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.
New method clusters signed graphs using matrix power means.
Study of metrics on positive-definite matrices from power potential, linking to power means.
Multilayer graphs encode different kind of interactions between the same set of entities. When one wants to cluster such a multilayer graph, the natural question arises how one should merge the information different layers. We introduce in this paper a one-parameter family of matrix power means for merging the Laplacia…
The paper derives Cramer-Rao bounds for Laplacian matrix estimation under various constraints.
We present a formula for the trace of any symmetric power of a matrix (with coefficients in a field) in terms of the ordinary powers of the matrix, an arbitrarily chosen linear function which vanishes on the identity matrix, and polynomial functions defined recursively.
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration" phenomenon induced by random matrix theory to perform a spectral analysis on the Gr…
A class of conserved models of wealth distributions are studied where wealth (or money) is assumed to be exchanged between a pair of agents in a population like the elastically colliding molecules of a gas exchanging energy. All sorts of distributions from exponential (Boltzmann-Gibbs) to something like Gamma distribut…
It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated high-dimensional data with unknown mean and dependence structures. Matrix-variate appr…
New method improves portfolio selection by filtering noisy covariance matrices.
The mean-field variant of the model of limit order driven market introduced recently by Maslov is formulated and solved. The agents do not have any strategies and the memory of the system is kept within the order book. We show that he evolution of the order book is governed by a matrix multiplicative process. The resul…
This paper solves the convergence problem for estimating MGGD parameters with a convex formulation.
Gaussian belief propagation (BP) has been widely used for distributed inference in large-scale networks such as the smart grid, sensor networks, and social networks, where local measurements/observations are scattered over a wide geographical area. One particular case is when two neighboring agents share a common obser…
This paper focuses on the estimation of the sample covariance matrix from low-dimensional random projections of data known as compressive measurements. In particular, we present an unbiased estimator to extract the covariance structure from compressive measurements obtained by a general class of random projection matri…
We study an extention of total variation denoising over images to over Cartesian power graphs and its applications to estimating non-parametric network models. The power graph fused lasso (PGFL) segments a matrix by exploiting a known graphical structure, , over the rows and columns. Our main results shows that for …
Paper proposes an efficient algorithm for nonnegative binary matrix factorization.
A new method for distributed PCA using matrix β-mean.
New MPNNs match 2-WL, faster distinguishing graphs.
Rk-means clusters relational data without full matrix, speeding up clustering.
Proposes a new regularizer for semi-supervised learning on multilayer graphs.
A framework for stable dynamic network embeddings using static methods.
We give a complete algorithm and source code for constructing what we refer to as heterotic risk models (for equities), which combine: i) granularity of an industry classification; ii) diagonality of the principal component factor covariance matrix for any sub-cluster of stocks; and iii) dramatic reduction of the facto…
Sharp inequalities for matrix means with unknown variance.
Machine learning and geostatistics are powerful mathematical frameworks for modeling spatial data. Both approaches, however, suffer from poor scaling of the required computational resources for large data applications. We present the Stochastic Local Interaction (SLI) model, which employs a local representation to impr…
Paper develops statistical tests for covariance matrix regression on manifold.
We show that the objective function of conventional k-means clustering can be expressed as the Frobenius norm of the difference of a data matrix and a low rank approximation of that data matrix. In short, we show that k-means clustering is a matrix factorization problem. These notes are meant as a reference and intende…
DeepTMR reorders matrices without prior knowledge of structural patterns.
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…
Paper analyzes singular subspace estimation in noisy matrix models.
M-learner estimates treatment effects in mediation models with subgroup identification.
A new RL algorithm POWR learns world models to estimate action-values.
In this article we consider means of positive operators on a Hilbert space. We extend the theory of matrix power means to arbitrary operator means in the sense of Kubo-Ando. The basis of the extension is relying on ideas coming from differential geometry. We consider generalized Karcher equations for positive operators…
Improved method for computing Fréchet means on SPD matrices.
A wide variety of application domains are concerned with data consisting of entities and their relationships or connections, formally represented as graphs. Within these diverse application areas, a common problem of interest is the detection of a subset of entities whose connectivity is anomalous with respect to the r…
Paper proposes a new method for PCA using generative models.
New method estimates log-determinant using trace powers, avoiding classical limitations.
Novel mean estimation method under user-level differential privacy reduces noise in continual mean estimates.
EPMF factorizes matrices by adjusting their entries to match a specified power.
Entropy regularization improves power k-means for high-dimensional data.
We accelerate the power method for strong low-rank approximation using fast sketching.
We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product decomposition. Our penalties encourage pairs of response category mean matrices to have equal…
The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When the distributions are locally low-dimensional, the proposed test can be made more powerful to distinguish certain alternatives by incorpora…
If a knot K has Seifert matrix V_K and has a prime power cyclic branched cover that is not a homology sphere, then there is an infinite family of non-concordant knots having Seifert matrix V_K.
New approach uses contrastive learning for better wireless power control.
A clustering algorithm uses the left Gram matrix for high dimensional data.
Diffusion models' consistency across splits explained by random matrix theory.
Neural-Kernel CME tackles scalability and expressiveness challenges in conditional distribution representation.
We study convex entire graphs evolving with normal velocity equal to a positive power of the mean curvature. Under mild assumptions we prove longtime existence.
Sharp threshold found for Frechet mean of inhomogeneous graphs.