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We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…

In modelling time series data coming from different sources, frequencies can easily vary since some variable can be measured at higher frequencies, others, at lower frequencies. Given data measured over spatial units and at varying…

Incorporating nonlinearity into quantum machine learning is essential for learning a complicated input-output mapping. We here propose quantum algorithms for nonlinear regression, where nonlinearity is introduced with feature maps when…

Motivated by normalizing DNA microarray data and by predicting the interest rates, we explore nonparametric estimation of additive models with highly correlated covariates. We introduce two novel approaches for estimating the additive…

This paper introduces a novel nonparametric framework for data imputation, coined multilinear kernel regression and imputation via the manifold assumption (MultiL-KRIM). Motivated by manifold learning, MultiL-KRIM models data features as a…

This paper studies a \textit{partial functional partially linear single-index model} that consists of a functional linear component as well as a linear single-index component. This model generalizes many well-known existing models and is…

Quantile regression is a powerful tool capable of offering a richer view of the data as compared to least-squares regression. Quantile regression is typically performed individually on a few quantiles or a grid of quantiles without…

We propose a nonparametric bivariate time-varying coefficient model for longitudinal measurements with the occurrence of a terminal event that is subject to right censoring. The time-varying coefficients capture the longitudinal…

The kernel smoothing with large bandwidth values causes oversmoothing or underfitting in general. However, when irrelevant variables are included, the corresponding large bandwidth values are known to have an effect of shrinking them. This…

Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…

We consider efficient estimation of the Euclidean parameters in a generalized partially linear additive models for longitudinal/clustered data when multiple covariates need to be modeled nonparametrically, and propose an estimation…

Inspired by the complexity of certain real-world datasets, this article introduces a novel flexible linear spline index regression model. The model posits piecewise linear effects of an index on the response, with continuous changes…

This paper provides new uniform rate results for kernel estimators of absolutely regular stationary processes that are uniform in the bandwidth and in infinite-dimensional classes of dependent variables and regressors. Our results are…

Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…

The use of kernels for nonlinear prediction is widespread in machine learning. They have been popularized in support vector machines and used in kernel ridge regression, amongst others. Kernel methods share three aspects. First, instead of…

Semi-structured networks (SSNs) merge the structures familiar from additive models with deep neural networks, allowing the modeling of interpretable partial feature effects while capturing higher-order non-linearities at the same time. A…

We suggest two nonparametric approaches, based on kernel methods and orthogonal series to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems, we derive optimal convergence…

We propose a set of kernel-based tools to evaluate the designs and tune the hyperparameters of conditional sequence models, with a focus on problems in computational biology. The backbone of our tools is a new measure of discrepancy between…

We consider the problem of estimating an additive regression function in an inverse regres- sion model with a convolution type operator. A smooth backfitting procedure is developed and asymptotic normality of the resulting estimator is…

In some real world applications, such as spectrometry, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of…