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.
We simplify matrix computations for block matrices, especially useful for covariance and correlation matrices.
Study isotropy groups for complex orthogonal and skew-symmetric matrices.
Paper solves a key problem in learning from high-dimensional covariance matrices.
Researchers developed a new Riemannian manifold for SPD matrix-valued optimal transport problems.
The paper uses deep learning to detect financial market regimes from correlation matrices.
Graph connection Laplacian (GCL) is a modern data analysis technique that is starting to be applied for the analysis of high dimensional and massive datasets. Motivated by this technique, we study matrices that are akin to the ones appearing in the null case of GCL, i.e the case where there is no structure in the datas…
This paper tackles fitting multilevel low rank matrices by addressing three problems.
The paper reduces the complexity of financial market correlation matrices to a 2x2 matrix.
New estimators reduce computation for Kendall's tau and conditional Kendall's tau matrices under structural assumptions.
We propose a modular extension of backpropagation for the computation of block-diagonal approximations to various curvature matrices of the training objective (in particular, the Hessian, generalized Gauss-Newton, and positive-curvature Hessian). The approach reduces the otherwise tedious manual derivation of these mat…
This paper solves matrix blind joint block diagonalization with noise.
Matrix Factorization (MF) on large scale matrices is computationally as well as memory intensive task. Alternative convergence techniques are needed when the size of the input matrix is higher than the available memory on a Central Processing Unit (CPU) and Graphical Processing Unit (GPU). While alternating least squar…
Proves conjecture linking WRT invariants and homological blocks for plumbed 3-manifolds.
Computes isotropy subgroups of orthogonal matrices acting on Hermitian matrices.
Algorithm finds isotropy subgroups of orthogonal similarity on symmetric matrices.
Proposes BONMI for integrating noisy matrices from multi-source data.
Correlation matrices are omnipresent in multivariate data analysis. When the number d of variables is large, the sample estimates of correlation matrices are typically noisy and conceal underlying dependence patterns. We consider the case when the variables can be grouped into K clusters with exchangeable dependence; t…
Enhanced EEG classification improves motor imagery detection with less computation.
Algorithm solves robust linear regression with block Lewis weights.
Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of space and run-time. Prompted by this observation, we study a convex optimization…
New algorithms learn graph structures privately, matching best results.
Localized sketching improves matrix multiplication and ridge regression complexity.
We study the problem of computing the matrix exponential of a block triangular matrix in a peculiar way: Block column by block column, from left to right. The need for such an evaluation scheme arises naturally in the context of option pricing in polynomial diffusion models. In this setting a discretization process pro…
New methods estimate mixed memberships in multi-layer networks.
Paper uses SSC for identifying layers with identical community structures in DIMPLE networks.
Biclustering structures in data matrices were first formalized in a seminal paper by John Hartigan (1972) where one seeks to cluster cases and variables simultaneously. Such structures are also prevalent in block modeling of networks. In this paper, we develop a unified theory for the estimation and completion of matri…
Differentially private random block coordinate descent improves utility in machine learning.
BLAST optimizes deep model inference by learning efficient matrix structures.
We construct a general procedure to extract the exclusive Racah matrices S and \bar S from the inclusive 3-strand mixing matrices by the evolution method and apply it to the first simple representations R =[1], [2], [3] and [2,2]. The matrices S and \bar S relate respectively the maps (R\otimes R)\otimes \bar R\longrig…
New method for estimating financial covariance matrices efficiently.
A common problem in large-scale data analysis is to approximate a matrix using a combination of specifically sampled rows and columns, known as CUR decomposition. Unfortunately, in many real-world environments, the ability to sample specific individual rows or columns of the matrix is limited by either system constrain…
A fast metric learning framework using Gershgorin disc alignment.
We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden communities even when the order of the maximum expected degree is as small as $\l…
Method estimates number of clusters in Block Markov Chain trajectories.
Two spectral clustering methods for multi-layer networks are analyzed and compared.
We introduce a framework and early results for massively scalable Gaussian processes (MSGP), significantly extending the KISS-GP approach of Wilson and Nickisch (2015). The MSGP framework enables the use of Gaussian processes (GPs) on billions of datapoints, without requiring distributed inference, or severe assumption…
Power of network tests degrades when vertices are misaligned.
Construction of (colored) knot polynomials for double-fat graphs is further generalized to the case when "fingers" and "propagators" are substituting R-matrices in arbitrary closed braids with m-strands. Original version of arXiv:1504.00371 corresponds to the case m=2, and our generalizations sheds additional light on …
Kernel methods are widespread in machine learning; however, they are limited by the quadratic complexity of the construction, application, and storage of kernel matrices. Low-rank matrix approximation algorithms are widely used to address this problem and reduce the arithmetic and storage cost. However, we observed tha…
The paper identifies redundant columns in matrices for feature selection and clustering.
Paper analyzes and improves GPSP algorithm for block sparse signal recovery.
The inverse covariance matrix provides considerable insight for understanding statistical models in the multivariate setting. In particular, when the distribution over variables is assumed to be multivariate normal, the sparsity pattern in the inverse covariance matrix, commonly referred to as the precision matrix, cor…
Two spectral algorithms for community detection in graphs with covariates are compared.
We establish an effective version of the classical Lie--Kolchin Theorem. Namely, let be quasi--unipotent matrices such that the Jordan Canonical Form of consists of a single block, and suppose that for all the matrix is also quasi--unipotent. Then and have a…
New framework finds more efficient linear layers over structured matrices.
Consider the problem of estimating a low-rank matrix when its entries are perturbed by Gaussian noise. If the empirical distribution of the entries of the spikes is known, optimal estimators that exploit this knowledge can substantially outperform simple spectral approaches. Recent work characterizes the asymptotic acc…
We present a solution to scale spectral algorithms for learning sequence functions. We are interested in the case where these functions are sparse (that is, for most sequences they return 0). Spectral algorithms reduce the learning problem to the task of computing an SVD decomposition over a special type of matrix call…
ALMA improves clustering of multilayer networks.