New decompositions misattribute differences between populations, even when outcomes are identical.
problem Misattribution of differences between populations using common functional decompositions.
method Extending the Kitagawa-Oaxaca-Blinder decomposition to nonlinear functional decompositions.
result Functional ANOVA and Accumulated Local Effects can misattribute differences even when outcomes are identical in two populations.
In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance matrix, thus reducing the number of samples required for estimation. To allow a sm…
New method splits unknown covariance Gaussians into independent parts.
problem Splitting multivariate Gaussian data with unknown covariance.
method Developed a general algorithm for decomposing unknown covariance Gaussians.
result Demonstrated decomposition for single multivariate Gaussian with unknown covariance.
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.
New findings on optimization landscape of Toeplitz covariance estimation.
problem Understanding the geometry of the Gaussian maximum-likelihood objective for Toeplitz covariance estimation.
method Overparameterized Carathéodory representation of positive definite Toeplitz covariance matrices, focusing on both amplitudes and frequencies.
result Joint optimization of amplitudes and frequencies leads to a benign population landscape, allowing for global recovery of the true Toeplitz covariance.
Solution to sparse PCA tuning problem using Empirical Bayes.
problem Sparse PCA multiple tuning problem (MTP).
method Empirical Bayes covariance decomposition for penalized PCA.
result Empirical Bayes approach efficiently solves MTP in sparse PCA.
New method estimates covariance in multi-view data with better accuracy and uncertainty.
problem Estimating covariance in multi-view data with shared and view-specific latent factors.
method Spectral decompositions and conditional conjugate priors for factor loadings and residual variances.
result Proves favorable asymptotic properties and excellent performance in simulations and real data.
It is well known that the curvature tensor of a pseudo-Riemannian manifold can be decomposed with respect to the pseudo-orthogonal group into the sum of the Weyl conformal curvature tensor, the traceless part of the Ricci tensor and of the scalar curvature. A similar decomposition with respect to the pseudo-unitary gro…
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.
Gradient flow solves optimal mass transport for covariance matrices.
problem Optimal mass transport for covariance matrices.
method Gradient flow on fiber bundle structure.
result Global convergence to polar decomposition.
Denise learns a function to quickly decompose covariance matrices robustly.
problem Robustly decomposing covariance matrices for feature extraction.
method Deep learning for symmetric positive semidefinite matrices.
result Denise achieves state-of-the-art performance in decomposition quality and speed.
The paper analyzes how re-weighting helps in reducing variance in high-dimensional kernel methods under covariate shifts.
problem The challenge of high-dimensional kernel methods under covariate shifts and the role of re-weighting.
method Derives asymptotic expansion of high-dimensional kernels under covariate shifts, analyzes bias-variance decomposition, and characterizes the regularized kernel.
result Re-weighting helps in decreasing variance and can be seen as a data-dependent regularization.
The paper explores totally geodesic submanifolds in SPD matrices and their properties.
problem Characterizing and understanding totally geodesic submanifolds in SPD matrices.
method Detailed geometric analysis and projection properties of SPD matrices.
result A non-linear projection on totally geodesic submanifolds has the minimizing property.
New risk decompositions clarify domain adaptation issues.
problem Domain adaptation challenges with different training and test distributions.
method Representation Bayesian Risk Decompositions, hybrid argument.
result Clarifies factors (2) and (3) as reasons for generalization failure.
Choosing a reference group in Oaxaca-Blinder decomposition can reverse conclusions.
problem The choice of reference group in Oaxaca-Blinder decomposition can lead to different conclusions.
method The study uses the Oaxaca-Blinder decomposition to investigate how the choice of reference group affects the results.
result The Oaxaca-Blinder decomposition can yield different conclusions based on the choice of reference group.
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.
Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and kernel embeddings of distributions. Operators acting on such spaces are, for instance, required to embed conditional probability distributi…
Algorithm improves SVM classification in non-Euclidean spaces.
problem Limitations of traditional SVM in non-Euclidean spaces.
method Covariance-adjusted SVM using Cholesky Decomposition.
result Cholesky-SVM outperforms traditional SVM in non-Euclidean spaces.
The paper introduces a new framework to assess generative model uncertainty.
problem Lack of a theoretical framework for assessing generative models' generalization and uncertainty.
method Bias-variance-covariance decomposition for kernel scores, with unbiased and consistent estimators.
result Kernel-based variance and entropy for uncertainty estimation are more predictive than existing methods.
Estimates covariance matrices for matrix-variate data via core covariance geometry.
problem Estimating covariance matrices for matrix-variate data with partial isotropy.
method Fixed-rank core covariance geometry, partial-isotropy rank-r core shrinkage estimator.
result The geometry of the space of rank-r cores is a smooth manifold.
Proposes a Gaussian process for Koopman mode decomposition.
problem Estimating Koopman mode decomposition quantities and latent variables.
method Unsupervised Gaussian process for simultaneous estimation.
result Efficient parameter estimation through low-rank approximations.
New method cleans cross-covariance matrices for better financial forecasting.
problem Asymptotically optimal cross-covariance cleaners fail in real-world, time-varying markets.
method Physics-informed neural network that learns from empirical singular values.
result Trained model outperforms analytical cleaners in out-of-sample cross-covariance prediction.
New asymmetric kernel methods improve feature learning.
problem Improving feature learning with asymmetric kernels.
method Coupled covariance eigenproblem and Nyström method.
result Empirical evaluations show benefits of KSVD.
We study the decomposition of the Riemannian curvature R tensor of an almost quaternion-Hermitian manifold under the action of its structure group Sp(n)Sp(1). Using the minimal connection, we show that most components are determined by the intrinsic torsion ξand its covariant derivative \widetilde\nablaξand determine r…
In this paper, we present a general, multistage framework for graphical model approximation using a cascade of models such as trees. In particular, we look at the problem of covariance matrix approximation for Gaussian distributions as linear transformations of tree models. This is a new way to decompose the covariance…
The study examines numerical aspects of Karhunen-Loève expansions for stochastic processes.
problem Constructing Karhunen-Loève expansions for second-order stochastic processes.
method Spectral decomposition of covariance operator via Fredholm integral equation, discretization, singular value decomposition of weight-scaled sample matrix.
result Consistent solutions for model-based and data-driven KLE construction, characterized by convergence of SVD-based eigenvalue estimates and KL coefficients distributions.
Proposes a method to predict responses from covariates over time.
problem Predicting responses from covariates with changing conditional distributions over time.
method Invariant Subspace Decomposition (ISD) framework that splits the conditional distribution into time-invariant and time-dependent components.
result The decomposition can be used for zero-shot and time-adaptation prediction tasks.
The paper studies Stein-Weiss operators on symmetric tensors, extending previous work.
problem Understanding Stein-Weiss operators on symmetric tensors of arbitrary rank.
method Analyzing the decomposition of tensor spaces into irreducible components and computing Weitzenbock formulas.
result Unified framework for second-order Stein-Weiss operators and tools for geometric analysis.
New method uses machine learning to improve statistical inference.
problem Performing inference on conditional functionals with scarce labeled data.
method Combines localization with prediction-based variance reduction.
result Valid and sharp confidence intervals for conditional functionals.
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.
Fitting high-dimensional data involves a delicate tradeoff between faithful representation and the use of sparse models. Too often, sparsity assumptions on the fitted model are too restrictive to provide a faithful representation of the observed data. In this paper, we present a novel framework incorporating sparsity i…
IKD uses eigen-decomposition for nonlinear dimensionality reduction.
problem Lack of sophisticated and nonlinear dimensionality reduction methods.
method Inverse Kernel Decomposition (IKD) based on eigen-decomposition of sample covariance matrix.
result IKD achieves comparable performance to optimization-based methods with faster running speeds.
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.
Generalizes randomized SVD for better matrix approximations using Gaussian vectors.
problem Computing accurate rank-k approximations of matrices with limited data.
method Extends randomized SVD to multivariate Gaussian vectors, incorporating prior knowledge and using Gaussian processes.
result Demonstrates improved accuracy in approximating matrices and Hilbert-Schmidt operators.
DAG models with hidden variables present many difficulties that are not present when all nodes are observed. In particular, fully observed DAG models are identified and correspond to well-defined sets ofdistributions, whereas this is not true if nodes are unobserved. Inthis paper we characterize exactly the set of dist…
A new method quickly identifies key variables and interactions.
problem Identifying key variables and interactions in high-dimensional data.
method Kernel trick for sparse orthogonal decomposition in O(# covariates) time.
result Outperforms existing methods for large, high-dimensional data sets.
Compared with global average pooling in existing deep convolutional neural networks (CNNs), global covariance pooling can capture richer statistics of deep features, having potential for improving representation and generalization abilities of deep CNNs. However, integration of global covariance pooling into deep CNNs …
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 work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition technique yields consistent parameter estimates from low-order observable moments, wit…
Evaluating AI investment strategies
problem Auditing a black-box algorithmic decision-maker
method Exact decomposition of cumulative regret
result Cumulative regret equals sum of per-period covariances
New method for uncertainty analysis in TabPFN, a state-of-the-art tabular transformer.
problem No method for uncertainty decomposition in TabPFN.
method Casted as a Bayesian predictive inference problem, derived variance estimators using predictive CLT.
result Fast to compute credible bands that target epistemic uncertainty and achieve near-nominal frequentist coverage.
This is the first of two papers where we address and partially confirm a conjecture of Deser and Schwimmer, originally postulated in high energy physics. The objects of study are scalar Riemannian quantities constructed out of the curvature and its covariant derivatives, whose integrals over compact manifolds are invar…
We consider the problem of estimating the mean and covariance of a distribution from iid samples in Rn, in the presence of an η fraction of malicious noise; this is in contrast to much recent work where the noise itself is assumed to be from a distribution of known type. The agnostic problem includes many…
Finite mixtures of regression models offer a flexible framework for investigating heterogeneity in data with functional dependencies. These models can be conveniently used for unsupervised learning on data with clear regression relationships. We extend such models by imposing an eigen-decomposition on the multivariate …
Covariance pooling is a feature pooling method with good classification accuracy. Because covariance features consist of second-order statistics, the scale of the feature elements are varied. Therefore, normalizing covariance features using a matrix square root affects the performance improvement. When pooling methods …
This paper, sixth in a series of eight, uses the geometric calculus on manifolds developed in previous papers of the series to introduce through the concept of a metric extensor field g a metric structure for a smooth manifold M. The associated Christoffel operators, a notable decomposition of that object and the assoc…
The paper introduces a method to decompose variance in twin networks for better treatment effect estimation.
problem Accurate treatment effect estimation requires reliable uncertainty measures to locate model failures.
method Layer-wise variance decomposition using Monte Carlo Dropout in twin networks.
result The encoder component dominates under distributional shift, providing a practical diagnostic for data collection.
In this paper, we present a novel framework incorporating a combination of sparse models in different domains. We posit the observed data as generated from a linear combination of a sparse Gaussian Markov model (with a sparse precision matrix) and a sparse Gaussian independence model (with a sparse covariance matrix). …