arXiv research

New method groups similar functional covariates for better modeling.

Linear and Quadratic Discriminant analysis (LDA/QDA) are common tools for classification problems. For these methods we assume observations are normally distributed within group. We estimate a mean and covariance matrix for each group and classify using Bayes theorem. With LDA, we estimate a single, pooled covariance m…

Study projective representations of infinite-dimensional Hilbert-Lie groups.

Selective inference for group lasso estimators across various distributions and covariates.

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…

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…

Proposes a boosting framework for sparsity in grouped covariates.

The paper proposes a test to assess rater accuracy while accounting for rater covariates.

A fast method estimates group-adaptive elastic net penalties using co-data.

The paper proposes a method to estimate treatment effects using CAR designs with additional covariates.

Develops MGQDA for multi-group classification with theoretical guarantees and practical applications.

Proposes a fusion method for many treatment groups in ITRs.

Develops a reduction theory for covariant field theories with gauge symmetries.

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.

We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental exact sequences of differential cohomology. We consider smooth Pontry…

BEGIN network models binary data without parametric assumptions.

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…

The classical Rankin-Cohen brackets are bi-differential operators from $C^\infty(\mathbb R)\times C^\infty(\mathbb R)$ into $C^\infty(\mathbb R)$. They are covariant for the (diagonal) action of ${\rm SL}(2,\mathbb R)$ through principal series representations. We construct generalizations of these operators, replacing…

Invariant covariant derivatives on homogeneous spaces are characterized.

New method improves conditional covariance estimation using targeted groups of assets.

Classifies scalar second-order PDEs with low-dimensional symmetry groups.

New method handles correlated responses and interaction effects in multi-response regression.

Choosing a reference group in Oaxaca-Blinder decomposition can reverse conclusions.

We sketch our recent application of a non-commutative version of the Cartan `moving-frame' formalism to the quantum Euclidean space $R^N_q$, the space which is covariant under the action of the quantum group $SO_q(N)$. For each of the two covariant differential calculi over $R^N_q$ based on the $R$-matrix formalism, we…

This paper considers the problem of estimating multiple related Gaussian graphical models from a $p$-dimensional dataset consisting of different classes. Our work is based upon the formulation of this problem as group graphical lasso. This paper proposes a novel hybrid covariance thresholding algorithm that can effecti…

We show that there is an infinite group of special automorphisms of the deformed group of diffeomorphisms, which describes parallel transports in Riemannian spaces of any variable curvature. Generators of translations of such group contain covariant derivatives, and structure functions - the curvature tensor.

Generalizes underlap coefficient for multivariate group separation.

Chronos-2 forecasts multivariate and covariate data without task-specific training.

GWIB improves counterfactual regression by balancing latent distributions and reducing selection bias.

Kandinsky conformal prediction expands conditional coverage guarantees.

We construct a covariant functor from a category of Abelian principal bundles over globally hyperbolic spacetimes to a category of *-algebras that describes quantized principal connections. We work within an appropriate differential geometric setting by using the bundle of connections and we study the full gauge group,…

A new method estimates treatment effects without strong assumptions.

Study of generalized vector bundles and their geometric tools.

Bayesian method models binary response and covariates for two groups, estimating causal relationships.

Flexible Cox model for time-dependent covariates with complex sparsity patterns.

The study examines fairness metrics in noisy covariate settings, providing theoretical guarantees.

Building on the universal covering group of the general linear group, we introduce the composite spinor bundle whose subbundles are Lorentz spin structures associated with different gravitational fields. General covariant transformations of this composite spinor bundle are canonically defined.

In the absence of unobserved confounders, matching and weighting methods are widely used to estimate causal quantities including the Average Treatment Effect on the Treated (ATT). Unfortunately, these methods do not necessarily achieve their goal of making the multivariate distribution of covariates for the control gro…

We consider the problem of predicting several response variables using the same set of explanatory variables. This setting naturally induces a group structure over the coefficient matrix, in which every explanatory variable corresponds to a set of related coefficients. Most of the existing methods that utilize this gro…

Generalizes underlap coefficient for multivariate group separation.

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 …

In this paper, we describe the group SpinT (n) and give some properties of this group. We construct SpinT spinor bundle S by means of the spinor representation of the group SpinT (n) and define covariant derivative operator and Dirac operator on S. Finally, Schrodinger-Lichnerowicz-type formula is derived by using thes…

Recent results in coupled or temporal graphical models offer schemes for estimating the relationship structure between features when the data come from related (but distinct) longitudinal sources. A novel application of these ideas is for analyzing group-level differences, i.e., in identifying if trends of estimated ob…

Class lecture notes at a beginning graduate level on the mathematical background needed to understand classical gauge theory. Covers group actions, fiber bundles, principal bundles, connections, gauge transformations, parallel transport, curvature, covariant derivatives, pseudo-riemannian manifolds, lagrangians, cliffo…

Proves stability of Minkowski space-time for Einstein-Yang-Mills equations.

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…

New method measures treatment effects across different groups.

Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce lower dimensional tensors --generalizing to one side Kaluza-Klein gauge fields and…