Related papers: Statistical inference using Regularized M-estimati…
Deep neural networks excel in high-dimensional problems, outperforming models such as kernel methods, which suffer from the curse of dimensionality. However, the theoretical foundations of this success remain poorly understood. We follow…
Missing data represents a fundamental challenge in machine learning applications, often reducing model performance and reliability. This problem is particularly acute in fields like bioinformatics and clinical machine learning, where…
Current meta-learning approaches focus on learning functional representations of relationships between variables, i.e. on estimating conditional expectations in regression. In many applications, however, we are faced with conditional…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…
Dealing with missing data is an important problem in statistical analysis that is often addressed with imputation procedures. The performance and validity of such methods are of great importance for their application in empirical studies.…
Quantitative measurements produced by mass spectrometry proteomics experiments offer a direct way to explore the role of proteins in molecular mechanisms. However, analysis of such data is challenging due to the large proportion of missing…
It is well known that kernel ridge regression (KRR) is a popular nonparametric regression estimator. Nonetheless, in the presence of a large data set with size $n\gg 1,$ the KRR estimator has the drawback to require an intensive…
We study optimal procedures for estimating a linear functional based on observational data. In many problems of this kind, a widely used assumption is strict overlap, i.e., uniform boundedness of the importance ratio, which measures how…
We propose a novel procedure for estimating and conducting inference on average marginal effects in partially linear instrumental regressions using Reproducing Kernel Hilbert Space methods. Our procedure relies on a single regularization…
Classical semiparametric inference with missing outcome data is not robust to contamination of the observed data and a single observation can have arbitrarily large influence on estimation of a parameter of interest. This sensitivity is…
Multiple imputation (MI) has become popular for analyses with missing data in medical research. The standard implementation of MI is based on the assumption of data being missing at random (MAR). However, for missing data generated by…
We investigate regularized algorithms combining with projection for least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space. We prove convergence results with respect…
This work constructs a hypothesis test for detecting whether an data-generating function $h: R^p \rightarrow R$ belongs to a specific reproducing kernel Hilbert space $\mathcal{H}_0$ , where the structure of $\mathcal{H}_0$ is only…
A common problem faced by statistical institutes is that data may be missing from collected data sets. The typical way to overcome this problem is to impute the missing data. The problem of imputing missing data is complicated by the fact…
Imputing missing values is an important preprocessing step in data analysis, but the literature offers little guidance on how to choose between different imputation models. This letter suggests adopting the imputation model that generates a…
We consider the problem of estimating a meta-model of an unknown regression model with non-Gaussian and non-bounded error. The meta-model belongs to a reproducing kernel Hilbert space constructed as a direct sum of Hilbert spaces leading to…
Matrix completion and extrapolation (MCEX) are dealt with here over reproducing kernel Hilbert spaces (RKHSs) in order to account for prior information present in the available data. Aiming at a faster and low-complexity solver, the task is…
Ridge regression (RR) is a regularization technique that penalizes the L2-norm of the coefficients in linear regression. One of the challenges of using RR is the need to set a hyperparameter ($\alpha$) that controls the amount of…
We develop semiparametrically efficient inference for kernel measures of noise heterogeneity in additive noise models. In many applications, the regression function is estimated using flexible machine learning methods. Downstream procedures…