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Imputation and propensity score weighting are two popular techniques for handling missing data. We address these problems using the regularized M-estimation techniques in the reproducing kernel Hilbert space. Specifically, we first use the…
Sum of Ranking Differences (SRD) is a relatively novel, non-para-metric statistical procedure that has become increasingly popular recently. SRD compares solutions via a reference by applying a rank transformation on the input and…
We introduce kernel thinning, a new procedure for compressing a distribution $\mathbb{P}$ more effectively than i.i.d. sampling or standard thinning. Given a suitable reproducing kernel $\mathbf{k}_{\star}$ and $O(n^2)$ time, kernel…
We describe the \proglang{R} package \pkg{glmmrBase} and an extension \pkg{glmmrOptim}. \pkg{glmmrBase} provides a flexible approach to specifying, fitting, and analysing generalised linear mixed models. We use an object-orientated class…
We propose a kernel-based nonparametric test of relative goodness of fit, where the goal is to compare two models, both of which may have unobserved latent variables, such that the marginal distribution of the observed variables is…
In the last decade, developments in tropical geometry have provided a number of uses directly applicable to problems in statistical learning. The TML package is the first R package which contains a comprehensive set of tools and methods…
Several emerging post-Bayesian methods target a probability distribution for which an entropy-regularised variational objective is minimised. This increased flexibility introduces a computational challenge, as one loses access to an…
We provide uniform confidence bands for kernel ridge regression (KRR), a widely used nonparametric regression estimator for nonstandard data such as preferences, sequences, and graphs. Despite the prevalence of these data--e.g., student…
We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and…
The continually increasing number of complex datasets each year necessitates ever improving machine learning methods for robust and accurate categorization of these data. This paper introduces Random Multimodel Deep Learning (RMDL): a new…
Determinantal Point Process (DPPs) are statistical models for repulsive point patterns. Both sampling and inference are tractable for DPPs, a rare feature among models with negative dependence that explains their popularity in machine…
Marginal maximum likelihood estimation (MMLE) in item response theory (IRT) is highly sensitive to aberrant responses, such as careless answering and random guessing, which can reduce estimation accuracy. To address this issue, this study…
Robust statistics aims to compute quantities to represent data where a fraction of it may be arbitrarily corrupted. The most essential statistic is the mean, and in recent years, there has been a flurry of theoretical advancement for…
We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical…
Bias evaluation is fundamental to trustworthy AI, both in terms of checking data quality and in terms of checking the outputs of AI systems. In testing data quality, for example, one may study the distance of a given dataset, viewed as a…
Manifold data analysis is challenging due to the lack of parametric distributions on manifolds. To address this, we introduce a series of Riemannian radial distributions on Riemannian symmetric spaces. By utilizing the symmetry, we show…
This paper presents an R package to handle and represent measurements with errors in a very simple way. We briefly introduce the main concepts of metrology and propagation of uncertainty, and discuss related R packages. Building upon this,…
This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of…
The availability of precise and accurate simulation is a limiting factor for interpreting and forecasting data in many fields of science and engineering. Often, one or more distinct simulation software applications are developed, each with…
This article describes the R package varrank. It has a flexible implementation of heuristic approaches which perform variable ranking based on mutual information. The package is particularly suitable for exploring multivariate datasets…