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…
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48 results for “Covariance constraints”
Study improves portfolio risk estimation methods using robust covariance and CVaR constraints.
problem Improving portfolio risk estimation in the presence of financial data noise and extreme market conditions.
method Exploration of robust covariance estimators, application of CVaR constraints, use of K-means clustering in optimization.
result Robust covariance estimators can outperform market-weighted benchmarks, especially during bull markets.
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.
New method for linear connections in ODEs with constraints.
problem Constructing linear connections for ODEs with and without constraints.
method Novel method using submodule covariant derivatives.
result Closed form expressions for Massa-Pagani connection and its extension.
Spatially constrained Gaussian mixture models reduce covariance complexity.
problem High dimensionality in finite mixture models for spatial data.
method Spatial covariance constraint with only four free parameters.
result Improves clustering of multi-way spatial data and inference of spatial patterns.
Novel approach for SEM in small samples with .
problem Small sample size and 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.
Paper proposes a new algorithm for graph learning with covariance constraints.
problem Graphical models and factor analysis not jointly leveraged in graph learning processes.
method Penalized maximum likelihood estimation of an elliptical distribution with Riemannian optimization.
result Effectiveness of the proposed approach demonstrated on real-world data sets.
Algorithm solves covariant exterior derivative equations in small regions.
problem Solving covariant exterior derivative equations in geometric and algorithmic ways.
method Linear homotopy operator of the Poincare lemma, constraints for parallel transport equations.
result Solves covariant constant and related equations in a geometric and algorithmic way.
Safety filter for unknown discrete-time systems with learned models and noise covariance.
problem Ensuring safety for unknown discrete-time linear systems with Gaussian noise.
method Develops a learning-based safety filter using empirical model and noise covariance, optimizing control actions to stay within safety constraints.
result Minimally modifies nominal control actions to ensure safety with high probability, tightening constraints as more data is collected.
We propose a general method for deformation quantization of any second-class constrained system on a symplectic manifold. The constraints determining an arbitrary constraint surface are in general defined only locally and can be components of a section of a non-trivial vector bundle over the phase-space manifold. The c…
Defines constraint tensor for null hypersurfaces, providing explicit geometry.
problem Defining constraint tensor for null hypersurfaces with any topology.
method Explicit definition in extrinsic geometry, covariant for any topology.
result Simple form of constraint tensor on transverse submanifolds.
Investigates portfolio optimization with and without gearing constraints.
problem Improving portfolio weights for better alignment with expected returns.
method Extends the alpha-weight angle bound to include gearing constraints and uses theoretical arguments and simulations.
result Equally weighted portfolios are not preferable to mean-variance portfolios even with poor forecast ability and a badly conditioned covariance matrix.
Optimizes SGLD noise structure for better generalization bounds.
problem Improving generalization bounds for large models trained with SGLD.
method Manipulates the noise structure in SGLD to optimize information-theoretical bounds.
result Optimal noise covariance is the square root of the expected gradient covariance under certain constraints.
Proposes a method to quantify uncertainty in predictions under covariate shift.
problem Uncertainty quantification challenges in machine learning with covariate shifts.
method Constructs PAC prediction sets with given importance weights and confidence intervals for weights.
result Algorithm gives prediction sets with the smallest average normalized size.
New method for private linear regression under privacy constraints, achieving optimal rates.
problem Statistical complexity of private linear regression under unknown, ill-conditioned covariates.
method Information-Weighted Regression method
result Optimal convergence rates for both central and local privacy models.
Several methods have been recently proposed for estimating sparse Gaussian graphical models using regularization on the inverse covariance matrix. Despite recent advances, contemporary applications require methods that are even faster in order to handle ill-conditioned high dimensional modern day datasets. I…
Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithmmath.ST
Paper optimizes federated PCA for covariance estimation under privacy constraints.
problem Privacy-preserving covariance estimation in federated learning.
method Federated PCA, matrix version of van Trees' inequality, three-layer spectral decomposition.
result Optimal rates of convergence for central server's estimation, robust to inconsistent local estimators.
Under covariate shift, training (source) data and testing (target) data differ in input space distribution, but share the same conditional label distribution. This poses a challenging machine learning task. Robust Bias-Aware (RBA) prediction provides the conditional label distribution that is robust to the worstcase lo…
End-to-end portfolio optimization framework bypassing covariance matrix estimation.
problem Optimizing portfolios with large numbers of assets and constraints.
method Deep learning approach that directly optimizes asset distributions without forecasting.
result Framework outperforms classical methods and handles various constraints.
Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Preconditionstat.ML
The paper explores optimal algorithms for linear regression under covariate shift, proving the optimality of certain transformations and SGD variants.
problem Optimal algorithms for linear regression under covariate shift with ellipse-shaped constraints.
method Establishes a tight lower generalization bound via Bayesian Cramer-Rao inequality, proves the optimality of certain transformations, and analyzes SGD variants.
result Optimal estimators and SGD variants achieve optimality under specific conditions.
In this work, we propose a new Gaussian process regression (GPR) method: physics information aided Kriging (PhIK). In the standard data-driven Kriging, the unknown function of interest is usually treated as a Gaussian process with assumed stationary covariance with hyperparameters estimated from data. In PhIK, we compu…
This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with known mean. In applications where the covariance matrix naturally possesses a certain structure, taking the prior structure information into account in the estimation procedure is benef…
Flexible VAEs using FIFs improve model likelihood on image datasets.
problem Limitations of diagonal Gaussian posteriors in VAEs.
method Regularized Free-form Injective Flow (FIF) for flexible posterior.
result Full covariance VAEs outperform diagonal Gaussian posteriors.
We consider the problem of Graphical lasso with an additional element-wise norm constraint on the precision matrix. This problem has applications in high-dimensional covariance decomposition such as in \citep{Janzamin-12}. We propose an ADMM algorithm to solve this problem. We also use a continuation st…
CaTs use DAGs with transformers to enforce causal constraints, improving neural network robustness.
problem Neural networks lack inherent causal structure respect, leading to reliability issues.
method Introducing Causal Transformers (CaTs) that operate under predefined causal constraints specified by DAGs.
result CaTs improve robustness and interpretability of neural networks under causal constraints.
A parameter-invariant variational problem with a manifestly covariant Lagrangian function of second order is considered, which covers the case of the free relativistic top at constraint manifold of constant acceleration
Efficiently private regression for unbounded data.
problem Privacy constraints in regression settings with unbounded covariates.
method Differential privacy techniques on mean and covariance estimation extended to sub-gaussian regime.
result Unbiased estimate of true regression vector learned up to a scaling factor.
GLSKF improves tensor completion by capturing both global and local variations.
problem Tensor completion with missing entries, especially in data with spatial or temporal side information.
method Integrates smoothness-constrained low-rank factorization with a locally correlated residual process.
result GLSKF achieves superior performance and scalability on real-world datasets.
Safe learning in uncertain systems with state measurements and optimization.
problem Safe learning in nonlinear control-affine systems with unknown additive uncertainty.
method Model uncertainty as Gaussian noise, learn mean and covariance, use optimization to adjust control input.
result Guaranteed safety with arbitrarily large probability while learning and control proceed simultaneously.
We consider a modification of the covariance function in Gaussian processes to correctly account for known linear constraints. By modelling the target function as a transformation of an underlying function, the constraints are explicitly incorporated in the model such that they are guaranteed to be fulfilled by any sam…
Stabilizing Private LASSO under Heterogeneous Covariates via Anisotropic Objective Perturbationstat.ML
New method stabilizes private LASSO for high-dimensional data with diverse covariate scales.
problem Privacy constraints and heterogeneity in covariate scales degrade LASSO stability and accuracy.
method Gram-based anisotropic objective perturbation to counteract covariate structure.
result Significantly improves convergence and statistical efficiency of private LASSO estimators.
Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture the correlations among the variables, the low rank plus diagonal structure was in…
Recently there has been sustained interest in modifying prediction algorithms to satisfy fairness constraints. These constraints are typically complex nonlinear functionals of the observed data distribution. Focusing on the path-specific causal constraints proposed by Nabi and Shpitser (2018), we introduce new theoreti…
Two-stage mechanism designs reduce regret in recommender systems with stochastic covariates.
problem Designing effective recommender systems with user covariates sampled online.
method Two-stage algorithm integrating incentivized exploration with offline learning methods.
result Achieves sublinear regret while maintaining incentive compatibility.
Streaming Approach to Quadratic Covariation Estimation Using Financial Ultra-High-Frequency Dataq-fin.CP
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.
We consider the problem of mean-variance portfolio optimization for a generic covariance matrix subject to the budget constraint and the constraint for the expected return, with the application of the replica method borrowed from the statistical physics of disordered systems. We find that the replica symmetry of the so…
Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly yields solutions that do not have a closed form or that are restricted to specific covariance funct…
Enhanced neural network framework improves constraint satisfaction with topological conditioning.
problem Maintaining semantic coherence while satisfying physical and logical constraints in neuro-symbolic reasoning.
method Integrates topological conditioning with gradient stabilization mechanisms using Forman-Ricci curvature, Deep Delta Learning, and Covariance Matrix Adaptation Evolution Strategy.
result Achieves mean energy reduction to 1.15 compared to baseline values of 11.68, with 95 percent success rate.
CASP improves portfolio optimization by considering asset covariance.
problem Infeasibility in cardinality-constrained portfolio optimization.
method CASP uses volatility-normalized selection and covariance-aware projection.
result CASP-Basic delivers lower portfolio variance than standard Euclidean repair.
In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance of the data. However, PCA has two major weaknesses. Firstly, it only considers li…
Fused Multinomial Logistic Regression Utilizing Summary-Level External Machine-learning Informationstat.ME
Proposes a method to use external machine-learning predictions in multinomial logistic regression.
problem Improving statistical inference using summary-level external machine-learning predictions.
method Empirical-likelihood framework incorporating moment constraints from external nonparametric machine-learning predictions.
result Fused estimator achieves strict efficiency gain over primary-only estimator under mild conditions.
Markowitz (1952, 1959) laid down the ground-breaking work on the mean-variance analysis. Under his framework, the theoretical optimal allocation vector can be very different from the estimated one for large portfolios due to the intrinsic difficulty of estimating a vast covariance matrix and return vector. This can res…
New lower bounds for private covariance estimation of Gaussian distributions are proven.
problem Proving tight lower bounds for private estimation tasks under differential privacy.
method Generalized fingerprinting method for exponential families and private Assouad method.
result Tight lower bounds for private covariance estimation in Frobenius and spectral norms.
High-dimensional covariance matrix estimators on simulated portfolios with complex structuresq-fin.CP
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.
Proposes SVI for covariate-shift generalization with sparse variable independence.
problem Covariate-shift generalization with limited data and unstable variables.
method Introduces sparsity constraint and combines reweighting and selection in an iterative way.
result Improves covariate-shift generalization performance on synthetic and real-world datasets.
Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing constraints on covariance, one can ensure consistency of linear response with the var…
We propose an explicit construction of the deformation quantization of the general second-class constrained system, which is covariant with respect to local coordinates on the phase space. The approach is based on constructing the effective first-class constraint (gauge) system equivalent to the original second-class o…
Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables. We give a precise graph-theoretic characterization of when submatrices of the cov…