

Algorithm learns dynamics from past observations.

Optimizes risk measures given known marginal distributions of two unknown factors.

An important form of prior information in clustering comes in form of cannot-link and must-link constraints. We present a generalization of the popular spectral clustering technique which integrates such constraints. Motivated by the recently proposed $1$-spectral clustering for the unconstrained problem, our method is…

The spectral $k$-support norm enjoys good estimation properties in low rank matrix learning problems, empirically outperforming the trace norm. Its unit ball is the convex hull of rank $k$ matrices with unit Frobenius norm. In this paper we generalize the norm to the spectral $(k,p)$-support norm, whose additional para…

Spectral deconfounding improves machine learning models by reducing hidden confounding effects.

Optimizes wavelets for graph classification using spectral wavelet signatures and persistence diagrams.

Considering the kinematics of the moving frame associated with a constant mean curvature surface immersed in S^3 we derive a linear problem with the spectral parameter corresponding to elliptic sinh-Gordon equation. The spectral parameter is related to the radius R of the sphere S^3. The application of the Sym formula …

The optimal dividend problem by De Finetti (1957) has been recently generalized to the spectrally negative Lévy model where the implementation of optimal strategies draws upon the computation of scale functions and their derivatives. This paper proposes a phase-type fitting approximation of the optimal strategy. We con…

Paper proposes a forecasting model combining autoregressive models with spectral attention.

Paper proposes AMP with spectral initialization for robust signal estimation.

CAST improves spectral clustering for multi-scale data by integrating reachability similarity.

Dirichlet-Neumann duality for Riemannian submersions

Clustering is concerned with coherently grouping observations without any explicit concept of true groupings. Spectral graph clustering - clustering the vertices of a graph based on their spectral embedding - is commonly approached via K-means (or, more generally, Gaussian mixture model) clustering composed with either…