Related papers: A Dual Geometric Test for Forward-Flatness

In many applied sciences a popular analysis strategy for high-dimensional data is to fit many multivariate generalized linear models in parallel. This paper presents a novel approach to address the resulting multiple testing problem by…

In this paper we propose a new test of heteroscedasticity for parametric regression models and partial linear regression models in high dimensional settings. When the dimension of covariates is large, existing tests of heteroscedasticity…

This paper presents a test for wide-sense stationarity (WSS) based on the geometry of the covariance function. We estimate local patches of the covariance surface and then check whether the directional derivative in the $(1,1,0)$ direction…

Recently, there has been a growing interest in the problem of learning rich implicit models - those from which we can sample, but can not evaluate their density. These models apply some parametric function, such as a deep network, to a base…

In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…

The field of causal discovery develops model selection methods to infer cause-effect relations among a set of random variables. For this purpose, different modelling assumptions have been proposed to render cause-effect relations…

Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random processes in geostatistical data. For second-order stationary processes, there exist subclasses of covariance functions that…

A key challenge in building theoretical foundations for deep learning is the complex optimization dynamics of neural networks, resulting from the high-dimensional interactions between the large number of network parameters. Such non-trivial…

The inference of deep hierarchical models is problematic due to strong dependencies between the hierarchies. We investigate a specific transformation of the model parameters based on the multivariate distributional transform. This…

We provide an implementation to compute the flat metric in any dimension. The flat metric, also called dual bounded Lipschitz distance, generalizes the well-known Wasserstein distance $W_1$ to the case that the distributions are of unequal…

Post-data statistical inference concerns making probability statements about model parameters conditional on observed data. When a priori knowledge about parameters is available, post-data inference can be conveniently made from Bayesian…

Large Reasoning Models have demonstrated remarkable performance with the advancement of test-time scaling techniques, which enhances prediction accuracy by generating multiple candidate responses and selecting the most reliable answer.…

We explore fairness from a statistical perspective by selectively utilizing either conditional distance covariance or distance covariance statistics as measures to assess the independence between predictions and sensitive attributes. We…

We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in…

This work proposes a novel procedure to test for common structures across two high-dimensional factor models. The introduced test allows to uncover whether two factor models are driven by the same loading matrix up to some linear…

The well-known generalization problem hinders the application of artificial neural networks in continuous-time prediction tasks with varying latent dynamics. In sharp contrast, biological systems can neatly adapt to evolving environments…

Hessian based measures of flatness, such as the trace, Frobenius and spectral norms, have been argued, used and shown to relate to generalisation. In this paper we demonstrate that for feed forward neural networks under the cross entropy…

The past few years have witnessed a remarkable crossover of string theoretical ideas from the abstract world of geometrical forms to the concrete experimental realm of condensed matter physics. The basis for this --- variously known as…

Continuous and strictly positive data that exhibit skewness and outliers frequently arise in many applied disciplines. Log-symmetric distributions provide a flexible framework for modeling such data. In this article, we develop new…

We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy…