New Riemannian metric for SPD matrices avoids swelling effect.
problem Efficiency and stability in computing with SPD matrices.
method Log-Cholesky decomposition and Lie group structure.
result Log-Cholesky average maintains determinant bounds.
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48 results for “Cholesky”
New quadrature method using randomly pivoted Cholesky outperforms existing techniques.
problem Efficiently approximating integrals of functions in reproducing kernel Hilbert spaces.
method Nodes drawn by randomly pivoted Cholesky algorithm.
result Randomly pivoted Cholesky quadrature is fast and achieves comparable accuracy to more computationally intensive methods.
New SPD metrics improve stability and efficiency in neural networks.
problem Designing stable and efficient Riemannian metrics on SPD manifolds.
method Cholesky decomposition to derive SPD metrics.
result Proposed metrics provide closed-form operators, computational efficiency, and improved numerical stability.
Paper proposes a new method for sparse covariance Cholesky factor estimation.
problem Estimating sparse covariance matrices for ordered data.
method Matrix loss penalization approach for sparse Cholesky factor estimation.
result The proposed method outperforms existing regression-based approaches in simulations and real data.
Method regularizes Cholesky factors to detect nonstationarity in longitudinal data.
problem Detecting nonstationarity in large covariance matrices of longitudinal data.
method Fused-Lasso regularization on Cholesky factors.
result Regularization leads to smooth subdiagonals, indicating nonstationarity.
Improved method for estimating precision matrices without knowing variable order.
problem Estimating precision matrices without knowing the order of variables.
method Combining multiple permutations and thresholding for sparse structure.
result Consistent property established under weak conditions, superior performance in simulations and real data.
Kernel clustering algorithm improved for large datasets using incomplete Cholesky factorization.
problem Large memory usage in kernel-based clustering for large-scale datasets.
method Approximate the kernel matrix using incomplete Cholesky factorization and apply linear -means clustering.
result The proposed method achieves similar performance to kernel -means clustering but handles large-scale datasets efficiently.
Paper proposes a fast algorithm to recover causal DAGs with latent variables.
problem Discovering causal relationships in the presence of latent variables.
method Cholesky factorization of covariance matrix with optimization for latent variables.
result The algorithm significantly outperforms previous methods in synthetic and real-world datasets.
The paper explores Cholesky decompositions for symmetric matrices and their geometric properties.
problem Understanding the structure and properties of symmetric matrices through Cholesky decompositions.
method Introducing cones of symmetric matrices, proving Cholesky-type factorizations, and showing geometric properties.
result Each symmetric matrix admits an uncountable family of Cholesky-type factorizations, and these cones are isometric Riemannian manifolds.
ARCS learns Bayesian networks by optimizing a regularized Cholesky score over permutations.
problem Learning Bayesian networks from data.
method Annealing on regularized Cholesky score (ARCS) for topological sorting.
result ARCS outperforms existing methods in learning Bayesian networks.
New method for geodesics of multivariate normals, derived from a Toda lattice.
problem Computing geodesics of multivariate normal distributions.
method Using block Cholesky decomposition and a natural Riemannian submersion, a new Toda lattice type Lax pair is derived.
result A new Toda lattice type Lax pair derived from geodesics and block Cholesky decomposition.
This paper develops a fast algorithm for solving nonlinear PDEs using sparse Cholesky factorization.
problem Efficiently solving nonlinear PDEs with Gaussian processes and kernel methods.
method Sparse Cholesky factorization for near-linear complexity.
result Near-linear complexity algorithm for working with kernel matrices of nonlinear PDEs.
Accelerated RPCholesky speeds up kernel matrix approximations.
problem Efficiently approximating large kernel matrices.
method Accelerated randomly pivoted Cholesky (RPCholesky) with block matrix computations and rejection sampling.
result Approximates kernel matrices up to 40 times faster.
A new method for efficient causal structure learning at scale.
problem Causal structure learning is computationally challenging at scale.
method Relaxed sparsest-permutation formulation with support-level relaxation and masked zero-fill incomplete Cholesky factorization.
result The method enables scalable comparison of candidate orderings and matches the accuracy of slower baselines.
Improved aircraft structure prediction using derivative-enhanced sparse Cholesky GP method.
problem Accurate real-time prediction of aircraft structure performance.
method Combining derivative data with a modified dynamic sparse Cholesky linear system solver.
result Improved prediction accuracy of aircraft structure performance.
A new method learns DAGs from Gaussian data without verifying acyclicity.
problem Learning DAGs from Gaussian data without verifying acyclicity.
method Relaxation technique for permutation matrix estimation and cyclic coordinatewise descent for sparse Cholesky factor estimation.
result The method recovers DAGs without verifying acyclicity constraints.
Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluationsmath.NA
RPCholesky approximates kernel matrices with few evaluations.
problem Approximating kernel matrices efficiently.
method Randomly pivoted partial Cholesky factorization.
result RPCholesky provides nearly optimal low-rank approximations.
A new framework approximates covariance matrices using tree decompositions.
problem Approximating covariance matrices for Gaussian distributions.
method Cascade of tree decompositions with Cholesky factorization.
result The proposed framework guarantees convergence and outperforms KL divergence.
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…
Two efficient ridge solutions improve BLS for new inputs, enhancing accuracy and speed.
problem Improving BLS for new added inputs in a learning system.
method Proposes recursive and square-root BLS algorithms using inverse and inverse Cholesky factor updates.
result Both proposed ridge solutions improve BLS accuracy and speed, especially with larger lambda.
FLOP algorithm speeds up causal structure learning for linear models.
problem Efficiently learning causal structures from discrete data.
method FLOP algorithm combines fast parent selection and iterative score updates.
result FLOP finds highly accurate causal structures with near-perfect recovery.
A new method reduces log determinant evaluation cost from cubic to quadratic.
problem Efficiently evaluating log determinants in machine learning.
method Variational Bayesian approximation with complexity O(n^2).
result State-of-the-art performance on synthetic and real-world datasets.
Two new ridge solutions improve BLS on added nodes, achieving better accuracy.
problem Improving the Broad Learning System (BLS) for new nodes.
method Proposed two ridge solutions for BLS output weights, updating efficiently.
result Proposed ridge solutions achieve better testing accuracy than original BLS.
New algorithm extends Greville's method for partitioned matrices efficiently and stably.
problem Efficiently compute pseudoinverse of partitioned matrices without retraining.
method Incorporates inverse Cholesky factorization to reduce computational complexity and improve stability.
result 1 iteration to compute pseudoinverse of whole matrix from first part, addressing all cases.
New pivoting strategy improves trace norm contraction in low-rank approximation.
problem Finding good low-rank approximations of symmetric, positive-definite matrices.
method Choosing rows with likelihood proportional to for randomly pivoted partial Cholesky algorithm.
result Same trace norm contraction result in Frobenius norm for improved pivoting strategy.
An Algorithm to perform Covariance-Adjusted Support Vector Classification in Non-Euclidean Spacescs.LG
Algorithm improves SVM classification in non-Euclidean spaces.
problem Limitations of traditional SVM in non-Euclidean spaces.
method Covariance-adjusted SVM using Cholesky Decomposition.
result Cholesky-SVM outperforms traditional SVM in non-Euclidean spaces.
A Cholesky decomposition-based asset selection heuristic for sparse tangent portfolio optimizationq-fin.MF
New heuristic selects fewer assets for efficient portfolios, reducing costs.
problem High transaction costs and fees from including many assets in portfolios.
method Surrogate formulation to select assets, re-optimizes portfolio with fewer assets.
result Effective in constructing portfolios with fewer assets, reducing costs.
Scalable Krylov Subspace Methods for Generalized Mixed-Effects Models with Crossed Random Effectsstat.ME
New Krylov subspace methods speed up mixed-effects models with crossed random effects.
problem Slow computations for high-dimensional crossed random effects in mixed-effects models.
method Krylov subspace-based methods for generalized mixed-effects models with cross effects.
result Speedups by factors of up to 10,000 in computations for mixed-effects models.
A new method for efficient Gaussian process inference using sparse approximations.
problem Scalable and accurate inference for latent Gaussian processes.
method Variational approximation with sparse inverse Cholesky factors and double Kullback-Leibler minimization.
result The proposed method can achieve highly accurate approximations with polylogarithmic time complexity.
New geometric framework for positive semidefinite matrices of fixed rank.
problem Statistical analysis of positive semidefinite matrices of fixed rank.
method Introducing a manifold with Riemannian geometry and Lie group structure.
result Analytical closed forms for geodesics and Fréchet means.
A new method improves convergence in large-scale stochastic optimisation.
problem Improving convergence in large-scale stochastic optimisation problems.
method A direct least-squares approach with a Cholesky factor and adaptive line search.
result Improved convergence compared to existing methods on real-world problems.
Scalable multi-task regression via sparse Gaussian process priors.
problem Efficiently modeling and predicting multiple related tasks.
method Direct Cholesky factorization for sparse parameterization of Gaussian process priors.
result Sparse parameterization improves scalability and accuracy in multi-task regression.
Task Agnostic Robust Learning on Corrupt Outputs by Correlation-Guided Mixture Density Networkscs.LG
A method for robust learning with noisy data using mixture density networks.
problem Weakly supervised learning with noisy training data for classification and regression.
method Estimates target distribution and data quality using correlation-guided Cholesky Block.
result Shows comparable or superior performance in handling noisy data compared to existing methods.
A new method samples DPPs without eigendecomposition, making it faster.
problem Sampling DPPs efficiently when dealing with many points.
method Uses Cholesky decompositions and a thinning procedure.
result The method avoids costly eigenvalue/eigenvector computations.
New method for robust fixed-point smoothing without state augmentation.
problem Estimating initial states in Gaussian smoothing algorithms.
method Cholesky-based formulation without state augmentation.
result Matches runtime and robustness of existing methods.
Large-Scale Sparse Inverse Covariance Estimation via Thresholding and Max-Det Matrix Completionstat.ML
Efficiently solves large-scale sparse covariance estimation problems.
problem Sparse inverse covariance estimation for large datasets.
method Thresholding the sample covariance matrix and solving a maximum determinant matrix completion problem using a Newton-CG algorithm.
result The algorithm converges to an ε-accurate solution in O(nlog(1/ε)) time and O(n) memory.
New method differentiates square-root Kalman filters robustly.
problem Gradient calculation issues in square-root Kalman filters.
method Closed-form chain rule derived from Gramian identity, resolves non-orthogonal and rank-deficient issues.
result Robust automatic differentiation for Kalman filters, resolving numerical stability and gradient issues.
Paper details Hilbert-curve for high-performance data mining.
problem Efficiently mapping multi-dimensional data to one dimension.
method Defines Hilbert-curve using finite automaton and context-free grammar.
result Cache-oblivious algorithms for matrix operations and clustering.
Efficiently discovers causal DAG permutations without additional assumptions.
problem Learning a DAG up to Markov equivalence.
method Utilizing DAG-specific problem structure, introduces an efficient algorithm for sparse permutations.
result Significant improvement in permutation discovery compared to existing algorithms.
New iterative methods improve Vecchia-Laplace approximations for large data sets.
problem Inaccurate and slow Vecchia-Laplace approximations for large data sets.
method Iterative methods to improve Vecchia-Laplace approximations, including preconditioners and novel methods for predictive variances.
result Order of magnitude speed-up and threefold increase in prediction accuracy compared to state-of-the-art methods.
Additive Covariance Matrix Models: Modelling Regional Electricity Net-Demand in Great Britainstat.AP
The paper forecasts joint electricity demand across 14 British regions using additive models.
problem Forecasting regional electricity demand with cross-regional dependencies.
method Modified Cholesky parametrisation for multivariate Gaussian model, gradient boosting for model selection.
result The proposed model outperforms non-Gaussian copula-based models in forecasting.
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…
New method computes pathwise gradients for non-reparameterizable distributions.
problem Computing gradients for complex distributions not directly amenable to the reparameterization trick.
method Using optimal transport theory, compute gradients for Gamma, Beta, and Dirichlet distributions.
result Optimal gradients have reduced variance and are competitive with other methods.
Whitening, or sphering, is a common preprocessing step in statistical analysis to transform random variables to orthogonality. However, due to rotational freedom there are infinitely many possible whitening procedures. Consequently, there is a diverse range of sphering methods in use, for example based on principal com…
New iterative solvers speed up Gaussian process regression with derivatives.
problem Scaling Gaussian process regression with derivatives for high-dimensional problems and large budgets.
method Iterative solvers using fast matrix-vector multiplications and pivoted Cholesky preconditioning.
result Bayesian optimization with derivatives can now scale to high-dimensional problems and large evaluation budgets.
We address the problem of likelihood based inference for correlated diffusion processes using Markov chain Monte Carlo (MCMC) techniques. Such a task presents two interesting problems. First, the construction of the MCMC scheme should ensure that the correlation coefficients are updated subject to the positive definite…
This paper improves simulation methods for rough Volterra stochastic volatility models.
problem Inefficient techniques in Monte-Carlo simulations for rough Volterra volatility models.
method Comparison and modification of three simulation methods: Cholesky, Hybrid, and rDonsker schemes.
result Suggests modifications to improve simulation accuracy and efficiency.
Scalable algorithm for sampling Gaussian processes using sparse grids and preconditioners.
problem Generating high-dimensional Gaussian random vectors for GP sampling is computationally challenging.
method Proposes a scalable algorithm using inducing points approximation with sparse grids and additive Schwarz preconditioners.
result Demonstrates the efficacy and accuracy of the proposed method through experiments and comparisons.