arXiv subjects

Jonathan Wells

Publications and source records attributed to Jonathan Wells.

3 recordsLinked to original sources

arXiv2025

HI-PMK: A Data-Dependent Kernel for Incomplete Heterogeneous Data Representation

Handling incomplete and heterogeneous data remains a central challenge in real-world machine learning, where missing values may follow complex mechanisms (MCAR, MAR, MNAR) and features can be of mixed types (numerical and categorical). Existing methods often rely on imputation, which may introduce bias or privacy risks, or fail to jointly address data heterogeneity and structured missingness. We propose the \textbf{H}eterogeneous \textbf{I}ncomplete \textbf{P}robability \textbf{M}ass \textbf{K}ernel (\textbf{HI-PMK}), a novel data-dependent representation learning approach that eliminates the need for imputation. HI-PMK introduces two key innovations: (1) a probability mass-based dissimilarity measure that adapts to local data distributions across heterogeneous features (numerical, ordinal, nominal), and (2) a missingness-aware uncertainty strategy (MaxU) that conservatively handles all three missingness mechanisms by assigning maximal plausible dissimilarity to unobserved entries. Our approach is privacy-preserving, scalable, and readily applicable to downstream tasks such as classification and clustering. Extensive experiments on over 15 benchmark datasets demonstrate that HI-PMK consistently outperforms traditional imputation-based pipelines and kernel methods across a wide range of missing data settings. Code is available at: https://github.com/echoid/Incomplete-Heter-Kernel

cs.LG↗

arXiv2024

Comparing multilevel and fixed effect approaches in the generalized linear model setting

We extend prior work comparing linear multilevel models (MLM) and fixed effect (FE) models to the generalized linear model (GLM) setting, where the coefficient on a treatment variable is of primary interest. This leads to three insights. (i) First, as in the linear setting, MLM can be thought of as a regularized form of FE (RegFE). This explains why group-level confounding can greatly bias MLM's treatment coefficient estimates. However, unlike the linear setting, there is not an exact equivalence between MLM and RegFE in GLMs. (ii) Second, we study a generalization of "bias-corrected MLM" (bcMLM) to the GLM setting, and a corresponding "bias-corrected RegFE" (bcRegFE). None of FE, bcMLM, or bcRegFE entirely solve MLM's bias problem in GLMs, but bcMLM and bcRegFE tend to show less bias than does FE. (iii) Third, as in the linear setting, MLM's default standard errors can misspecify the true intragroup dependence structure in the GLM setting, which can yield downwardly biased standard errors. A cluster bootstrap is a more agnostic alternative. We also consider a cluster-robust standard error for (bc)RegFE. Ultimately, for non-linear GLMs, we recommend bcMLM for estimating the treatment coefficient, and a cluster bootstrap for standard errors and confidence intervals. If a bootstrap is not computationally feasible, then we recommend bcRegFE with cluster-robust standard errors, or FE with cluster-robust standard errors when group sizes are larger.

stat.ME↗

arXiv2020

Modelling a novel Coronavirus (COVID-19): A stochastic SEIR-HCD approach, with real-time parameter estimation & forecasting for Scotland

Faced with the 2020 SARS-CoV2 epidemic, public health officials have been seeking models that could be used to predict not only the number of new cases but also the levels of hospitalisation, critical care and deaths. In this paper we present a stochastic compartmental model capable of real-time monitoring and forecasting of the pandemic incorporating multiple streams of real-world data, reported cases, testing intensity, deaths, hospitalisations and critical care occupancy. Model parameters are estimated via a Bayesian particle filtering technique. The model successfully tracks the key variables (reported cases, critical care and deaths) throughout the two waves (March-June and September-November 2020) of the COVID-19 outbreak in Scotland. The model hospitalisation predictions in Summer 2020 are consistently lower than the recorded data, but consistent with the change to the reporting criteria by the Health Protection Scotland on 15th September. Most parameter estimates were constant over the two waves, but the infection rate and consequently the reproductive number decrease in the later stages of the first wave and increase again from July 2020. The death rates are initially high but decrease over Summer 2020 before rising again in November. The model can also be used to provide short-term predictions. We show that the 2-week predictability is very good for the period from March to June 2020, even at early stages of the pandemic. The model has been slower to pick up the increase in the case numbers in September 2020 but forecasting improves again in the later stages of the epidemic.

q-bio.PE↗