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.
HD algorithm simulates dynamics on random matrix ensembles without generating full matrices.
Extends spectral number variance convergence to random matrix ensembles for twisted Laplacians.
Random matrix ensembles yield uniform distributions on manifolds.
In this work a novel method to quantify spectral ergodicity for random matrices is presented. The new methodology combines approaches rooted in the metrics of Thirumalai-Mountain (TM) and Kullbach-Leibler (KL) divergence. The method is applied to a general study of deep and recurrent neural networks via the analysis of…
New matrix ensembles better match deep neural network spectral densities.
We generalize the recently discovered relationship between JT gravity and double-scaled random matrix theory to the case that the boundary theory may have time-reversal symmetry and may have fermions with or without supersymmetry. The matching between variants of JT gravity and matrix ensembles depends on the assumed s…
Sharp threshold found for Frechet mean of inhomogeneous graphs.
Study finds Calabi-Yau models' operator spectra match random matrix theory.
SPQR improves Q-ensemble diversity in reinforcement learning.
Paper solves a key problem in learning from high-dimensional covariance matrices.
A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or "spike") is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughou…
In this paper, we solve a semi-supervised regression problem. Due to the lack of knowledge about the data structure and the presence of random noise, the considered data model is uncertain. We propose a method which combines graph Laplacian regularization and cluster ensemble methodologies. The co-association matrix of…
Expected centre of mass for random embeddings is constant.
We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations severely limits the effect of diversification in a credit portfolio if the corre…
In this paper we examine the effect of applying ensemble learning to the performance of collaborative filtering methods. We present several systematic approaches for generating an ensemble of collaborative filtering models based on a single collaborative filtering algorithm (single-model or homogeneous ensemble). We pr…
The paper analyzes bootstrap ensemble classifiers in high-dimensional settings.
Study shows energy levels on hyperbolic surfaces follow GOE fluctuations.
We improve prediction risk estimation for large datasets using sketching and ridge regression.
Random Matrix Theory explains loss surface Hessians in neural networks.
We use a cluster ensemble to determine the number of clusters, k, in a group of data. A consensus similarity matrix is formed from the ensemble using multiple algorithms and several values for k. A random walk is induced on the graph defined by the consensus matrix and the eigenvalues of the associated transition proba…
The paper analyzes an ensemble of randomly projected linear discriminants for high-dimensional data.
Lower bounds show linear complexity for linear regression.
Unified treatment of eigenvalue processes using Riemannian geometry.
Ensemble clustering has been a popular research topic in data mining and machine learning. Despite its significant progress in recent years, there are still two challenging issues in the current ensemble clustering research. First, most of the existing algorithms tend to investigate the ensemble information at the obje…
A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, in which a prominent eigenvector is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughout the sciences. Baik, Ben Arous and Pé…
We relate the distribution of eigenvalues of a random symmetric matrix in the Gaussian Orthogonal Ensemble to the distribution of critical values of a random linear combination of eigenfunctions of the Laplacian on a compact Riemann manifold. We then prove a central limit theorem describing what happens when the dimens…
We use methods of random matrix theory to analyze the cross-correlation matrix C of price changes of the largest 1000 US stocks for the 2-year period 1994-95. We find that the statistics of most of the eigenvalues in the spectrum of C agree with the predictions of random matrix theory, but there are deviations for a fe…
Matrices satisfying the Restricted Isometry Property (RIP) play an important role in the areas of compressed sensing and statistical learning. RIP matrices with optimal parameters are mainly obtained via probabilistic arguments, as explicit constructions seem hard. It is therefore interesting to ask whether a fixed mat…
Ensemble methods that average over a collection of independent predictors that are each limited to a subsampling of both the examples and features of the training data command a significant presence in machine learning, such as the ever-popular random forest, yet the nature of the subsampling effect, particularly of th…
We study a new ensemble of random correlation matrices related to multivariate Student (or more generally elliptic) random variables. We establish the exact density of states of empirical correlation matrices that generalizes the Marcenko-Pastur result. The comparison between the theoretical density of states in the St…
Unified framework for ensemble sampling in nonlinear contextual bandits with provable regret bounds.
New methods improve tree ensemble models by compressing them while maintaining accuracy.
We analyse the structure of the distribution of eigenvalues of the stock market correlation matrix with increasing length of the time series representing the price changes. We use 100 highly-capitalized stocks from the American market and relate result to the corresponding ensemble of Wishart random matrices. It turns …
Signatures of universality are detected by comparing individual eigenvalue distributions and level spacings from financial covariance matrices to random matrix predictions. A chopping procedure is devised in order to produce a statistical ensemble of asset-price covariances from a single instance of financial data sets…
Solves weakly supervised regression using low-rank approximations and manifold regularization.
The paper shows Gaussian fluctuations in eigenvalue statistics of random hyperbolic surfaces.
Persistence diagrams from random matrices follow RMT universality, offering a new spectral diagnostic.
The study investigates kernel-target alignment in tree ensemble kernels.
In this paper, we apply tools from the random matrix theory (RMT) to estimates of correlations across volatility of various assets in the S&P 500. The volatility inputs are estimated by modeling price fluctuations as GARCH(1,1) process. The corresponding correlation matrix is constructed. It is found that the distribut…
Paper uses Random Matrix Theory for optimal training-testing data split.
Study on Gaussian ensemble of matrix products with mixed moments computed.
We define a random-matrix ensemble given by the infinite-time covariance matrices of Ornstein-Uhlenbeck processes at different temperatures coupled by a Gaussian symmetric matrix. The spectral properties of this ensemble are shown to be in qualitative agreement with some stylized facts of financial markets. Through the…
The paper develops a new algorithm for RBMs using dynamical mean-field theory.
The paper provides exact multivariate amplitude distributions for non-stationary Gaussian or algebraic fluctuations.
A new test validates ensemble models against the null hypothesis.
Method detects neural network equivalence via matrix ensembles and spectral analysis.
Random matrix theory explains how neural networks adapt to data.
The paper connects Riemannian Gaussian distributions to random matrix theory and diffusion kernels.