In this paper, we present a simple non-parametric method for learning the structure of undirected graphs from data that drawn from an underlying unknown distribution. We propose to use Brownian distance covariance to estimate the conditional independences between the random variables and encodes pairwise Markov graph. …
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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.
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48 results for “Brownian Distance Covariance”
DeepBDC improves few-shot classification by measuring joint distributions of image features.
problem Few-shot classification with limited training data.
method DeepBDC method using deep learning and Brownian Distance Covariance.
result DeepBDC significantly outperforms existing methods on various benchmarks.
New bounds for private matrix approximation using Gaussian noise and Dyson Brownian Motion.
problem Private approximation of symmetric matrices with Gaussian noise.
method Viewing Gaussian noise as Dyson Brownian Motion to track eigenvalue and eigenvector evolution.
result Improved bounds on Frobenius-distance utility for private matrix approximation.
Under a complete Ricci flow, we construct a coupling of two Brownian motion such that their -distance is a supermartingale. This recovers a result of Lott [J. Lott, Optimal transport and Perelman's reduced volume, Calc. Var. Partial Differential Equations 36 (2009), no. 1, 49--84.] on the monotonicity of…
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.
Proves CLT for Brownian paths on pinched negative curvature manifolds.
problem Distribution of Brownian paths on pinched negative curvature manifolds.
method Proof of central limit theorem for distances and Green functions.
result Central limit theorem holds for Brownian paths in pinched negative curvature.
Study radial processes in sub-Riemannian Brownian motions, proving stochastic completeness and eigenvalue estimates.
problem Analyzing sub-Riemannian Brownian motions and their radial processes.
method Application of Itô's formula and sub-Laplacian comparison theorems to prove stochastic completeness and eigenvalue estimates.
result Proved Cheng's type estimates for Dirichlet eigenvalues of sub-Riemannian metric balls.
Variations of the sub-Riemannian distance on Sasakian manifolds with applications to couplingmath.DG
Maps on Sasakian manifolds limit to sub-Riemannian distance bounds.
problem Understanding sub-Riemannian distances on Sasakian manifolds.
method Parallel and mirror maps along geodesics of a taming Riemannian metric.
result Limits of transport maps outside sub-Riemannian cut-locus provide bounds on sub-Riemannian distance.
New method generates synthetic time series paths with more flexibility.
problem Restrictions in generating synthetic paths using Brownian reference.
method Introduces Triangular-Reference Schrödinger Bridges (TR-SBTS) for time series generation.
result Generates synthetic paths with more flexibility in stochastic volatility and correlated noise.
Universal approximation for stochastic processes using Brownian motion.
problem Approximating stochastic processes with linear functionals.
method Establishing -type universal approximation theorems for rough path spaces.
result Linear functionals on the signature of time-extended Brownian motion can approximate any -integrable stochastic process.
The paper uses distance covariance to improve fairness in machine learning models.
problem Improving fairness in machine learning models.
method Using conditional and distance covariance statistics to assess independence and add a penalty for fairness.
result The method effectively reduces the fairness gap in machine learning models.
Unified framework for Brownian motion distances on specific geometric manifolds.
problem Understanding Brownian motion distances on radially isoparametric manifolds.
method Developed a geometric framework and derived drift-window inequalities.
result Unified framework for coadapted Brownian couplings on RIM.
Quaternionic Brownian motion on flag manifold linked to sphere diffusion.
problem Modeling quaternionic stochastic areas on quaternionic flag manifolds.
method Relating quaternionic Brownian motion to symplectic Brownian motion and using radial dynamics.
result Quaternionic stochastic areas follow a multivariate normal distribution.
Study on estimating distances between covariance operators and Gaussian processes.
problem Estimating distances between covariance operators and Gaussian processes.
method Riemannian distances, concentration results for Hilbert space-valued random variables, RKHS covariance and cross-covariance operators.
result Both distances converge in the Hilbert-Schmidt norm and can be consistently and efficiently estimated.
Model tracks structural changes in Brownian particle configurations on a sphere.
problem Tracking structural changes in Brownian particle configurations on a sphere.
method Introduces Frustrated Distance Matrix (FDM) model for dynamic distance matrices on S^2.
result Preserves static BBS template with dynamics as redistributed spectral mass.
We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the projection to the manifold of Brownian motions developed in the frame bundle lead …
Proofs Fisher-Rao distance on Gaussian covariance manifold.
problem Proving Fisher-Rao distance on Gaussian covariance manifold.
method Basic Riemannian geometry.
result Proof of Fisher-Rao distance on covariance cone.
Identifying statistical dependence between the features and the label is a fundamental problem in supervised learning. This paper presents a framework for estimating dependence between numerical features and a categorical label using generalized Gini distance, an energy distance in reproducing kernel Hilbert spaces (RK…
This study approximates distances between Gaussian processes and covariance operators using RKHS.
problem Approximating distances between Gaussian processes and covariance operators from finite samples.
method Using reproducing kernel Hilbert space (RKHS) covariance and cross-covariance operators, the study shows how to consistently and efficiently estimate Sinkhorn divergence from finite samples.
result Convergence rates are dimension-independent and of the same order as Hilbert-Schmidt distance.
Escaping the Brownian stalkersq-fin.TR
We propose a simple model for the behaviour of longterm investors on a stock market, consisting of three particles, which represent the current price of the stock and the opinion of the buyers, respectively sellers, about the right trading price. As time evolves, both groups of traders update their opinions with respec…
Study on the geometric Dyson Brownian motion of non-square matrix products.
problem Understanding the spectrum of a product of non-square random matrices.
method Proportional depth-width limit followed by mean-field limit, solving Burgers equation.
result Free log-normal law is obtained in the identity-start case.
The study examines the behavior of Gaussian processes' minimums and overshoots.
problem Understanding the behavior of Gaussian processes' minimums and overshoots.
method Analyzing conditional distributions and subsequential limits of minimizers.
result The scaled overshoot converges to an exponential random variable with mean σ_*^2.
The study examines the chaos of fractional Brownian fields as Hurst parameter approaches zero.
problem Understanding the chaos of fractional Brownian fields as their Hurst parameter tends to zero.
method Defining normalizing kernels and using Berestycki's ``good points'' approach to derive the limiting measure of multiplicative chaos.
result The limiting measure of multiplicative chaos converges to a log-correlated Gaussian field as the Hurst parameter approaches zero.
This monograph develops the theory of covariant Schrödinger semigroups acting on sections of vector bundles over noncompact Riemannian manifolds from scratch. Contents: I. Sobolev spaces on vector bundles II. Smooth heat kernels on vector bundles III. Basis differential operators in Riemannian manifolds IV. Some specif…
Unified geometric framework for Brownian motion on various manifolds.
problem Modeling Brownian motion on complex Riemannian manifolds.
method Constructing stochastic differential equations with noise and drift terms aligned with Laplace-Beltrami operators.
result Geometrically transparent and mathematically consistent foundation for diffusion processes.
This note improves correlation stress tests using geodesic distance.
problem Improving financial risk management through better covariance stress tests.
method Proposes a new geometrically invariant definition of correlation stress tests.
result Demonstrates a submanifold approach to stress testing covariance matrices.
We show that on a manifold whose Riemannian metric evolves under backwards Ricci flow two Brownian motions can be coupled in such a way that the expectation of their normalized L-distance is non-increasing. As an immediate corollary we obtain a new proof of a recent result of Topping (J. reine angew. Math. 636 (2009), …
Study on overlaps of singular vectors in Gaussian matrix submatrices.
problem Analyzing overlaps of singular vectors in submatrices of Gaussian matrices.
method Utilizes dynamics of singular vectors and specific resolvents for Brownian trajectories.
result Explicit forms for limiting rescaled mean squared overlaps in the bulk of spectra.
Lyons and Sullivan have shown how to discretize harmonic functions on a Riemannian manifold whose Brownian motion satisfies a certain recurrence property called -recurrence. We study analogues of this discretization for tensor fields which are harmonic in the sense of the covariant Laplacian. We show that, un…
We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence to mutual dependence, while the other two measures are sums of squared distance…
Dynamic Black-Littermanq-fin.PM
Dynamic Black-Litterman integrates expert views with portfolio optimization over varying time horizons.
problem Incorporating expert views with varying horizons in portfolio optimization.
method Exploiting graphical structure, deriving conditional distribution of asset returns, and using affine factor models.
result Explicit expression for optimal dynamic investment policy and hedging demand analysis.
Transfer Learning with Distance Covariance for Random Forest: Error Bounds and an EHR Applicationstat.ML
Method uses random forest with distance covariance for transfer learning in healthcare.
problem Transfer learning in random forests with sparse differences between source and target.
method Distance covariance-based feature weights in residual random forest.
result Upper bound on mean square error rate for transfer learning in RF.
Cluster Analysis on Locally Asymptotically Self-similar Processes with Known Number of Clustersstat.ML
We conduct cluster analysis on a class of locally asymptotically self-similar stochastic processes, which includes multifractional Brownian motion as a representative. When the true number of clusters is supposed to be known, a new covariance-based dissimilarity measure is introduced, from which we obtain the approxima…
Study heat profiles and eigenfunctions using Brownian motion.
problem Investigate heat profiles and eigenfunctions of Laplace equations.
method Probabilistic tools based on Brownian motion and Feynman-Kac formulae.
result Supremum norm bounds for ground state Dirichlet eigenfunctions and comparison of maximum temperatures.
This work examines the sensitivity of energy distance to mean differences compared to covariance differences.
problem The sensitivity of energy distance to mean differences compared to covariance differences when distributions are close.
method Analyzes the energy distance in the case where distributions are close, focusing on sensitivity to mean and covariance differences.
result Energy distance is more sensitive to mean differences than covariance differences when distributions are close.
Optimizes sample reweighting to match laws under covariate shift using Wasserstein distance.
problem Matching laws of samples with different distributions under covariate shift.
method Minimizes Wasserstein distance between empirical measures of samples using Nearest Neighbors weights.
result Consistent reweighting leads to asymptotic convergence of empirical measures.
This work extends stochastic localization to joint probability measures for data analysis.
problem Data distributional analysis in high-dimensional probability.
method Unified stochastic localization under Eldan's α-scheme, coupled probability measures via shared Brownian motion.
result Eldan's α-distance as a scalable surrogate for Wasserstein distance.
New estimator handles covariate shift with closed-form solution and super-efficiency.
problem Handling covariate shift in missing data and causal inference problems.
method Minimum Wasserstein distance estimation framework.
result Closed-form expression and super-efficiency relative to semiparametric efficient estimator.
Paper estimates non-causal graphical models using covariance extension and transportation distance.
problem Estimating non-causal graphical models with smoothing relations.
method Proposes a covariance extension problem and uses transportation distance to minimize error with white noise.
result Solution is a double-sided autoregressive non-causal graphical model.
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.
FDBM models use fractional Brownian motion to model complex stochastic processes.
problem Capturing memory effects and long-range dependencies in stochastic processes.
method Developed a generative diffusion bridge framework using a Markovian approximation of fractional Brownian motion.
result FDBM outperforms standard models in predicting future states and unpaired data translation.
Proposes a new Sliced-Wasserstein distance for covariance matrices in M/EEG signals.
problem Efficiently dealing with distributions of covariance matrices in M/EEG multivariate time series.
method Defines a Sliced-Wasserstein distance for symmetric positive definite matrices and applies it to brain-age prediction and Brain Computer Interface applications.
result Demonstrates computational efficiency and strong theoretical guarantees for the proposed distance.
In a 2006 article (\cite{A1}), Allouba gave his quadratic covariation differentiation theory for Itô's integral calculus. He defined the derivative of a semimartingale with respect to a Brownian motion as the time derivative of their quadratic covariation and a generalization thereof. He then obtained a systematic diff…
Meta learns low-rank covariance factors for better uncertainty estimation.
problem Sub-optimal covariance matrices in multi-task settings.
method Meta learns diagonal or diagonal plus low-rank factors using an attentive set encoder.
result Efficiently constructed task-specific covariance matrices improve uncertainty estimation.
Covariance and histogram image descriptors provide an effective way to capture information about images. Both excel when used in combination with special purpose distance metrics. For covariance descriptors these metrics measure the distance along the non-Euclidean Riemannian manifold of symmetric positive definite mat…
A Bayesian Nonparametric Perspective on Mahalanobis Distance for Out of Distribution Detectionstat.ML
Bayesian nonparametric models improve OOD detection, especially with complex covariance structures.
problem Improving out-of-distribution detection methods, especially in complex scenarios.
method Proposes Bayesian nonparametric mixture models with hierarchical priors that generalize the Mahalanobis distance score.
result Bayesian nonparametric methods outperform existing OOD methods, especially in complex scenarios.
Geodesic curves improve flexibility in covariance estimation.
problem Inflexible covariance families limit spatiotemporal modeling.
method Use geodesic curves to build more flexible covariance families.
result Natural projection minimizes geodesic distance to sample covariance.
Paper proves CLTs for Q-learning with asynchronous updates.
problem Establishing convergence rates for Q-learning algorithms.
method Polyak-Ruppert averaging, non-asymptotic and functional CLTs.
result Convergence rates in Wasserstein distance for Q-learning.