A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper tackles joint learning of linear systems, improving accuracy with pooled data.
To each dynamic equivalence of two control systems is associated an infinite permutation matrix. We investigate how such matrices are related to the existence of dynamic equivalences.
A new model uses Toeplitz matrices to analyze time-series data transitions.
In this paper we generalize the known DDVV-type inequalities for real (skew-)symmetric and complex (skew-)Hermitian matrices to arbitrary real, complex and quaternionic matrices. Inspired by the Erdős-Mordell inequality, we establish the DDVV-type inequalities for matrices in the subspaces spanned by a Clifford system …
A new real-time method estimates system matrices and states using Kalman filter.
We show that the adjacency matrices of the intersection graphs of chord diagrams satisfy the 2-term relations of Bar-Natan and Garoufalides [bg], and hence give rise to weight systems. Among these weight systems are those associated with the Conway and HOMFLYPT polynomials. We extend these ideas to looking at a space o…
Overview of high-dimensional dynamical systems and their applications to machine learning.
Paper derives explicit expression of Alekseev-Meinrenken diffeomorphism.
Kalman filtering and smoothing algorithms are used in many areas, including tracking and navigation, medical applications, and financial trend filtering. One of the basic assumptions required to apply the Kalman smoothing framework is that error covariance matrices are known and given. In this paper, we study a general…
The paper solves PDEs from matrices with orthogonal columns, linking them to Hessian metrics and symmetric spaces.
Study extends symmetries of sphere points to surface mapping classes.
Gradient flow solves optimal mass transport for covariance matrices.
New estimator learns symmetric dynamics from few observations.
New metric tensor field on symmetric matrices simplifies eigenvector computation.
BP fails to find sparsest solution for structured matrices.
Complex systems are typically represented by large ensembles of observations. Correlation matrices provide an efficient formal framework to extract information from such multivariate ensembles and identify in a quantifiable way patterns of activity that are reproducible with statistically significant frequency compared…
Unified approach to constructing integrable systems using Stäckel lifts.
Recommender system research suffers from a disconnect between the size of academic data sets and the scale of industrial production systems. In order to bridge that gap, we propose to generate large-scale user/item interaction data sets by expanding pre-existing public data sets. Our key contribution is a technique tha…
Recommender System research suffers currently from a disconnect between the size of academic data sets and the scale of industrial production systems. In order to bridge that gap we propose to generate more massive user/item interaction data sets by expanding pre-existing public data sets. User/item incidence matrices …
Multiresolution Matrix Factorization (MMF) was recently introduced as a method for finding multiscale structure and defining wavelets on graphs/matrices. In this paper we derive pMMF, a parallel algorithm for computing the MMF factorization. Empirically, the running time of pMMF scales linearly in the dimension for spa…
We present explicit formulas for the coordinates in which the Hamiltonians of the Benenti systems with flat metrics take natural form and the metrics in question are represented by constant diagonal matrices.
The paper updates SVD of evolving matrices using projection techniques.
Physics-guided neural network improves power flow analysis.
Deep neural networks solve Raven's Progressive Matrices with high accuracy.
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related characteristics. Based on several natural complex dynamical systems, like the str…
This work compresses heavy-tailed weight matrices for tighter generalization bounds.
A new coordinate system for SPD matrices simplifies computations and generative modeling.
We propose a method to clean covariance matrices of nonstationary systems by using time-independent eigenvalues.
Integrable dynamics explained via geometric maps and cluster algebras.
We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson correlation matrices to the realm of complex eigenvalues. We employ some recent random…
New algorithm extends Greville's method for partitioned matrices efficiently and stably.
This paper addresses the problem of identifying sparse linear time-invariant (LTI) systems from a single sample trajectory generated by the system dynamics. We introduce a Lasso-like estimator for the parameters of the system, taking into account their sparse nature. Assuming that the system is stable, or that it is eq…
Methods from learning theory are used in the state space of linear dynamical and control systems in order to estimate the system matrices. An application to stabilization via algebraic Riccati equations is included. The approach is illustrated via a series of numerical examples.
CMF is a technique for simultaneously learning low-rank representations based on a collection of matrices with shared entities. A typical example is the joint modeling of user-item, item-property, and user-feature matrices in a recommender system. The key idea in CMF is that the embeddings are shared across the matrice…
Bayesian method infers transition matrices from incomplete graph data with topological constraints.
Random feature matrices' singular values concentrate near their full expectation in high dimensions.
Nowadays, multivariate time series data are increasingly collected in various real world systems, e.g., power plants, wearable devices, etc. Anomaly detection and diagnosis in multivariate time series refer to identifying abnormal status in certain time steps and pinpointing the root causes. Building such a system, how…
A new method learns noise characteristics for better state estimation in real-time systems.
Paper explores geometry of covariance matrices using associated bundles.
In the first part of the paper, we solve the boundary and monodromy problems for the isomonodromy equation of the meromorphic linear system of ordinary differential equations with Poncaré rank . In particular, we derive an explicit expression of the Stokes matrices of the linear system, via the boundary …
Density matrices are positively semi-definite Hermitian matrices with unit trace that describe the states of quantum systems. Many quantum systems of physical interest can be represented as high-dimensional low rank density matrices. A popular problem in {\it quantum state tomography} (QST) is to estimate the unknown l…
Estimates multiple linear systems on a graph with smoothness constraints.
A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real quaternion) stochastic time series representing two "remote" complex systems. The first paper in a series provides a detailed spectral theory of non-Hermi…
The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density matrices in trace regression models used in quantum state tomography (in particular, i…
A formula for the Riemannian metric tensor of differentiable manifolds of linear dynamical systems of same McMillan degree is presented in terms of their transfer function matrices. The necessary calculations for its application to ARMA and state space overlapping parametrizations are drafted. The importance of this ap…
Graph neural networks improve AMG convergence for sparse systems.
Coupled nonlinear integrable systems are generated from usual zero curvature equation. The relevant Maurer-Cartan forms are constructed by combining suitably chosen matrices (nilpotent, Hadamard, idempotent and k-idempotent) and Lie algebraic elements via Kronecker product. In each case a closure type property among th…
We identify linear dynamical systems under convex constraints with fewer samples.