Study connects covariance cleaning theory to information theory for heavy-tailed distributions.
problem Optimizing covariance matrices for heavy-tailed distributions using information theory.
method Minimizing Frobenius norm and information loss between true and estimated covariance matrices.
result Asymptotic regime of large matrices minimizes information loss for Student's t distributions.
Method minimizes total cost of classification by acquiring covariates efficiently.
problem Minimizing total cost of classification in applications with covariate acquisition costs.
method Formalizes optimization goal using Bayes risk, introduces assumptions for computable solution.
result Proposed method achieves lowest total costs compared to previous methods on medical datasets.
This paper studies geodesics between covariance matrices of different ranks using the Bures-Wasserstein metric.
problem Geodesics between covariance matrices of varying ranks.
method Analyzes the Bures-Wasserstein distance on covariance matrices, completing previous work on geodesics and providing explicit formulas.
result The set of all minimizing geodesics between two covariance matrices is parametrized by a closed unit ball in R(k−r)imes(l−r). The paper defines minimal norm tensors for curvature and divergence tensors, explaining Weyl and Cotten tensors.
problem Understanding curvature tensors and their minimal norm.
method Analyzing minimal norm tensors for third and fourth covariant tensors, including Riemannian curvature and divergence.
result Weyl tensor and Cotten tensor are identified as minimal norm tensors of Riemannian curvature and divergence tensors, respectively.
This study optimizes covariate density and propensity score for efficient ATE estimation.
problem Efficiently estimating average treatment effects (ATEs) with minimal variance.
method Adaptive experiment optimizing both covariate density and propensity score.
result Proposed method minimizes the semiparametric efficiency bound for ATE estimation.
New methods improve portfolio risk minimization by estimating covariance matrix more accurately.
problem Uncertainty in estimating covariance matrix leads to unreliable hedge trades.
method Proposes two new estimators of the inverse covariance matrix using l2 and l1 norms.
result Portfolio formed using proposed estimators achieves substantial risk reduction and improved returns.
Covariate shift relaxes the widely-employed independent and identically distributed (IID) assumption by allowing different training and testing input distributions. Unfortunately, common methods for addressing covariate shift by trying to remove the bias between training and testing distributions using importance weigh…
The paper optimizes regret using covariance between costs and decisions.
problem Optimizing expected regret in decision-making problems.
method Developed derivative theory of covariance regret functional, derived Gâteaux derivative, and extended to constrained optimization.
result Gradient of covariance regret is the cost covariance matrix, with implications for portfolio optimization.
A new one-step method for covariate shift adaptation.
problem Real-world data often violates the assumption of same distribution for training and test samples.
method Proposes a one-step optimization approach to jointly learn the model and weights.
result The proposed method achieves a generalization error bound and is empirically effective.
Paper proposes a new method for SP with covariates using PADR and ERM.
problem Stochastic programming with covariate information.
method Empirical risk minimization (ERM) with nonconvex piecewise affine decision rules (PADR).
result The method provides theoretical consistency and computational tractability for nonconvex SP problems.
Neural network method estimates covariate-dependent graphical models with statistical guarantees.
problem Estimating graph structure from covariate-dependent data.
method Neural network approach that allows flexible functional dependency on covariates.
result Theoretical PAC guarantees for the method's performance.
NICE learns a representation to avoid bad controls in causal inference.
problem Avoiding bad controls in causal inference from observational data.
method Uses invariant risk minimization (IRM) to learn a representation of covariates that avoids bad controls.
result NICE outperforms adjusting for all covariates in cases with unknown collider variables and bad controls.
The paper proves a new method to improve generalization in covariate-shift scenarios.
problem Improving performance on test distributions that differ from training distributions.
method Independence-driven importance weighting algorithms for feature selection.
result Theoretical proof that these algorithms can identify optimal variables for covariate-shift generalization.
New method for factor analysis using nuclear and ℓ0 norms.
problem Finding a low-rank plus sparse decomposition from noisy covariance matrix.
method Formulated an optimization problem with nuclear norm, ℓ0 norm, and KL divergence. Used alternating minimization algorithm. result Algorithm effectively decomposes covariance matrices in synthetic and real datasets.
New method estimates covariance matrices without restrictive assumptions.
problem Estimating high-dimensional covariance matrices under restrictive assumptions.
method Distributionally robust covariance estimation problems with mild conditions.
result Robust estimators are efficient, consistent, and perform well.
Paper tackles domain generalization by minimizing domain-based covariance.
problem Training data and test data have different distributions, leading to poor generalization.
method Find a central subspace minimizing domain-based covariance while preserving functional relationships.
result The proposed method achieves better generalization performance on unseen test datasets.
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…
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
Graphical models for covariance matrices improve structure learning.
problem Learning structure in graphical models for covariance matrices.
method Structural learning via ℓ1-penalized loss minimization. result Method outperforms alternatives in simulations and real-world applications.
Paper introduces a method to create robust representations against covariate shifts.
problem Distribution shift between training and testing data in machine learning.
method Introduces a variational objective with two components: discriminative representation and invariant support.
result Optimal representations ensure robustness to covariate shifts, improving performance on DomainBed.
This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used for approximate minimization of smooth and strongly convex losses, and specificall…
Geometric families of low-rank covariances improve flexibility and tractability in high dimensions.
problem Interpolating and identifying covariance matrices in high dimensions with limited data.
method Differential geometric construction of low-rank covariance families, interpolation on manifolds, and distance minimization for identification.
result Differential geometric covariance families offer significant flexibility and computational tractability.
DRSS method identifies unnecessary samples and features in DR covariate shift.
problem Identifying unnecessary samples and features in DR covariate shift.
method Combines DR learning and safe screening techniques.
result DRSS method provides reliable identification of unnecessary samples and features under specified distribution uncertainty.
Study analyzes bond price covariation robustly under no-arbitrage conditions.
problem Identifying the number of statistically relevant factors in the bond market.
method Nonparametric analysis of realized covariations in a general no-arbitrage setting.
result A high number of factors is needed to describe term structure evolution and term structure of volatility varies over time.
Differentially private method for estimating individualized treatment rules.
problem Estimating individualized treatment rules while preserving privacy.
method Differentially private two-stage empirical risk minimization (DP-2ERM).
result Improved privacy-utility trade-off demonstrated through simulations and applications.
Paper addresses regret minimization and inference in high-dimensional online decision-making.
problem Regret minimization and statistical inference in high-dimensional online decision-making.
method Integrates ε-greedy bandit algorithm with hard thresholding for sparse bandit parameters and debiasing method for inference.
result Achieves either O(T1/2) regret or O(T1/2)-consistent inference, with trade-off between exploration and exploitation. We introduce new families of Integral Probability Metrics (IPM) for training Generative Adversarial Networks (GAN). Our IPMs are based on matching statistics of distributions embedded in a finite dimensional feature space. Mean and covariance feature matching IPMs allow for stable training of GANs, which we will call M…
Statistical modeling of spatiotemporal phenomena often requires selecting a covariance matrix from a covariance class. Yet standard parametric covariance families can be insufficiently flexible for practical applications, while non-parametric approaches may not easily allow certain kinds of prior knowledge to be incorp…
Improved sampling for Diffusion Models by accounting for covariance.
problem Sampling quality degradation in few-step Diffusion Models.
method Covariance-aware sampler using Tweedie's formula and Fourier-space decomposition.
result Consistently superior samples compared to state-of-the-art samplers.
Derives Lagrangian for minimal surfaces, proving tangential variations vanish.
problem Variational calculus for minimal surfaces.
method Lagrangian formulation, pullback covariant derivative, geometric argument.
result Tangential variations vanish for minimal surfaces.
We study the basic problem of robust subspace recovery. That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed underlying subspace. We first estimate "robust inverse sample covariance" by solvi…
We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to perform feature selection via a constrained optimization problem involving the tra…
Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the covariates. The estimated linear combinations include all covariates, making res…
This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an i.i.d. Gaussian random sample, we establish high dimensional rates of convergence to…
An algorithm finds optimal covariates for blocking in randomized experiments.
problem Minimizing variance in causal effect estimates from heterogeneous data.
method Using causal graphs, an algorithm identifies optimal covariates for blocking.
result An efficient algorithm reduces variance in causal effect estimates.
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 approach for semi-supervised learning under covariate shifts.
problem Semi-supervised learning under covariate shifts where labeled and unlabeled data distributions differ.
method Information-theoretical approach, addressing covariate shifts.
result Improved performance compared to previous methods.
We consider generators of algebraic covariant derivative curvature tensors R' which can be constructed by a Young symmetrization of product tensors W*U or U*W, where W and U are covariant tensors of order 2 and 3. W is a symmetric or alternating tensor whereas U belongs to a class of the infinite set S of irreducible s…
Paper explores geometry of covariance matrices using associated bundles.
problem Geometry of fixed-rank covariance matrices.
method Associated bundle approach to Bures--Wasserstein geometry.
result Established a one-to-one correspondence between geodesics.
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…
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…
New method calibrates models under covariate shifts.
problem Calibration of models can be lost under covariate shifts.
method Importance sampling based approach.
result Efficacy demonstrated on real-world and synthetic datasets.
Several methods have been recently proposed for estimating sparse Gaussian graphical models using ℓ1 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…
CDST improves ensemble prediction by adjusting model weights based on covariates.
problem Improving ensemble prediction accuracy in complex scenarios.
method Covariate-dependent stacking (CDST) with flexible model weights estimated via cross-validation.
result CDST consistently outperforms conventional model averaging methods in complex datasets.
Recently, there has been focus on penalized log-likelihood covariance estimation for sparse inverse covariance (precision) matrices. The penalty is responsible for inducing sparsity, and a very common choice is the convex l1 norm. However, the best estimator performance is not always achieved with this penalty. The …
Optimizes ellipsoids for uncertainty regions in parameter estimation.
problem Learning minimal volume uncertainty ellipsoids for parameter estimation.
method Differentiable optimization approach using neural networks to approximate optimal ellipsoids.
result Approximately computed ellipsoids are smaller and more accurate than existing methods.
Optimally tackles covariate shift in RKHS-based nonparametric regression.
problem Covariate shift in nonparametric regression over RKHS.
method Two families of covariate shift problems defined using likelihood ratios. Minimax rate-optimal estimators for KRR and reweighted KRR.
result KRR is minimax rate-optimal and strictly sub-optimal compared to naive estimator under covariate shift.
We consider in this paper the problem of optimal experiment design where a decision maker can choose which points to sample to obtain an estimate β^ of the hidden parameter β⋆ of an underlying linear model. The key challenge of this work lies in the heteroscedasticity assumption that we make, meaning that…