Study high-dimensional covariance matrix estimators for complex portfolios, improving financial metrics.
problem Estimating covariance matrices in high-dimensional portfolios with nested and one-factor structures.
method Combining random matrix theory, free probability, deterministic equivalents, and two-step covariance estimators.
result Two-step estimators improve financial metrics in complex and one-factor covariance models.
Flexible Cox model for time-dependent covariates with complex sparsity patterns.
problem Lack of flexibility in enforcing specific sparsity patterns in time-dependent Cox models.
method Proposes a flexible framework for variable selection in time-dependent Cox models, accommodating complex selection rules.
result Achieves accurate estimation with low false alarm rates for complex covariate structures.
Energy trees handle complex data structures with multiple variable types.
problem Handling intricate data structures with various types of covariates.
method Energy trees, a regression and classification model, use energy statistics to accommodate structured covariates of different types.
result Energy trees maintain statistical foundations, interpretability, and robustness to overfitting.
Vanilla SGD learns SIM from anisotropic data without explicit covariance estimation.
problem Learning SIM from anisotropic Gaussian inputs.
method Vanilla Stochastic Gradient Descent (SGD) trained on SIM with anisotropic input.
result Vanilla SGD adapts to anisotropic data's covariance structure.
The covariance of a stationary process X is diagonalized by a Fourier transform. It does not take into account the complex Fourier phase and defines Gaussian maximum entropy models. We introduce a general family of phase harmonic covariance moments, which rely on complex phases to capture non-Gaussian properties. The…
We study the problem of recovering the structure underlying large Gaussian graphical models or, more generally, partial correlation graphs. In high-dimensional problems it is often too costly to store the entire sample covariance matrix. We propose a new input model in which one can query single entries of the covarian…
This work investigates how gradient-based learning performs with structured data, revealing issues and improvements.
problem Gradient-based learning under structured data, particularly with a spiked covariance structure.
method Investigates the effect of a spiked covariance structure on gradient-based feature learning and proposes weight normalization.
result Gradient-based dynamics may fail to recover the true direction in anisotropic settings, but weight normalization can improve performance.
Hybrid ResNet and RMT improve covariance matrix estimation for cryptocurrency portfolios.
problem Noisy, non-Gaussian financial data leads to unstable covariance matrices.
method Combines RMT regularization and ResNet learning for data-driven corrections.
result Hybrid estimator outperforms traditional methods in portfolio optimization.
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.
It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated high-dimensional data with unknown mean and dependence structures. Matrix-variate appr…
Graphical notation simplifies complex polynomial constraints in linear models.
problem Complex polynomial constraints in linear structural equation models are impractical.
method Developed a graphical notation to represent these constraints.
result The graphical notation simplifies the representation of many polynomial constraints.
Bayesian framework for analyzing heterogeneous covariance data with a novel MoE-Wishart model.
problem Analyzing complex multivariate systems with varying covariance structures.
method Comprehensive Bayesian framework using mixture-of-experts Wishart model with predictor-dependent mixture weights.
result Accurate subpopulation recovery and estimation in heterogeneous covariance scenarios.
Analyzing multivariate time series data is important to predict future events and changes of complex systems in finance, manufacturing, and administrative decisions. The expressiveness power of Gaussian Process (GP) regression methods has been significantly improved by compositional covariance structures. In this paper…
We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization problems. Recently, it was shown that the underlying principle behind their succ…
Proposes CoDEAL for estimating heterogeneous treatment effects in panel data models.
problem Estimating heterogeneous treatment effects in causal panel data models with covariate effects.
method Covariate-Adjusted Deep Causal Learning (CoDEAL) integrating neural networks and autoencoders.
result Establishes theoretical guarantees and demonstrates compelling performance in simulations and real data.
Scalable GP model handles functional covariates and multitasks.
problem Uncertainty quantification in complex mechanical systems with time-dependent inputs.
method Introduced a fully separable kernel structure for functional covariates and multitask problems, leveraging Kronecker structure for scalability.
result The model significantly improves over single task GPs, requiring fewer samples for accurate predictions.
Method detects critical events in complex systems by learning latent causal structure.
problem Detecting onset of epileptic seizures, customer churn, or pandemics from hidden causal interactions.
method A machine learning method that learns an optimal feature representation from powers of the empirical covariance or precision matrix.
result Proves structural consistency and demonstrates competitive results in seizure and churn prediction.
We show that the Teukolsky connection, which defines generalized wave operators governing the behavior of massless fields on Einstein spacetimes of Petrov type D, has its origin in a distinguished conformally and GHP covariant connection on the conformal structure of the spacetime. The conformal class has a (metric com…
Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and non-uniformly smooth spatial boundaries. A Gaussian process regression using a non-stat…
We uncover scaling laws and statistical structure in complex datasets.
problem Understanding universal traits in complex datasets.
method Analogizing data to physical systems, using statistical physics and RMT.
result Real-world datasets and Gaussian data with long-range correlations share the same RMT universality class.
DOPE efficiently estimates ATE with complex covariates.
problem Efficient estimation of ATE from complex covariates.
method Proposed DOPE framework for efficient adjustment.
result DOPE retains efficiency even with highly predictive covariates.
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.
A new method for efficient portfolio optimization using graph structures.
problem Optimizing portfolio weights while reducing computational complexity.
method Hierarchical graph structures and Schur complement method.
result Optimal portfolio weights can be computed efficiently by inverting small submatrices.
We analyze geometrical structures necessary to represent bulk and surface interactions of standard and substructural nature in complex bodies. Our attention is mainly focused on the influence of diffuse interfaces on sharp discontinuity surfaces. In analyzing this phenomenon, we prove the covariance of surface balances…
In this paper we prove some classification theorems of real hypersur- faces in Mn(c) satisfying certain conditions on the covariant derivative of the structure Jacobi operator. We also prove the non-existence of real hypersurfaces with Codazzi type structure Jacobi operator in Mn(c).
Optimistic covariance-adaptive algorithms improve combinatorial semi-bandits regret.
problem Optimal regret in stochastic combinatorial semi-bandits with adaptive covariance estimation.
method Design of OLS-UCB-C and COS-V algorithms leveraging online covariance estimation.
result Improved gap-free regret with T^1/2 complexity for COS-V.
New method improves PCA for high-dimensional data with n < p.
problem PCA struggles in high-dimensional settings with n < p.
method Pairwise differences covariance estimation with four regularized versions.
result Proposed methods outperform existing estimators in high-dimensional data settings.
Efficiently estimates prediction error in regression with Gaussian covariates under privacy constraints.
problem Private regression with Gaussian covariates under differential privacy constraints.
method Sum-of-Squares framework combined with robust estimators.
result Sample-optimal private regression algorithm with optimal error rates.
Two new regularization methods improve neural network performance and complexity control.
problem Improving neural network performance and complexity control with correlated or high-dimensional features.
method Two regularization strategies: covariance-aware ridge and covariance-aware lasso.
result Improves predictive performance and complexity control over standard penalties.
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 fast algorithm for fitting multilevel factor models.
problem Fitting multilevel factor models with covariance structure.
method Novel expectation-maximization algorithm tailored for multilevel factor models.
result Shows efficient computation of inverse of positive definite MLR matrix.
EiGLasso speeds up sparse Kronecker-sum covariance estimation.
problem Sparse Kronecker-sum inverse covariance estimation challenges in scalability and parameter identification.
method Newton's method combined with eigendecomposition of sample and feature graphs, approximating Hessian for speed.
result Two to three orders-of-magnitude speed-up on simulated and real-world data.
Probabilistic programming languages represent complex data with intermingled models in a few lines of code. Efficient inference algorithms in probabilistic programming languages make possible to build unified frameworks to compute interesting probabilities of various large, real-world problems. When the structure of mo…
Anisotropic data structure affects learning dynamics and generalization error in linear networks.
problem Understanding the impact of data anisotropy on learning dynamics and generalization error in linear networks.
method Examined a spiked covariance structure as a model of anisotropy in a two-layer linear network in a linear regression setting.
result Learning dynamics proceed in two phases: initially driven by input-output correlation, then by other principal directions of the data structure. Derived an analytical expression for the generalization error.
ULA estimates covariance of log-concave distributions efficiently.
problem Estimating covariance matrices of log-concave distributions efficiently.
method Unadjusted Langevin algorithm (ULA) for sampling and covariance estimation.
result Sample complexity of single-chain ULA is smaller than that of parallel ULA by a logarithmic factor.
We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span a low dimensional linear subspace in the space of symmetric matrices, our aim i…
Structured credal learning separates covariate shift and label disagreement.
problem Uncertainty in real-world learning tasks due to covariate shift and noisy labels.
method Introduces a structured credal learning framework that explicitly separates these sources.
result Geometric bounds and decomposition reveal how covariate shifts affect label disagreement contributions.
The paper provides PAC bounds for estimating causal effects using covariate adjustment with a valid set.
problem Estimating causal effects in high-dimensional settings without randomized experiments.
method PAC learning perspective, valid adjustment set, $\eps$-Markov blanket, constraint-based algorithms.
result PAC-bounds the estimation error of covariate adjustment by a term exponential in the size of the adjustment set.
BGM-IV uses AI to estimate causal effects in complex data.
problem Estimating causal effects in high-dimensional, nonlinear settings with endogeneity.
method Structured latent generative modeling for posterior inference in a causally structured latent space.
result BGM-IV outperforms existing methods in high-dimensional covariate regimes.
Spectral mixture (SM) kernels comprise a powerful class of generalized kernels for Gaussian processes (GPs) to describe complex patterns. This paper introduces model compression and time- and phase (TP) modulated dependency structures to the original (SM) kernel for improved generalization of GPs. Specifically, by adop…
The covariant canonical formalism is a covariant extension of the traditional canonical formalism of fields. In contrast to the traditional canonical theory, it has a remarkable feature that canonical equations of gauge theories or gravity are not only manifestly Lorentz covariant but also gauge covariant or diffeomorp…
Estimates covariance matrices using Markov chain Monte Carlo with improved sample complexity.
problem Complexity of covariance matrix estimation for Gibbs distributions.
method Uses Markov chain Monte Carlo with conditions on the chain's spectral gap and Poincaré inequality.
result Achieves similar sample complexity as i.i.d. samples with better query complexity.
Optimizes spectral density estimation for stationary and nonstationary processes.
problem Estimating spectral density of time series with complex structure.
method Optimally adaptive Bayesian spectral density estimation using smoothing spline covariance structure.
result Optimal eigendecomposition provides superior performance compared to alternative covariance functions.
Proposes spBART for risk prediction using epigenetic signatures and covariates.
problem Complex high-dimensional epigenetic data and low-dimensional covariates for risk prediction.
method Semi-parametric Bayesian Additive Regression Trees (spBART) with cross-validation for variable selection.
result Achieves strong out-of-sample discrimination (AUC = 0.96) in held-out validation set.
In the present paper a generalized Kählerian space G1KN of the first kind is considered, as a generalized Riemannian space GRN with almost complex structure Fih, that is covariantly constant with respect to the first kind of covariant derivative. Using the non-symmetr…
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.
New spectral clustering method handles discrete covariates for better community detection.
problem Community detection in networks with discrete covariates.
method Spectral algorithm that separates latent network structure from observed covariates.
result Achieves perfect clustering with high probability in large, sparse networks.
Novel approach for SEM in small samples with p>n.
problem Small sample size and p>n issues in factor-based SEM. method Reformulates covariance structure into self-covariance and cross-covariance, defines a feasible set with relative error constraint.
result Improved stability and directional information in small-sample settings.