Related papers: Identifiability in penalized function-on-function …

It is well known that nonparametric regression estimation and inference procedures are subject to the curse of dimensionality. Moreover, model interpretability usually decreases with the data dimension. Therefore, model-free variable…

In this paper, we tackle a critical issue in nonparametric inference for systems of interacting particles on Riemannian manifolds: the identifiability of the interaction functions. Specifically, we define the function spaces on which the…

Performative prediction is an emerging paradigm in machine learning that addresses scenarios where the model's prediction may induce a shift in the distribution of the data it aims to predict. Current works in this field often rely on…

This paper addresses intervention-based causal representation learning (CRL) under a general nonparametric latent causal model and an unknown transformation that maps the latent variables to the observed variables. Linear and general…

Many imputation methods are based on statistical models that assume that the variable of interest is a noisy observation of a function of the auxiliary variables or covariates. Misspecification of this model may lead to severe errors in…

We consider a spatial functional linear regression, where a scalar response is related to a square integrable spatial functional process. We use a smoothing spline estimator for the functional slope parameter and establish a finite sample…

Regularization methods allow one to handle a variety of inferential problems where there are more covariates than cases. This allows one to consider a potentially enormous number of covariates for a problem. We exploit the power of these…

Collinearity and near-collinearity of predictors cause difficulties when doing regression. In these cases, variable selection becomes untenable because of mathematical issues concerning the existence and numerical stability of the…

Identifiability concerns finding which unknown parameters of a model can be quantified from given input-output data. Many linear ODE models, used in systems biology and pharmacokinetics, are unidentifiable, which means that parameters can…

This paper presents tests to formally choose between regression models using different derivatives of a functional covariate in scalar-on-function regression. We demonstrate that for linear regression, models using different derivatives can…

Statistical latent class models are widely used in social and psychological researches, yet it is often difficult to establish the identifiability of the model parameters. In this paper we consider the identifiability issue of a family of…

Choosing a suitable model and determining its associated parameters from fitting to experimental data is fundamental for many problems in biomechanics. Models of shear-thinning complex fluids, dating from the work of Bird, Carreau, Cross…

We propose a roughness regularization approach in making nonparametric inference for generalized functional linear models. In a reproducing kernel Hilbert space framework, we construct asymptotically valid confidence intervals for…

We propose a framework for the assessment of uncertainty quantification in deep regression. The framework is based on regression problems where the regression function is a linear combination of nonlinear functions. Basically, any level of…

Although neural networks are powerful function approximators, the underlying modelling assumptions ultimately define the likelihood and thus the hypothesis class they are parameterizing. In classification, these assumptions are minimal as…

This paper studies a regression model with functional dependent and explanatory variables, both of which exhibit nonstationary dynamics. The model assumes that the nonstationary stochastic trends of the dependent variable are explained by…

This paper addresses the problem of providing robust estimators under a functional logistic regression model. Logistic regression is a popular tool in classification problems with two populations. As in functional linear regression,…

Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…

Structural identifiability is a property of a differential model with parameters that allows for the parameters to be determined from the model equations in the absence of noise. The method of input-output equations is one method for…

We introduce a fine-grained framework for uncertainty quantification of predictive models under distributional shifts. This framework distinguishes the shift in covariate distributions from that in the conditional relationship between the…