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.
A framework estimates multiple precision matrices with shared structures.
New method proves Jones Polynomial's connect sum property.
Minimal submanifolds in matrix spaces proven for specific ranks.
Study optimizes shared singular subspace estimation from noisy matrices.
Advances in molecular "omics'" technologies have motivated new methodology for the integration of multiple sources of high-content biomedical data. However, most statistical methods for integrating multiple data matrices only consider data shared vertically (one cohort on multiple platforms) or horizontally (different …
Multiple clustering aims at exploring alternative clusterings to organize the data into meaningful groups from different perspectives. Existing multiple clustering algorithms are designed for single-view data. We assume that the individuality and commonality of multi-view data can be leveraged to generate high-quality …
The (stochastic) gradient descent and the multiplicative update method are probably the most popular algorithms in machine learning. We introduce and study a new regularization which provides a unification of the additive and multiplicative updates. This regularization is derived from an hyperbolic analogue of the entr…
New algorithm reduces matrix multiplication time for sparse matrices.
Non-orthogonal joint diagonalization (NJD) free of prewhitening has been widely studied in the context of blind source separation (BSS) and array signal processing, etc. However, NJD is used to retrieve the jointly diagonalizable structure for a single set of target matrices which are mostly formulized with a single da…
Several modern applications require the integration of multiple large data matrices that have shared rows and/or columns. For example, cancer studies that integrate multiple omics platforms across multiple types of cancer, pan-omics pan-cancer analysis, have extended our knowledge of molecular heterogenity beyond what …
We introduce Bayesian multi-tensor factorization, a model that is the first Bayesian formulation for joint factorization of multiple matrices and tensors. The research problem generalizes the joint matrix-tensor factorization problem to arbitrary sets of tensors of any depth, including matrices, can be interpreted as u…
New algorithm for active learning in multiple matrix completion problems.
It is shown that the multiplicative monoids of Temperley-Lieb algebras generated out of the basis are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself. Such a self-adjunction is found in a category whose arrows are matrices, and the functor adjoint to itself is based on the…
Recently low displacement rank (LDR) matrices, or so-called structured matrices, have been proposed to compress large-scale neural networks. Empirical results have shown that neural networks with weight matrices of LDR matrices, referred as LDR neural networks, can achieve significant reduction in space and computation…
A new algorithm speeds up matrix multiplication without actual multiplication.
This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free Probability, with an emphasis on the Marchenko-Pastur equation that provides informatio…
Localized sketching improves matrix multiplication and ridge regression complexity.
Method estimates M-matrices in graphical models with improved accuracy.
This paper analyzes AJIVE for estimating shared subspace across multiple datasets, revealing its strengths and limitations.
New methods for sketching non-PSD matrices improve regression and optimization tasks.
Multi-view Multi-instance Multi-label Learning(M3L) deals with complex objects encompassing diverse instances, represented with different feature views, and annotated with multiple labels. Existing M3L solutions only partially explore the inter or intra relations between objects (or bags), instances, and labels, which …
It is shown that the multiplicative monoids of Brauer's centralizer algebras generated out of the basis are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself, and where, moreover, a kind of symmetry involving the self-adjoint functor is satisfied. As in a previous paper, of …
If a knot is represented by an m-strand braid, then HOMFLY polynomial in representation R is a sum over characters in all representations Q\in R^{\otimes m}. Coefficients in this sum are traces of products of quantum R-matrices along the braid, but these matrices act in the space of intertwiners, and their size is equa…
Algorithm recovers multiple low-rank matrices from unlabeled data.
We consider the problem of jointly estimating multiple inverse covariance matrices from high-dimensional data consisting of distinct classes. An -penalized maximum likelihood approach is employed. The suggested approach is flexible and generic, incorporating several other -penalized estimators as specia…
New algorithms reduce communication in GNN training.
An algorithm for computing positive semidefinite factorizations of matrices.
Proposes a Bayesian approach for integrating multiple linked matrices.
A new model uses Toeplitz matrices to analyze time-series data transitions.
Efficient and accurate low-rank approximations of multiple data sources are essential in the era of big data. The scaling of kernel-based learning algorithms to large datasets is limited by the O(n^2) computation and storage complexity of the full kernel matrix, which is required by most of the recent kernel learning a…
This paper tackles fitting multilevel low rank matrices by addressing three problems.
A method for community detection in multilayer networks using data matrices.
Generalised matrix-matrix multiplication forms the kernel of many mathematical algorithms. A faster matrix-matrix multiply immediately benefits these algorithms. In this paper we implement efficient matrix multiplication for large matrices using the floating point Intel Pentium SIMD (Single Instruction Multiple Data) a…
We obtain general, exact formulas for the overlaps between the eigenvectors of large correlated random matrices, with additive or multiplicative noise. These results have potential applications in many different contexts, from quantum thermalisation to high dimensional statistics. We find that the overlaps only depend …
Paper introduces a novel method for dynamic covariance estimation with random forests.
We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even when the dimens…
Constructs coordinates to diagonalize Toda flow on matrices with simple spectrum.
Connections between nodes of fully connected neural networks are usually represented by weight matrices. In this article, functional transfer matrices are introduced as alternatives to the weight matrices: Instead of using real weights, a functional transfer matrix uses real functions with trainable parameters to repre…
Simplified optimization for structured matrices in deep learning.
Learning by integrating multiple heterogeneous data sources is a common requirement in many tasks. Collective Matrix Factorization (CMF) is a technique to learn shared latent representations from arbitrary collections of matrices. It can be used to simultaneously complete one or more matrices, for predicting the unknow…
Method estimates multiple related Gaussian distributions using Laplacian regularization.
Racah matrices and higher -symbols are used in description of braiding properties of conformal blocks and in construction of knot polynomials. However, in complicated cases the logic is actually inverted: they are much better deduced from these applications than from the basic representation theory. Following the re…
Sparse GCA finds linear relationships in multiple datasets, using gradient descent.
We show that, for each alpha in the interval (-1,1), the only Riemannian metrics on the space of positive definite matrices for which the alpha and -alpha-connections are mutually dual are matrix multiples fo the Wigner-Yanase-Dyson metric. If we further impose that the metric be monotone, then this set is reduced to s…
MCCA extracts shared structure from multiple tensor datasets.
Multiresolution Matrix Factorization (MMF) was recently introduced as an alternative to the dominant low-rank paradigm in order to capture structure in matrices at multiple different scales. Using ideas from multiresolution analysis (MRA), MMF teased out hierarchical structure in symmetric matrices by constructing a se…
NMF with specific constraints is equivalent to LDA.
New method tackles high-dimensional SBL without covariance matrices.