Related papers: A Dual Geometric Test for Forward-Flatness
Rapid progress in representation learning has led to a proliferation of embedding models, and to associated challenges of model selection and practical application. It is non-trivial to assess a model's generalizability to new, candidate…
The objective of goodness-of-fit testing is to assess whether a dataset of observations is likely to have been drawn from a candidate probability distribution. This paper presents a rank-based family of goodness-of-fit tests that is…
We propose a method to determine the smoothness of sufficiently flat solutions of one phase Hele-Shaw problems. The novelty is the observation that under a flatness assumption the free boundary --represented by the hodograph transform of…
Stability and convergence of full discretizations of various surface evolution equations are studied in this paper. The proposed discretization combines a higher-order evolving-surface finite element method (ESFEM) for space discretization…
This paper deals with two-sample tests for functional time series data, which have become widely available in conjunction with the advent of modern complex observation systems. Here, particular interest is in evaluating whether two sets of…
We propose a class of nonparametric two-sample tests with a cost linear in the sample size. Two tests are given, both based on an ensemble of distances between analytic functions representing each of the distributions. The first test uses…
We study the problem of conditional two-sample testing, which aims to determine whether two populations have the same distribution after accounting for confounding factors. This problem commonly arises in various applications, such as…
We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…
Reliable state estimation depends on accurately modeled noise covariances, which are difficult to determine in practice. This paper formulates the noise covariance estimation as a bilevel optimization problem that factorizes the joint…
In this paper, we prove that the dynamical model of a quadrotor subject to linear rotor drag effects is differentially flat in its position and heading. We use this property to compute feed-forward control terms directly from a reference…
We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate…
Modern statistical learning theory and deep learning characterize generalization primarily in terms of continuous capacity control (e.g., norm-based regularization, margin maximization, low-rank bias). While highly successful in continuous…
Latent variable models are popularly used to measure latent factors (e.g., abilities and personalities) from large-scale assessment data. Beyond understanding these latent factors, the covariate effect on responses controlling for latent…
With growing capabilities of large language models, prompting them has become the dominant way to access them. This has motivated the development of strategies for automatically selecting effective language prompts. In this paper, we…
Data depth provides a centre-outward ordering for multivariate data. Recently, some univariate GoF tests based on data depth have been studied by Li (2018). This paper discusses some univariate goodness of fit tests based on centre-outward…
This paper proposes a novel two-step strategy for testing the goodness-of-fit of parametric regression models in ultra-high dimensional sparse settings, where the predictor dimension far exceeds the sample size. This regime usually renders…
Using the fact that some depth functions characterize certain family of distribution functions, and under some mild conditions, distribution of the depth is continuous, we have constructed several new multivariate goodness of fit tests…
We present a new stability and error analysis of fully discrete approximation schemes for the transient Stokes equation. For the spatial discretization, we consider a wide class of Galerkin finite element methods which includes both inf-sup…
This paper revisits the classical notion of sampling in the setting of real-time temporal logics for the modeling and analysis of systems. The relationship between the satisfiability of Metric Temporal Logic (MTL) formulas over…
Using the properties of differential flatness, a controllable system, such as a quadcoper model, may be transformed into a linear equivalent system via a coordinate change and an input mapping. This is a straightforward advantage for the…