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.
Paper proposes a new method for sparse covariance Cholesky factor estimation.
Method regularizes Cholesky factors to detect nonstationarity in longitudinal data.
This paper develops a fast algorithm for solving nonlinear PDEs using sparse Cholesky factorization.
Paper proposes a fast algorithm to recover causal DAGs with latent variables.
A new method for efficient causal structure learning at scale.
A new method learns DAGs from Gaussian data without verifying acyclicity.
New SPD metrics improve stability and efficiency in neural networks.
Kernel-based clustering algorithm can identify and capture the non-linear structure in datasets, and thereby it can achieve better performance than linear clustering. However, computing and storing the entire kernel matrix occupy so large memory that it is difficult for kernel-based clustering to deal with large-scale …
The paper explores Cholesky decompositions for symmetric matrices and their geometric properties.
RPCholesky approximates kernel matrices with few evaluations.
The modified Cholesky decomposition is commonly used for precision matrix estimation given a specified order of random variables. However, the order of variables is often not available or cannot be pre-determined. In this work, we propose to address the variable order issue in the modified Cholesky decomposition for sp…
In this paper, we present a general, multistage framework for graphical model approximation using a cascade of models such as trees. In particular, we look at the problem of covariance matrix approximation for Gaussian distributions as linear transformations of tree models. This is a new way to decompose the covariance…
This paper proposes the recursive and square-root BLS algorithms to improve the original BLS for new added inputs, which utilize the inverse and inverse Cholesky factor of the Hermitian matrix in the ridge inverse, respectively, to update the ridge solution. The recursive BLS updates the inverse by the matrix inversion…
New algorithm extends Greville's method for partitioned matrices efficiently and stably.
We present a new Riemannian metric, termed Log-Cholesky metric, on the manifold of symmetric positive definite (SPD) matrices via Cholesky decomposition. We first construct a Lie group structure and a bi-invariant metric on Cholesky space, the collection of lower triangular matrices whose diagonal elements are all posi…
New quadrature method using randomly pivoted Cholesky outperforms existing techniques.
The original Broad Learning System (BLS) on new added nodes and its existing efficient implementation both assume the ridge parameter lambda -> 0 in the ridge inverse to approximate the generalized inverse, and compute the generalized inverse solution for the output weights. In this paper, we propose two ridge solution…
New method differentiates square-root Kalman filters robustly.
Bayesian networks are a class of popular graphical models that encode causal and conditional independence relations among variables by directed acyclic graphs (DAGs). We propose a novel structure learning method, annealing on regularized Cholesky score (ARCS), to search over topological sorts, or permutations of nodes,…
We consider multi-task regression models where observations are assumed to be a linear combination of several latent node and weight functions, all drawn from Gaussian process (GP) priors that allow nonzero covariance between grouped latent functions. We show that when these grouped functions are conditionally independ…
New Krylov subspace methods speed up mixed-effects models with crossed random effects.
A new method for efficient Gaussian process inference using sparse approximations.
New method for geodesics of multivariate normals, derived from a Toda lattice.
Accelerated RPCholesky speeds up kernel matrix approximations.
Develops a fast algorithm for fitting multilevel factor models.
Improved aircraft structure prediction using derivative-enhanced sparse Cholesky GP method.
Solving systems of linear equations is a problem occuring frequently in water engineering applications. Usually the size of the problem is too large to be solved via direct factorization. One can resort to iterative approaches, in particular the conjugate gradients method if the matrix is symmetric positive definite. P…
Most machine learning methods require careful selection of hyper-parameters in order to train a high performing model with good generalization abilities. Hence, several automatic selection algorithms have been introduced to overcome tedious manual (try and error) tuning of these parameters. Due to its very high sample …
We observe that gradients computed via the reparameterization trick are in direct correspondence with solutions of the transport equation in the formalism of optimal transport. We use this perspective to compute (approximate) pathwise gradients for probability distributions not directly amenable to the reparameterizati…
We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence structure in the model. Incorporating sparsity in the precision matrix allows the Gaus…
We propose an algorithmic framework for convex minimization problems of a composite function with two terms: a self-concordant function and a possibly nonsmooth regularization term. Our method is a new proximal Newton algorithm that features a local quadratic convergence rate. As a specific instance of our framework, w…
In this paper, we propose a scalable algorithm for spectral embedding. The latter is a standard tool for graph clustering. However, its computational bottleneck is the eigendecomposition of the graph Laplacian matrix, which prevents its application to large-scale graphs. Our contribution consists of reformulating spect…
FLOP algorithm speeds up causal structure learning for linear models.
The paper forecasts joint electricity demand across 14 British regions using additive models.
New pivoting strategy improves trace norm contraction in low-rank approximation.
Algorithm improves SVM classification in non-Euclidean spaces.
New heuristic selects fewer assets for efficient portfolios, reducing costs.
During recent years there has been an increased interest in stochastic adaptations of limited memory quasi-Newton methods, which compared to pure gradient-based routines can improve the convergence by incorporating second order information. In this work we propose a direct least-squares approach conceptually similar to…
Gaussian random fields are a powerful tool for modeling environmental processes. For high dimensional samples, classical approaches for estimating the covariance parameters require highly challenging and massive computations, such as the evaluation of the Cholesky factorization or solving linear systems. Recently, Anit…
The sparse inverse covariance estimation problem is commonly solved using an -regularized Gaussian maximum likelihood estimator known as "graphical lasso", but its computational cost becomes prohibitive for large data sets. A recent line of results showed--under mild assumptions--that the graphical lasso esti…
New geometric framework for positive semidefinite matrices of fixed rank.
Paper proposes a method to find approximate SOSP for nonconvex conic optimization problems.
We demonstrate an equivalence between reproducing kernel Hilbert space (RKHS) embeddings of conditional distributions and vector-valued regressors. This connection introduces a natural regularized loss function which the RKHS embeddings minimise, providing an intuitive understanding of the embeddings and a justificatio…
New method for robust fixed-point smoothing without state augmentation.
A scalable algorithm for GP regression selects relevant covariates efficiently.
Paper introduces a new identifiability criterion for DAGs using conditional variances.
Kernel-based tests for shape constraints in finance.
Conjugate gradient methods improve efficiency for high-dimensional GLMMs.