A streaming algorithm estimates quadratic covariation from financial data efficiently.
problem Estimating quadratic covariation from ultra-high-frequency financial data with limited memory.
method Formulated multi-scale, realized kernel, pre-averaging, and modulated realized covariance estimators with fixed bandwidth.
result Fixed bandwidth estimators require higher bandwidth for positive semidefiniteness.
Enhances power of covariance matrix tests for high-dimensional data.
problem Testing large covariance matrices in high-dimensional data.
method Proposes a new Fisher's combined probability test for quadratic form and maximum form statistics.
result Boosts power against more general alternatives.
A new QDA classifier for high-dimensional data with spiked covariance.
problem Classifying high-dimensional data with distinct covariance matrices.
method Proposes a novel quadratic classification technique with parameters chosen to maximize the fisher-discriminant ratio.
result The proposed classifier outperforms classical R-QDA and requires lower computational complexity.
We consider high-dimensional quadratic classifiers in non-sparse settings. The target of classification rules is not Bayes error rates in the context. The classifier based on the Mahalanobis distance does not always give a preferable performance even if the populations are normal distributions having known covariance m…
Develops MGQDA for multi-group classification with theoretical guarantees and practical applications.
problem Complex multi-group classification problems with nonlinear decision boundaries and group-specific covariance patterns.
method MGQDA, a method based on quadratic discriminant analysis that projects predictors onto a lower-dimensional subspace.
result MGQDA achieves competitive or improved predictive performance compared to existing methods.
When estimating high-frequency covariance (quadratic covariation) of two arbitrary assets observed asynchronously, simple assumptions, such as independence, are usually imposed on the relationship between the prices process and the observation times. In this paper, we introduce a general endogenous two-dimensional nonp…
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.
The paper tests properties of trees in graphical models using covariance queries.
problem Testing properties of trees in graphical models.
method Covariance queries model, randomized tests for tree properties.
result Efficient testing of global tree properties using sub-quadratic number of queries.
The covariance matrix of a p-dimensional random variable is a fundamental quantity in data analysis. Given n i.i.d. observations, it is typically estimated by the sample covariance matrix, at a computational cost of O(np2) operations. When n,p are large, this computation may be prohibitively slow. Moreover, …
Study resolvent convergence for random matrices with general covariance profiles.
problem Analyzing resolvent convergence for random matrices with non-identically distributed columns.
method Using moments of quadratic forms and deterministic equivalents, the study provides bounds on the trace of matrix products.
result The trace of matrix products is close to the trace of a deterministic equivalent, controlled by matrix norms.
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to largely outperform the sample covariance matrix estimate and to compete with state…
A new classification rule for FDA improves classification performance by accounting for unequal covariance matrices.
problem Unequal covariance matrices in practical situations affect the performance of FDA and its variants.
method Proposes a novel classification rule for FDA that accounts for unequal covariance matrices, applicable to many FDA variants.
result The new classification rule improves classification performance compared to original FDA and variants.
Statistical inference and information processing of high-dimensional data often require efficient and accurate estimation of their second-order statistics. With rapidly changing data, limited processing power and storage at the acquisition devices, it is desirable to extract the covariance structure from a single pass …
Develops a hedging method for multi-asset derivatives with correlation risk.
problem Hedging multi-asset derivatives exposed to correlation and covariance risk.
method Combines dynamic trading with static hedging instruments using Galtchouk--Kunita--Watanabe decomposition.
result Explicit semi-static replication formulas for covariance swaps and geometric dispersion trades.
Adaptive classifier optimizes high-dimensional data with spiked covariance structure.
problem Classification of high-dimensional data with spiked covariance structure.
method Adaptive classifier that whitens data, screens features, and applies Fisher linear discriminant.
result The classifier is Bayes optimal under certain conditions and performs well on real and synthetic data.
New analysis improves SGD for robust and quantile regression with sub-quadratic convergence.
problem Improving SGD for robust and quantile regression with sub-quadratic convergence.
method Piecewise Lyapunov function for first-order differentiable functions.
result First geometrical convergence result for sub-quadratic SGD.
New method solves constrained stochastic optimization problems efficiently.
problem Online statistical inference of constrained stochastic nonlinear optimization problems.
method Stochastic Sequential Quadratic Programming (StoSQP) with iterative sketching solver.
result The rescaled primal-dual sequence converges to a mean-zero Gaussian distribution.
This paper optimizes portfolio selection for multivariate affine and quadratic Volterra models with rough volatilities.
problem Optimizing portfolio selection for multivariate models with rough volatilities and stochastic correlations.
method Investigates continuous-time Markowitz mean-variance problem for multivariate affine and quadratic Volterra models using Riccati backward stochastic differential equations (BSDEs).
result Derives explicit solutions for BSDEs in affine Volterra models and new analytic formulae for quadratic models.
Improved graph matching using covariates for network data integration.
problem Matching networks without unique identifiers.
method Two novel covariate-assisted seeded graph matching methods.
result Improved alignment accuracy through covariate information.
Joint sparsity regularization in multi-task learning has attracted much attention in recent years. The traditional convex formulation employs the group Lasso relaxation to achieve joint sparsity across tasks. Although this approach leads to a simple convex formulation, it suffers from several issues due to the loosenes…
We consider the problem of high-dimensional classification between the two groups with unequal covariance matrices. Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and linear dimension reduction on original data, with the subsequent application of quadr…
In this work, we develop a novel principal component analysis (PCA) for semimartingales by introducing a suitable spectral analysis for the quadratic variation operator. Motivated by high-dimensional complex systems typically found in interest rate markets, we investigate correlation in high-dimensional high-frequency …
Linear and Quadratic Discriminant analysis (LDA/QDA) are common tools for classification problems. For these methods we assume observations are normally distributed within group. We estimate a mean and covariance matrix for each group and classify using Bayes theorem. With LDA, we estimate a single, pooled covariance m…
Quadratic Killing tensors on Lie groups are always decomposable.
problem Characterize Killing tensors on Lie groups.
method Analyzing the algebraic structure of Killing tensors on Lie groups.
result Quadratic Killing tensors on compact Lie groups are decomposable.
New findings on kernel regression in the quadratic regime, improving understanding of machine learning models.
problem Understanding kernel ridge regression in the quadratic asymptotic regime.
method Extended study of kernel regression to the quadratic regime, establishing approximation bounds and spectral distributions.
result Broad class of inner-product kernels exhibit behavior similar to a quadratic kernel, with precise asymptotic training and test errors characterized.
The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov Random Field, from very limited samples. We propose a novel algorithm for solving the…
Develops robust methods for infinite-dimensional stochastic processes.
problem Measuring covariations in stochastic evolution equations in infinite dimensions.
method Asymptotic theory for jump robust measurement of covariations.
result Identifies scaling limits for realized covariations.
A new method reduces high-dimensional filtering to quadratic complexity.
problem High-dimensional dynamical systems inference and simulation.
method Low-rank Kalman filtering using dynamical low-rank integrator.
result The method reproduces exact Kalman filter in low-rank limit.
Sub-Riemannian cubics are a generalisation of Riemannian cubics to a sub-Riemannian manifold. Cubics are curves which minimise the integral of the norm squared of the covariant acceleration. Sub-Riemannian cubics are cubics which are restricted to move in a horizontal subspace of the tangent space. When the sub-Riemann…
We introduce a variant of (sparse) PCA in which the set of feasible support sets is determined by a graph. In particular, we consider the following setting: given a directed acyclic graph G on p vertices corresponding to variables, the non-zero entries of the extracted principal component must coincide with vertice…
We establish an explicit expression for the conditional Laplace transform of the integrated Volterra Wishart process in terms of a certain resolvent of the covariance function. The core ingredient is the derivation of the conditional Laplace transform of general Gaussian processes in terms of Fredholm's determinant and…
Proposes a new framework for invariant quadratic P&L predictions in option books.
problem Inconsistent second-order P&L predictions across different factor parameterizations.
method Local, model-agnostic framework using covariant Hessian defined by an affine connection.
result Coordinate-invariant quadratic P&L predictions that match desk targets.
New algorithm reduces runtime for robust sparse mean estimation.
problem Efficiently estimating mean from corrupted data with sparse constraints.
method Subquadratic time algorithm using poly(k, log d, 1/ε) samples.
result First subquadratic time algorithm for robust sparse mean estimation.
Reinforcement learning (RL) has been successfully used to solve many continuous control tasks. Despite its impressive results however, fundamental questions regarding the sample complexity of RL on continuous problems remain open. We study the performance of RL in this setting by considering the behavior of the Least-S…
A scalable algorithm for GP regression selects relevant covariates efficiently.
problem Scalable variable selection in large GP regression models.
method VGPR algorithm using Vecchia approximation for sparse precision matrix, mini-batch subsampling.
result Improved scalability and accuracy in selecting relevant covariates.
Paper analyzes holdout cross-validation for large non-Gaussian covariance estimation.
problem Estimating large covariance matrices for non-Gaussian data.
method Use of Weingarten calculus and Ledoit-Péché formula for theoretical error derivation.
result Optimal train-test split ratio is proportional to square root of matrix dimension.
Policy gradient methods find Nash equilibrium in noisy games.
problem Finding Nash equilibrium in noisy games.
method Policy gradient methods with noise added.
result Policy gradient methods converge to Nash equilibrium in noisy games.
Although there is a rich literature on methods for allowing the variance in a univariate regression model to vary with predictors, time and other factors, relatively little has been done in the multivariate case. Our focus is on developing a class of nonparametric covariance regression models, which allow an unknown p …
Extends QHawkes to MQHawkes for analyzing financial co-jumps.
problem Capturing endogenous co-jumps in financial markets.
method Develops MQHawkes process with quadratic kernels, investigates stationarity, and derives Yule-Walker equations.
result Volatility distribution exhibits power-law behavior with computable exponents.
Study precise sample covariance error for Gaussian centered data.
problem Precise characterization of sample covariance error for Gaussian data.
method Developed a Random Duality Theory (RDT) framework to determine upper and lower bounds.
result Upper and lower bounds match in large-dimensional contexts, matching the spectral norm's limiting value.
A new framework for efficient sequence maps using Bayesian filtering and covariance.
problem Designing efficient recurrent sequence maps from explicit memory assumptions.
method Design-model framework, exact Bayesian filtering, query-dependent readout, linear-Gaussian instantiation.
result Improved robustness and retrieval performance across various benchmarks.
Gradients help find global optima in complex functions.
problem Finding global optima in functions with many local minima.
method A principle for generating search directions from non-local quadratic approximants based on gradients.
result The proposed algorithm and CMA-ES perform better than random reinitialized BFGS.
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…
Study variance-optimal hedging of forward curve derivatives under stochastic volatility.
problem Variance-optimal hedging of forward curve derivatives with stochastic volatility.
method Assumes HJM-Musiela dynamics modulated by stochastic covariance, uses Galtchouk-Kunita-Watanabe projection.
result Density of finite-maturity strategies, convergence of finite-rank projections, decomposition of hedging error.
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
Develops an online method for solving constrained optimization problems with debiasing techniques.
problem Online inference of solutions to constrained optimization problems with equality and inequality constraints.
method Stochastic Sequential Quadratic Programming (SSQP) with momentum debiasing.
result Achieves global almost-sure convergence and local asymptotic normality with optimal primal-dual limiting covariance.
PAMA learns covariate importance for better matching in observational studies.
problem Poor performance of conventional matching methods when covariates differ in relevance.
method PAMA is a semi-supervised framework that learns covariate importance from paired data and optimizes a weighted quadratic score.
result PAMA outperforms standard methods, particularly in high-dimensional settings and under model misspecification.
This work improves variational inference by reducing gradient variance.
problem Hard optimization of flexible variational distributions.
method Control variate based on quadratic approximation of the model's mean and covariance.
result Significant improvement in gradient variance and optimization convergence.