Simplified proof of Gaussian concentration inequality using covariance.
problem Gaussian concentration inequality proof
method Covariance representation based on characteristic functions
result Elementary proof of Gaussian concentration inequality
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48 results for “covariance representation”
Proposes a method to represent high-dimensional covariates for causal inference.
problem Inefficient and unreliable causal inference with high-dimensional covariates.
method Machine-learning-assisted covariate representation approach.
result Statistical reliability and performance guarantees for proposed methods.
SL(n) covariant valuations on Orlicz spaces are represented and characterized.
problem Representing SL(n) covariant valuations on Orlicz spaces.
method Representation theorem established for continuous, SL(n) covariant vector-valued valuations.
result Unique characterization of SL(n) covariant valuations as moment vectors.
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.
We simplify matrix computations for block matrices, especially useful for covariance and correlation matrices.
problem Complex computations for block matrices, especially for covariance and correlation matrices.
method Obtained a canonical representation for block matrices, facilitating computation of various matrix operations.
result Simplified computation of matrix operations for block matrices, particularly useful for covariance and correlation matrices.
Improved AutoDML estimator for causal inference using outcome-adapted shared covariate representation.
problem Efficiency in estimating treatment or policy effects in causal inference.
method Outcome-adapted AutoDML estimator that uses a shared covariate representation that is predictive of the outcome but not the Riesz representer.
result Outcome-adapted AutoDML estimator is asymptotically more efficient than baseline AutoDML.
Paper tackles CATE estimation with missing treatment info.
problem Challenges in estimating CATE with missing treatment information.
method Developed MTRNet, a novel CATE estimation algorithm using domain adaptation.
result Improves CATE estimation over state-of-the-art methods.
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.
Study on Blaschke locus with covariance metric properties.
problem Riemannian structure of Blaschke locus.
method Analysis of Blaschke locus as a manifold, study of covariance metric properties.
result Geodesics in Blaschke locus have infinite length with respect to the covariance metric.
Study projective representations of infinite-dimensional Hilbert-Lie groups.
problem Characterize and classify representations of Hilbert-Lie groups.
method Use covariance with respect to one-parameter groups of automorphisms and implement perturbation theory.
result Explicit determination of central extensions for projective representations.
MediEncoder: Nonlinear Representation Learning for High-Dimensional Causal Mediation Analysisstat.ME
MediEncoder learns nonlinear representations for causal mediation analysis.
problem High-dimensional noisy covariates and mediators in biomedical studies.
method Coupled encoder-decoder architecture with cross-factor network.
result Improves estimation accuracy in high-dimensional causal mediation analysis.
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 …
New method prevents posterior collapse in iVAE models.
problem Posterior collapse in iVAE models where observations and ICs are independent given covariates.
method Developed CI-iVAE by considering a mixture of encoder and posterior distributions in the objective function.
result Prevents posterior collapse, resulting in latent representations with more information of the observations.
Improves representation learning for individual treatment effect estimation.
problem Estimating individual treatment effects with high accuracy.
method Introduces a structure keeper to maintain correlation between baseline covariates and representations, trains a discriminator to balance representation and information loss.
result Proposed SMRL algorithm minimizes treatment estimation error and outperforms state-of-the-art methods.
Abstract: Review and definitions of generalised spin structures, their connections, and symmetry algebra.
problem Understanding and characterizing generalised spin structures and their properties.
method Definitions, basic notions, connections, covariant Lie derivative, covariant Cartan calculus, symmetry algebra.
result Characterization of homogeneous generalised spin structures.
Introduces intrinsic Riemannian cross-covariance for manifold-valued random objects.
problem Covariance estimation for random objects on Riemannian manifolds.
method Defines covariance and correlation via parallel transport.
result Proposed covariance is independent of coordinate choices.
Covariance fieldsmath.ST
We introduce and study covariance fields of distributions on a Riemannian manifold. At each point on the manifold, covariance is defined to be a symmetric and positive definite (2,0)-tensor. Its product with the metric tensor specifies a linear operator on the respected tangent space. Collectively, these operators form…
DeepMatch: Balancing Deep Covariate Representations for Causal Inference Using Adversarial Trainingstat.ML
We study optimal covariate balance for causal inferences from observational data when rich covariates and complex relationships necessitate flexible modeling with neural networks. Standard approaches such as propensity weighting and matching/balancing fail in such settings due to miscalibrated propensity nets and inapp…
Special orthogonal representations from octonions have geometric properties linked to binary cubics.
problem Understanding geometric properties of special orthogonal representations from octonions.
method Using octonions and their derivations, spinors, and covariants to show geometric properties.
result Covariants and Mathews identities of these representations are related to the Fano plane and .
BEGIN network models binary data without parametric assumptions.
problem Conditional independence in non-parametric families of binary data.
method BEGIN network models binary data using sparse linear representations and block factorizations.
result BEGIN network captures conditional independence for arbitrary binary and multinomial variables.
Motivated by positive energy representations, we classify those continuous central extensions of the compactly supported gauge Lie algebra that are covariant under a 1-parameter group of transformations of the base manifold.
This paper studies covariant derivatives for Lie groupoids with representation-valued forms.
problem Understanding covariant derivatives for Lie groupoids with representation-valued forms.
method The paper explores two approaches: linear connections and multiplicative Ehresmann connections, both yielding geometrically richer curved double complexes.
result The horizontal exterior covariant derivative is a key finding, generalizing the well-known operator from principal bundles.
CSTs improve stability in covariance spectrum analysis without training.
problem Stability and expressiveness in covariance spectrum analysis.
method Sequential application of covariance wavelet filters to input data.
result Stable and expressive hierarchical representations in low-data settings.
Scattering representations simplify SBI for images without extra compression.
problem Efficiently performing simulation-based inference on images with limited data.
method Use scattering representations for compression and learning, combined with spatial averaging and expressive density estimators.
result Scattering representations provide more information than traditional methods, without requiring additional simulations.
Spatial Adapter: Structured Spatial Decomposition and Closed-Form Covariance for Frozen Predictorsstat.ML
Spatial Adapter adds structured spatial representation to frozen predictors.
problem Efficiently adding spatial structure to pre-trained models.
method Structured spatial decomposition and closed-form covariance for residual fields.
result Adapter improves spatial prediction and uncertainty quantification.
Unsupervised Domain Adaptation aims to learn a model on a source domain with labeled data in order to perform well on unlabeled data of a target domain. Current approaches focus on learning \textit{Domain Invariant Representations}. It relies on the assumption that such representations are well-suited for learning the …
Improved covariate shift handling with node-based Bayesian neural networks.
problem Improving generalization under covariate shift in neural networks.
method Introduced node-based Bayesian neural networks that learn latent noise variables to represent input corruptions.
result Node-based BNNs perform well under covariate shift due to input perturbations, improving uncertainty estimation and robustness.
New method tests conditional independence using spectral representations.
problem Untestable conditional independence in many settings.
method Spectral representations of partial covariance operators, bi-level contrastive learning.
result Asymptotic validity and power guarantees for CI testing.
Unified framework for debiased machine learning using Riesz representer and Bregman divergence.
problem Estimating causal and structural parameters in machine learning.
method Generalized Riesz regression for fitting Riesz representer via Bregman divergence minimization.
result Automatic covariate balancing and Neyman orthogonality properties for debiased estimation.
The Matérn covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Matérn class is that it is possible to get precise control over the degree of mean-square differentiability of the random process. However, the Matérn class possesses e…
Statistical characteristics of deep network representations, such as sparsity and correlation, are known to be relevant to the performance and interpretability of deep learning. When a statistical characteristic is desired, often an adequate regularizer can be designed and applied during the training phase. Typically, …
Proposes L-VAE for longitudinal data analysis.
problem Analyse high-dimensional longitudinal data with missing values.
method Uses a multi-output additive Gaussian process (GP) prior to extend VAE's capability.
result Achieves highly accurate predictive performance.
Deconfounds neural network representation similarity metrics to improve consistency and accuracy.
problem Confounding by population structure in similarity metrics like RSA and CKA.
method Covariate adjustment regression to adjust for confounders.
result Improves detection of semantically similar neural networks and consistency in transfer learning.
Revisiting Counterfactual Regression through the Lens of Gromov-Wasserstein Information Bottleneckcs.LG
GWIB improves counterfactual regression by balancing latent distributions and reducing selection bias.
problem Selection bias between control and treatment groups negatively impacts counterfactual regression performance.
method GWIB uses Gromov-Wasserstein information bottleneck to maximize mutual information between covariates and outcomes while penalizing kernelized mutual information between latent representations and covariates.
result GWIB consistently outperforms state-of-the-art CFR methods in ITE estimation tasks.
Standard models assign disease progression to discrete categories or stages based on well-characterized clinical markers. However, such a system is potentially at odds with our understanding of the underlying biology, which in highly complex systems may support a (near-)continuous evolution of disease from inception to…
Spectral measurements reveal hidden representation geometry in language model training.
problem Hidden internal representation in language model training is hard to examine.
method Empirical protocol using activation covariance and per-sample gradient SVD spectra.
result Batch size affects representation geometry, and activation spectra predict token efficiency.
New method learns useful disentangled representations from weakly labeled data.
problem Learning useful representations from weakly labeled data.
method Model pairs of non-i.i.d. images, learn disentangled representations without requiring annotation.
result Learn disentangled representations reliably from pairs of images without requiring group, individual factor, or number of changed factors annotation.
FSRL balances fairness and sufficiency in learning representations.
problem Ensuring unbiased predictions and decisions in machine learning.
method A convex combination of sufficiency and fairness objectives using distance covariance.
result FSRL achieves a superior trade-off between fairness and accuracy.
In this paper, we present a graph-based semi-supervised framework for hyperspectral image classification. We first introduce a novel superpixel algorithm based on the spectral covariance matrix representation of pixels to provide a better representation of our data. We then construct a superpixel graph, based on carefu…
Novel neural GP kernels learn stable, flexible covariance structures.
problem Scalable and flexible covariance kernels for Gaussian processes.
method Directly learn kriging coefficients and conditional standard deviations using deep neural architectures exploiting permutation-equivariant structure.
result Improved training stability and data efficiency with expressive, non-stationary kernels.
Study semi-supervised learning with noisy proxy covariates, deriving bounds and showing gains.
problem Learning from noisy proxy covariates with scarce labels.
method Two-stage estimator learning kernel eigenfeatures from all proxy covariates and fitting a ridge predictor on labeled data.
result Finite sample bounds show fast labeled sample rates and consistent gains over supervised and semi-supervised baselines.
The interpretation of complex high-dimensional data typically requires the use of dimensionality reduction techniques to extract explanatory low-dimensional representations. However, in many real-world problems these representations may not be sufficient to aid interpretation on their own, and it would be desirable to …
Finding a new mathematical representations for graph, which allows direct comparison between different graph structures, is an open-ended research direction. Having such a representation is the first prerequisite for a variety of machine learning algorithms like classification, clustering, etc., over graph datasets. In…
Study forecasts volatility and risk in electricity markets using matrix-HAR models.
problem Forecasting volatility and risk in electricity markets.
method Constructed a parsimonious matrix-HAR type model to estimate realized covariation and risk premia in electricity markets.
result Inclusion of longer time horizons and renewable generation information improves forecasts.
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.
SDR outperforms IDR in multimodal data analysis, especially with fewer samples.
problem Understanding and optimizing data efficiency in multimodal representation learning.
method Generative linear model to synthesize multimodal data, comparing IDR and SDR methods.
result Linear SDR methods yield higher-quality, more succinct reduced-dimensional representations with smaller datasets.
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.
This study approximates distances between Gaussian processes and covariance operators using RKHS.
problem Approximating distances between Gaussian processes and covariance operators from finite samples.
method Using reproducing kernel Hilbert space (RKHS) covariance and cross-covariance operators, the study shows how to consistently and efficiently estimate Sinkhorn divergence from finite samples.
result Convergence rates are dimension-independent and of the same order as Hilbert-Schmidt distance.