arXiv subjects

Niels Hagenbuch

Publications and source records attributed to Niels Hagenbuch.

3 recordsLinked to original sources

arXiv2026

Bernoulli amputation

A novel, stochastic approach to amputation, the process of introducing missing values to a complete dataset, is presented. It allows one to construct a wide variety of missingness patterns by only having to specify distributions of missingness indicators as opposed to specifying each missingness pattern manually. Missingness indicators are modeled in a principled way via copulas and Bernoulli margins, thus allowing one to incorporate dependence in missingness patterns. Besides more classical missingness mechanisms such as missing completely at random, missing at random, and missing not at random, the approach is able to model structured missingness such as block missingness and, via mixtures, monotone missingness, which are patterns of missing data frequently found in real-life datasets. Properties such as joint missingness probabilities or missingness correlation are derived mathematically. The flexibility of the approach in capturing different missingness patterns while only requiring to specify distributional assumptions on missingness indicators is demonstrated with mathematical examples and empirical illustrations in terms of a well-known example dataset of sufficiently small sample size that allows to identify each missing data point visually. Finally, an example application to multivariate financial time series is provided.

stat.AP↗

arXiv2023

A Complete Characterisation of Structured Missingness

Our capacity to process large complex data sources is ever-increasing, providing us with new, important applied research questions to address, such as how to handle missing values in large-scale databases. Mitra et al. (2023) noted the phenomenon of Structured Missingness (SM), which is where missingness has an underlying structure. Existing taxonomies for defining missingness mechanisms typically assume that variables' missingness indicator vectors $M_1$, $M_2$, ..., $M_p$ are independent after conditioning on the relevant portion of the data matrix $\mathbf{X}$. As this is often unsuitable for characterising SM in multivariate settings, we introduce a taxonomy for SM, where each ${M}_j$ can depend on $\mathbf{M}_{-j}$ (i.e., all missingness indicator vectors except ${M}_j$), in addition to $\mathbf{X}$. We embed this new framework within the well-established decomposition of mechanisms into MCAR, MAR, and MNAR (Rubin, 1976), allowing us to recast mechanisms into a broader setting, where we can consider the combined effect of $\mathbf{X}$ and $\mathbf{M}_{-j}$ on ${M}_j$. We also demonstrate, via simulations, the impact of SM on inference and prediction, and consider contextual instances of SM arising in a de-identified nationwide (US-based) clinico-genomic database (CGDB). We hope to stimulate interest in SM, and encourage timely research into this phenomenon.

stat.ME↗

arXiv2023

Learning from data with structured missingness

Missing data are an unavoidable complication in many machine learning tasks. When data are `missing at random' there exist a range of tools and techniques to deal with the issue. However, as machine learning studies become more ambitious, and seek to learn from ever-larger volumes of heterogeneous data, an increasingly encountered problem arises in which missing values exhibit an association or structure, either explicitly or implicitly. Such `structured missingness' raises a range of challenges that have not yet been systematically addressed, and presents a fundamental hindrance to machine learning at scale. Here, we outline the current literature and propose a set of grand challenges in learning from data with structured missingness.

stat.ML↗