New proof shows coupling-based flows converge linearly to diagonalize data covariance.
problem Understanding convergence of coupling-based normalizing flows to arbitrary data distributions.
method Proved linear convergence rate for whitening of data distribution.
result Coupling-based flows achieve linear convergence to diagonalize data covariance.
New asymmetric kernel methods improve feature learning.
problem Improving feature learning with asymmetric kernels.
method Coupled covariance eigenproblem and Nyström method.
result Empirical evaluations show benefits of KSVD.
Covariance shrinkage via stochastic interpolation
problem High-dimensional covariance estimation
method Recasting shrinkage as empirical risk minimization
result Reduces statistical risk through scheduling, flow maps, and early stopping
Improved covariance matrix estimation for multiple classes with limited data.
problem Estimating covariance matrices for multiple classes with scarce data.
method Coupled regularized sample covariance matrix estimator (RSCM) that combines pooled SCM and scaled identity matrix for regularization.
result The coupled RSCM estimators outperform cross-validation in classification tasks with comparable accuracy but faster computation.
We introduce a novel kernel that models input-dependent couplings across multiple latent processes. The pairwise joint kernel measures covariance along inputs and across different latent signals in a mutually-dependent fashion. A latent correlation Gaussian process (LCGP) model combines these non-stationary latent comp…
We examine several aspects of explicability of a classification system built from neural networks. The first aspect is the pairwise explicability, which is the ability to provide the most accurate prediction when the range of possibilities is narrowed to just two. Next we consider explicability in development, which me…
We define a random-matrix ensemble given by the infinite-time covariance matrices of Ornstein-Uhlenbeck processes at different temperatures coupled by a Gaussian symmetric matrix. The spectral properties of this ensemble are shown to be in qualitative agreement with some stylized facts of financial markets. Through the…
Random features are improved by variance-reducing couplings, enhancing machine learning models.
problem Improving the efficiency and accuracy of random features in machine learning.
method Using optimal transport theory to find couplings that reduce variance in random features.
result Theoretical and practical gains in efficiency and accuracy for various machine learning models.
New method tackles high-dimensional SBL without covariance matrices.
problem Sparse coding problem in high-dimensional settings.
method Parallel solution of multiple linear systems using conjugate gradient algorithm.
result Our method scales better in computation time and memory.
SchNarc combines SchNet and SHARC for efficient photodynamics simulations.
problem Efficiently simulate excited-state dynamics of complex molecules.
method Combines SchNet for multiple electronic states with SHARC for molecular dynamics, learning energies, forces, and couplings.
result Paves the way for efficient photodynamics simulations of complex systems.
Develop a framework for barycentric projections of optimal transport plans on Riemannian manifolds.
problem Optimal transport couplings are probabilistic objects, while many learning pipelines require deterministic maps.
method Develop a framework for barycentric projections of transport couplings on Riemannian manifolds.
result The intrinsic projection maps each source point to the conditional Fréchet mean of its destination law and is shown to be the best deterministic representative under squared geodesic loss.
New method estimates covariance in deep heteroscedastic regression without labels.
problem Estimating covariance in deep heteroscedastic models is challenging due to sample-dependent covariance and lack of ground truth.
method Proposes a self-supervised approach using KL Divergence and 2-Wasserstein distance for covariance estimation and a neighborhood-based heuristic for pseudo labels.
result Demonstrates effective pseudo labels and a computationally cheaper yet accurate deep heteroscedastic regression.
Solves steering problem with continuous time, Hilbert-Schmidt cost, and matrix ODEs.
problem Fixed horizon linear quadratic covariance steering in continuous time with a specific terminal cost.
method Formulates necessary conditions as a coupled matrix ODE two-point boundary value problem, designs a matricial recursive algorithm, and proves convergence.
result Proposes and proves the convergence of a matricial recursive algorithm for solving the steering problem.
Metabolic flux balance analyses are a standard tool in analysing metabolic reaction rates compatible with measurements, steady-state and the metabolic reaction network stoichiometry. Flux analysis methods commonly place unrealistic assumptions on fluxes due to the convenience of formulating the problem as a linear prog…
Paper proposes an online covariance estimator for sketched Newton methods.
problem Estimating the limiting covariance matrix of sketched Newton methods.
method Proposes a fully online covariance matrix estimator from Newton iterates.
result Establishes the consistency and convergence rate of the proposed estimator.
Unified bounds for iterative algorithms with Gaussian data matrices.
problem Establishing non-asymptotic bounds for iterative algorithms with Gaussian data.
method Explicit coupling between iterates and Gaussian process with deterministic covariance.
result Tight, dimension-free bounds for generalized first-order methods.
Paper develops a new method for solving IBVPs on star-shaped domains.
problem Solving Inverse Boundary Value Problems (IBVP) for parallel transport equations.
method Covariant tomography, integrating geometric decomposition with specific interior extensions.
result Formal solvability criterion for higher-order IBVPs, validated through examples.
Average Oracle outperforms DCC+NLS in portfolio optimization.
problem Optimizing portfolio performance in volatile markets.
method Comparing the Average Oracle to various DCC+NLS variants.
result The Average Oracle consistently yields higher Sharpe ratios.
Paper introduces Floer theory for field theories, proving periodic solutions for particle-field systems.
problem Defining Hamiltonian Floer theory for covariant field theories, especially those with degenerate action functionals.
method Regularization procedure to handle degeneracy, leading to Floer curves that converge to periodic solutions.
result Existence of Floer curves and space-time periodic solutions for coupled particle-field systems.
Develops a nonparametric method to estimate isotropic covariance functions efficiently.
problem Estimating isotropic covariance functions without assuming a specific parametric form.
method Uses Bernstein polynomials and sieve maximum likelihood estimation.
result Consistent estimator with improved performance compared to parametric and nonparametric alternatives.
We consider dimensional reduction of gauge theories with arbitrary gauge group in a formalism based on equivariant principal bundles. For the classical gauge groups we clarify the relations between equivariant principal bundles and quiver bundles, and show that the reduced quiver gauge theories are all generically buil…
Scattering representations simplify SBI for images without extra compression.
problem Efficiently performing simulation-based inference on images with limited data.
method Use scattering representations for compression and learning, combined with spatial averaging and expressive density estimators.
result Scattering representations provide more information than traditional methods, without requiring additional simulations.
The analysis of nonstationary time series is of great importance in many scientific fields such as physics and neuroscience. In recent years, Gaussian process regression has attracted substantial attention as a robust and powerful method for analyzing time series. In this paper, we introduce a new framework for analyzi…
Paper analyzes Langevin dynamics for multimodal Gaussian mixtures, controlling errors across dimensions.
problem Challenges in obtaining stable diffusion-based samplers in high- and infinite-dimensional settings.
method Study of preconditioned Annealed Langevin Dynamics (ALD) for Gaussian mixtures, focusing on Euler-Maruyama (EM) and exponential-integrator schemes.
result Proves dimension-uniform KL bounds for the exponential-integrator scheme, allowing arbitrarily small divergence with dimension.
Model financial time series with MOGP for imputation and prediction.
problem Impute missing financial data due to dependencies among multiple series.
method Use a multi-output Gaussian process (MOGP) with expressive covariance functions.
result The model outperforms other MOGPs and independent Gaussian process on real financial data.
Proves stability of Minkowski space-time for Einstein-Yang-Mills equations.
problem Stability of Minkowski space-time for perturbations governed by Einstein-Yang-Mills equations.
method Proves exterior energy estimates for tensorial non-linear wave equations in Minkowski space-time.
result Proves exterior stability of Minkowski space-time for Einstein-Yang-Mills equations.
Improved LDA using a nonlinear covariance estimator for better performance.
problem Inefficient LDA when data covariance is ill-conditioned.
method Regularized LDA with a positive semidefinite ridge-type estimator of the inverse covariance matrix.
result The proposed NL-RLDA classifier outperforms state-of-the-art methods across multiple datasets.
MediEncoder learns nonlinear representations for causal mediation analysis.
problem High-dimensional noisy covariates and mediators in biomedical studies.
method Coupled encoder-decoder architecture with cross-factor network.
result Improves estimation accuracy in high-dimensional causal mediation analysis.
We propose a simple imputation method for high-dimensional linear regression with missing data.
problem Handling missing covariates in high-dimensional linear regression.
method Impute missing entries with conditional mean of observed covariates and use standard LASSO or square-root LASSO.
result The imputation scheme retains minimax estimation rate and is pivotal for the square-root LASSO.
A reservoir computer is a complex dynamical system, often created by coupling nonlinear nodes in a network. The nodes are all driven by a common driving signal. In this work, three dimension estimation methods, false nearest neighbor, covariance and Kaplan-Yorke dimensions, are used to estimate the dimension of the res…
Enhances Gaussian process models for handling variable error variances and multiple responses.
problem Limited ability of Gaussian process models to capture abrupt changes and heteroscedastic errors.
method Introduces a novel heteroscedastic Gaussian process (HeGP) framework coupled with variational inference and EM algorithm.
result Effective modeling of multivariate responses with varying error variances.
Newton's method solves variational problems on manifolds.
problem Solving variational equations on manifolds.
method Newton's method with affine covariant damping strategy.
result Numerical results for variational problems demonstrated.
Gaussian processes (GPs) provide a powerful non-parametric framework for reasoning over functions. Despite appealing theory, its superlinear computational and memory complexities have presented a long-standing challenge. State-of-the-art sparse variational inference methods trade modeling accuracy against complexity. H…
This paper extends SLS controllers to two stocks, proving the RPE property with cross-coupling.
problem Extending SLS controllers to two stocks without exploiting correlations.
method Developed a novel architecture for cross-coupling two SLS controllers, derived a closed-form expected value, and proved the RPE property.
result Guaranteed RPE property with cross-coupling for a large class of stock dynamics.
Probabilistic matrix factorization (PMF) is a powerful method for modeling data associ- ated with pairwise relationships, Finding use in collaborative Filtering, computational bi- ology, and document analysis, among other areas. In many domains, there are additional covariates that can assist in prediction. For example…
Polyak-Ruppert CLT for SA-Adam with momentum and non-convergent adaptive preconditioning
problem Adaptive optimizers combining momentum and non-convergent preconditioning
method Proving positive drift stability and a non-autonomous Polyak-Ruppert CLT for SA-Adam
result The iterate-marginal covariance is exactly the plain stochastic gradient descent (SGD) sandwich
Proposes sparsified intervals for high-dimensional regression coefficients.
problem Challenges of high-dimensional regression coefficient inference.
method Sparsified simultaneous confidence intervals.
result Intervals can shrink some coefficients to zero, indicating unimportance.
Lie algebroid Yang-Mills theories are a generalization of Yang-Mills gauge theories, replacing the structural Lie algebra by a Lie algebroid E. In this note we relax the conditions on the fiber metric of E for gauge invariance of the action functional. Coupling to scalar fields requires possibly nonlinear representatio…
Study of most probable paths for anisotropic Brownian motions on manifolds.
problem Characterizing paths of Brownian motions with anisotropic diffusion on manifolds.
method Using stochastic development and fiber bundle of linear frames, the study provides a comprehensive characterization of most probable paths.
result Explicit equations and integration methods for most probable paths on different geometries, including constant curvature surfaces.
Recent results in coupled or temporal graphical models offer schemes for estimating the relationship structure between features when the data come from related (but distinct) longitudinal sources. A novel application of these ideas is for analyzing group-level differences, i.e., in identifying if trends of estimated ob…
New method uses optimal transport for better covariate matching in causal effect estimation.
problem Estimating causal effects in observational studies with high-dimensional covariates.
method Multimarginal unbalanced optimal transport for interpretable matching.
result Method provides interpretable weights and competitive performance with k-nearest neighbors.
A method removes treatment-covariate dependence for counterfactual prediction without adversarial training.
problem Counterfactual prediction under assignment bias.
method Information-theoretic approach learning a stochastic representation Z to minimize mutual information with outcomes.
result The method performs favorably in likelihood, counterfactual error, and policy evaluation compared to adversarial baselines.
Study on feature learning dynamics in infinite-depth neural networks, focusing on ResNets.
problem Understanding how features evolve during training in deep neural networks, especially in the large-depth limit.
method Conditional Gaussian representations and SDE system with decoupled backward weights.
result Depth-induced suppression of forward-backward coupling in infinite-depth networks, leading to a decoupled forward-backward SDE system.
The paper studies how to use AI-generated labels in econometrics to avoid bias.
problem Small misclassification errors in AI-generated labels can lead to large biases in econometric estimators.
method The paper proposes a coupled-label bootstrap method to correct bias and deliver valid inference.
result The coupled-label bootstrap method is valid without the strong independence condition between true and imputed labels.
Method for initializing Gaussian mixtures for variational inference with multi-modal distributions.
problem Challenges in variational inference with Gaussian mixtures due to multimodality and nonconvex loss functions.
method Optimization to find local maxima, local Gaussian approximations, and constrained least squares regression.
result Robust initialization improves variational inference performance and scalability.
New meta-reinforcement learning method improves performance in finite-horizon MDPs.
problem Improving meta-reinforcement learning in finite-horizon MDPs with shared optimal action-value functions.
method Proposes MTSRL and MTSRL+ algorithms with learned priors and covariance, coupled with prior-alignment technique for meta-regret guarantees.
result Achieves meta-regret guarantees with learned priors and covariance, outperforming prior-independent RL and bandit-only meta-baselines.
Motivated by the study of coupled Kähler-Einstein metrics by Hultgren and Witt Nyström and coupled Kähler-Ricci solitons by Hultgren, we study in this paper coupled Sasaki-Einstein metrics and coupled Sasaki-Ricci solitons. We first show an isomorphism between the Lie algebra of all transverse holomorphic vector fields…
Defines coupled embeddability for maps on products of spaces, generating examples and nonexamples.
problem Understanding when maps on products of spaces can be embedded.
method Uses known results for nonsingular biskew and bilinear maps, studies genericity properties, extends Whitney embedding theorems, and relates to Z/2-coindex of embedding spaces. result Generates strong obstructions to coupled embeddability in terms of combinatorics of triangulations.