Bayesian method improves clinical trial efficiency.
problem Increase treatment effect estimates in clinical trials.
method Combines prognostic covariate adjustment with a Bayesian framework.
result Substantial increase in statistical power with controlled type I error.
Identifying statistical dependence between the features and the label is a fundamental problem in supervised learning. This paper presents a framework for estimating dependence between numerical features and a categorical label using generalized Gini distance, an energy distance in reproducing kernel Hilbert spaces (RK…
The paper shows objective derivatives are covariant derivatives on Riemannian metrics.
problem The definition and interpretation of objective derivatives in continuum mechanics.
method Demonstrates that objective derivatives correspond to covariant derivatives on the manifold of Riemannian metrics.
result Objective derivatives are unified as covariant derivatives on the manifold of Riemannian metrics.
Energy trees handle complex data structures with multiple variable types.
problem Handling intricate data structures with various types of covariates.
method Energy trees, a regression and classification model, use energy statistics to accommodate structured covariates of different types.
result Energy trees maintain statistical foundations, interpretability, and robustness to overfitting.
Many modern statistical applications ask for the estimation of a covariance (or precision) matrix in settings where the number of variables is larger than the number of observations. There exists a broad class of ridge-type estimators that employs regularization to cope with the subsequent singularity of the sample cov…
We revisit the Lichnerowicz-York method, and an alternative method of York, in order to obtain some conformally covariant systems. This type of parameterization is certainly more natural for non constant mean curvature initial data.
We propose a nonparametric test of independence, termed optHSIC, between a covariate and a right-censored lifetime. Because the presence of censoring creates a challenge in applying the standard permutation-based testing approaches, we use optimal transport to transform the censored dataset into an uncensored one, whil…
CovRegRF estimates covariance matrix from covariates using random forests.
problem Estimating conditional covariances or correlations among multivariate responses.
method Random forest trees with a custom splitting rule to maximize covariance difference.
result Accurate covariance matrix estimates and controlled Type-1 error.
The aim of this work is to build financial crisis indicators based on spectral properties of the dynamics of market data. After choosing an optimal size for a rolling window, the historical market data in this window is seen every trading day as a random matrix from which a covariance and a correlation matrix are obtai…
We consider the class of locally boost isotropic spacetimes in arbitrary dimension. For any spacetime with boost isotropy, the corresponding curvature tensor and all of its covariant derivatives must be simultaneously of alignment type D relative to some common null frame. Such spacetimes are known as type ${\b…
The paper examines extreme value statistics of high-dimensional sample covariances, with applications in finance and image analysis.
problem Statistical validation of normal conditions in high-dimensional time series data.
method Generalizes the maximal deviation of sample autocovariances to high dimensions and applies Gumbel-type extreme value asymptotics.
result Gumbel-type extreme value asymptotics holds true for high-dimensional sample covariances.
Machine learning boosts RCT efficiency by controlling type I error and improving statistical power.
problem Improving statistical efficiency in RCTs with complex covariate adjustments.
method Machine learning-assisted adjustment under Rosenbaum's framework for exact tests.
result The proposed method robustly controls type I error and significantly boosts statistical efficiency.
Optimizes clustering in Gaussian mixtures with varying covariance matrices.
problem Clustering with anisotropic Gaussian mixture models where covariance matrices vary.
method Proposes a computationally feasible hard EM type algorithm.
result Achieves optimal clustering rate with few iterations.
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.
New method for estimating covariance with robustness to outliers.
problem Estimating covariance from noisy data with outliers.
method Cross-fitted clipped covariance estimator with computable Bernstein certificates.
result The method balances certified stochastic error and robust hold-out proxy for clipping bias.
The paper explores how multiway data from PDEs can be accurately tracked using EnKF with specific covariance and precision estimators.
problem Tracking sparse and multiway structures in dynamical processes governed by PDEs.
method Examined several multiway covariance and precision matrix estimators in the context of physics-driven forecasting and EnKF.
result Multiway data from Poisson and convection-diffusion PDEs can be accurately tracked using EnKF with appropriate estimators.
We consider the estimation of integrated covariance (ICV) matrices of high dimensional diffusion processes based on high frequency observations. We start by studying the most commonly used estimator, the realized covariance (RCV) matrix. We show that in the high dimensional case when the dimension p and the observati…
A latent force model is a Gaussian process with a covariance function inspired by a differential operator. Such covariance function is obtained by performing convolution integrals between Green's functions associated to the differential operators, and covariance functions associated to latent functions. In the classica…
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.
Two new regularization methods improve neural network performance and complexity control.
problem Improving neural network performance and complexity control with correlated or high-dimensional features.
method Two regularization strategies: covariance-aware ridge and covariance-aware lasso.
result Improves predictive performance and complexity control over standard penalties.
Network-assisted regression uses conformal prediction for valid inference.
problem Predicting node attributes using network and conventional covariates with valid statistical inference.
method Network analog of conformal prediction under mild joint exchangeability assumption.
result Achieves finite sample validity and asymptotic conditional validity for various network covariates.
We give coordinate formula and geometric description of the curvature of the tensor product connection of linear connections on vector bundles with the same base manifold. We define the covariant differential of geometric fields of certain types with respect to a pair of a linear connection on a vector bundle and a lin…
High precision analytical approximation is proposed for variance-covariance based risk allocation in a portfolio of risky assets. A general case of a single-period multi-factor Merton-type model with stochastic recovery is considered. The accuracy of the approximation as well as its speed are compared to and shown to b…
The n-th order covariant derivative on a smooth manifold with an affine connection is a differential operator which turns a function into a tensor field of type (0,n). In this paper the properties of this operatior related to the permutation of indices are investigated by means of non-associative algebra. The general f…
Study improves Cox model for predicting stock trading signs using Japanese market data.
problem Improving Cox model for predicting stock trading signs using Japanese market data.
method Added new covariates and used high-frequency trading data for 222 Nikkei 225 stocks.
result Cox-type model performs well in Japanese market and identifies key factors for accurate estimation.
New model identifies cell-specific genes for cancer prognosis.
problem No statistical model to integrate multiscale cancer data.
method Bayesian generalized promotion time cure models (GPTCMs).
result Improves cancer prognosis by identifying cell-specific genes.
Develops a reduction theory for covariant field theories with gauge symmetries.
problem Handling gauge symmetries in covariant field theories.
method Utilizes generalized principal connections and fiberwise action of Lie groups.
result Relates vertical reduced equations to the Noether theorem.
There has been a lot of work fitting Ising models to multivariate binary data in order to understand the conditional dependency relationships between the variables. However, additional covariates are frequently recorded together with the binary data, and may influence the dependence relationships. Motivated by such a d…
We present a family of four-dimensional Lorentzian manifolds whose invariant classification requires the seventh covariant derivative of the curvature tensor. The spacetimes in questions are null radiation, type N solutions on an anti-de Sitter background. The large order of the bound is due to the fact that these spac…
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 D is a key finding, generalizing the well-known operator from principal bundles. This work develops a model to distinguish network and covariate information.
problem Identifying unique network and covariate information.
method Low-rank model with two-step estimation: spectral method followed by refinement.
result The method accurately recovers joint and individual components.
This study evaluates cluster search algorithms using Gaussian mixture models.
problem Determining the optimal number of clusters in data sets generated by Gaussian mixture models.
method Examined centroid- and model-based cluster search algorithms in various cases.
result Model-based algorithms are more robust to cluster overlap and covariance type than centroid-based methods.
New methods improve inference after prediction without strong model assumptions.
problem Improper inference after prediction can lead to invalid results.
method Angelopoulos et al. (2023) and Wang et al. (2020) propose corrections to inference.
result Angelopoulos et al. method controls type 1 error and provides correct coverage.
Model predicts operational risk using HMMs with economic covariates.
problem Predicting operational risk losses with time-dependent structures and economic covariates.
method Hidden Markov Models extended to multivariate observations with an auxiliary economic variable.
result Calibration results show relevance of including economic covariates.
Longitudinal study designs are indispensable for studying disease progression. Inferring covariate effects from longitudinal data, however, requires interpretable methods that can model complicated covariance structures and detect nonlinear effects of both categorical and continuous covariates, as well as their interac…
Bayesian neural networks improve cancer dynamics prediction.
problem Predicting cancer dynamics under treatment due to heterogeneity and sparse data.
method Hierarchical Bayesian model using baseline covariates and Bayesian neural networks for nonlinear interactions.
result Bayesian neural networks outperform linear models in predicting cancer dynamics with interactions.
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.
Study on Ricci solitons and related metrics in 3D trans-Sasakian manifolds.
problem Exploring metrics like Ricci solitons in 3D trans-Sasakian manifolds.
method Analyzing properties of metrics and structure functions in 3D trans-Sasakian manifolds.
result Characterization of Ricci solitons and scalar curvature in 3D trans-Sasakian manifolds.
Unified analysis of kernel-based methods under covariate shift.
problem Covariate shift in learning problems.
method Unified analysis of nonparametric methods in RKHS.
result Sharp convergence rates for general loss functions.
We investigate the triviality of compact Ricci solitons under general scalar conditions involving the Weyl tensor. More precisely, we show that a compact Ricci soliton is Einstein if a generic linear combination of divergences of the Weyl tensor contracted with suitable covariant derivatives of the potential function v…
A new method identifies class-specific covariates in multi-class prediction tasks.
problem Identifying covariates specifically associated with one or more outcome classes in multi-class prediction tasks.
method Introducing multi forests (MuFs) with multi-way and binary splits to measure class-associated discriminatory ability.
result The multi-class VIM specifically ranks class-associated covariates highly, unlike conventional VIMs.
Missing data estimation is an important challenge with high-dimensional data arranged in the form of a matrix. Typically this data matrix is transposable, meaning that either the rows, columns or both can be treated as features. To model transposable data, we present a modification of the matrix-variate normal, the mea…
The paper refines classical covariance asymptotics using geometric information geometry.
problem Deviation of finite-sample behavior from classical predictions in curved models.
method Develops a curvature-aware refinement by viewing parametric families as Riemannian manifolds with Fisher-Rao metric.
result Derives an \(n^{-2}\) correction to the leading \(n^{-1}I(θ)^{-1}\) covariance term for score-root estimators.
Certain momentum-dependent terms in the fermion sector of the Lorentz-violating Standard Model Extension (SME) yield solvable classical lagrangians of a type not mentioned in the literature. These cases yield new relatively simple examples of Finsler and pseudo-Finsler structures. One of the cases involves antisymmetri…
Estimates linear model from noisy covariates and instruments using spectral regularization.
problem Estimating a linear model from many noisy covariates and instruments.
method Two-stage least squares with spectral regularization of canonical correlations.
result Upper and lower bounds on estimation error, proving optimality of the method with noisy data.
A new classification rule for FDA improves classification performance by accounting for unequal covariance matrices.
problem Unequal covariance matrices in practical situations affect the performance of FDA and its variants.
method Proposes a novel classification rule for FDA that accounts for unequal covariance matrices, applicable to many FDA variants.
result The new classification rule improves classification performance compared to original FDA and variants.
Paper shows how Non-Abelian T-duality solves pure spinor equations in supersymmetric vacua.
problem Preserving N=1 supersymmetry in Type II supergravity requires specific pure spinor equations. method Demonstrates that Non-Abelian T-duality (NATD) is a solution generating transformation for these pure spinor equations, showing covariance under Pin(d,d) transformations. result Non-Abelian T-duality (NATD) generates a flux that matches the geometric flux associated with the isometry group.
Adaptive Prespecification improves precision in randomized trials.
problem Selecting optimal covariates for precision in randomized trials.
method Adaptive Prespecification using V-fold cross-validation and influence curve-squared loss function.
result Substantial gains in precision, equivalent to 20-43% reductions in sample size for the same power.