arXiv research

We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to be imposed on a dictionary of vector-valued Reproducing Kernel Hilbert Spaces. W…

We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to be imposed on a dictionary of vector-valued Reproducing Kernel Hilbert Spaces. W…

New algorithms compute Volterra signature efficiently for time series analysis.

Stein variational gradient descent (SVGD) is a particle-based inference algorithm that leverages gradient information for efficient approximate inference. In this work, we enhance SVGD by leveraging preconditioning matrices, such as the Hessian and Fisher information matrix, to incorporate geometric information into SV…

Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the reproducing kernel Hilbert space and develop a method for learning prediction func…

A new method estimates SDEs using occupation kernels.

We consider a model for linear transient price impact for multiple assets that takes cross-asset impact into account. Our main goal is to single out properties that need to be imposed on the decay kernel so that the model admits well-behaved optimal trade execution strategies. We first show that the existence of such s…

We consider stochastic partial differential equations appearing as Markovian lifts of matrix valued (affine) Volterra type processes from the point of view of the generalized Feller property (see e.g., \cite{doetei:10}). We introduce in particular Volterra Wishart processes with fractional kernels and values in the con…

Classifies contravariant matrix-valued valuations on polytopes without continuity assumptions.

The paper extends log-Sobolev inequalities to matrix-valued settings using combinatorial methods.

Classifies SL(n) covariant matrix-valued valuations on Lp-spaces.

We propose a new non-parametric framework for learning incrementally stable dynamical systems x' = f(x) from a set of sampled trajectories. We construct a rich family of smooth vector fields induced by certain classes of matrix-valued kernels, whose equilibria are placed exactly at a desired set of locations and whose …

Study finds weak solutions for complex map flows with optimal lifespan.

Holomorphic functions from knot complements link to quantum modular forms.

A new algorithm improves sampling for graph learning models.

Paper improves matrix-valued data classification using nonparametric LDA.

Researchers developed a new Riemannian manifold for SPD matrix-valued optimal transport problems.

Recovering matrix valued potentials from wave equation data on stationary spacetimes.

Differential privacy mechanism design has traditionally been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding i.i.d. noise to each element of the matrix, this method is often suboptimal as it for…

We extend Kyle's model to include stochastic liquidity and multiple assets.

Paper introduces a new kernel model for PSD-valued functions with theoretical guarantees and applications.

Paper develops a new test for high-dimensional matrix-valued data.

We give a complete classification of conformally covariant differential operators between the spaces of $i$-forms on the sphere $S^n$ and $j$-forms on the totally geodesic hypersphere $S^{n-1}$. Moreover, we find explicit formulæ for these new matrix-valued operators in the flat coordinates in terms of basic operators …

Let $A:[0,1]\rightarrow\mathbb{H}_m$ (the space of Hermitian matrices) be a matrix valued function which is low rank with entries in Hölder class $Σ(β,L)$. The goal of this paper is to study statistical estimation of $A$ based on the regression model $\mathbb{E}(Y_j|τ_j,X_j) = \langle A(τ_j), X_j \rangle,$ where $τ_j$ …

Paper introduces new neural network models and theories.

Study proposes efficient estimators for matrix-valued linear regression under sparsity assumptions.

We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly incorporates row and column features, smoothing kernels, and other sources of sid…

Online graph learning from matrix-valued time series data.

In safety-critical applications a probabilistic model is usually required to be calibrated, i.e., to capture the uncertainty of its predictions accurately. In multi-class classification, calibration of the most confident predictions only is often not sufficient. We propose and study calibration measures for multi-class…

Symplectic GP regression models Hamiltonian systems for particle tracing.

New method clusters matrix-valued data by latent variables.

Long term optimal investment problems are studied in a factor model with matrix valued state variables. Explicit parameter restrictions are obtained under which, for an isoelastic investor, the finite horizon value function and optimal strategy converge to their long-run counterparts as the investment horizon approache…

Uniform-in-time analysis for Stein Variational Gradient Descent across various metrics.

LoRA and privacy: Random projections help but not always.

MuonEq improves training of matrix-valued parameters by rebalancing momentum before orthogonalization.

Researchers compute Wodzicki residue for pseudo-differential operators on compact Lie groups.

New analysis of Muon and SignSGD on matrix-valued least squares problems.

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…

In computer vision, image datasets used for classification are naturally associated with multiple labels and comprised of multiple views, because each image may contain several objects (e.g. pedestrian, bicycle and tree) and is properly characterized by multiple visual features (e.g. color, texture and shape). Currentl…

We investigate solutions of the elliptic sinh-Gordon equation of spectral genus g<3. These solutions are parametrized by complex matrix-valued polynomials called potentials. On the space of these potentials there act two commuting flows. The orbits of these flows are called Polynomial Killing fields and are double peri…

Model liquidity premia using a risk-sharing economy with quadratic costs.

Improved hypothesis testing and change-point detection using diffusion-based methods.

Study noncommutative Sobolev inequalities using quantum state metrics.

In this paper, we prove a mean value formula for bounded subharmonic Hermitian matrix valued function on a complete Riemannian manifold with nonnegative Ricci curvature. As its application, we obtain a Liouville type theorem for the complex Monge-Ampère equation on product manifolds.

Introduces a new model for mapping matrices to matrices, subsuming linear regression.

We study holomorphic foliations with an affine homogeneous transverse structure. We give a friendly characterization of the case of transversely affine foliations in terms of matrix valued pairs of differential forms. This leads naturally to the study of the case of foliations with singularities. A first extension theo…

This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been motivated by a large and growing use of matrix-valued affine processes in finance, including multi-asset option pricing with stochastic volatil…

Optimal portfolio choice with cross-impact propagators, solving complex equations.