arXiv subjects

Dean A. Bodenham

Publications and source records attributed to Dean A. Bodenham.

6 recordsLinked to original sources

arXiv2026

CHASM: Online Changepoint Detection in Temporal and Cross-Variable Dependence

Changepoint detection identifies times when the generative process of a time series changes, with applications in healthcare, cybersecurity, and finance. In multivariate settings, changes in cross-variable and temporal dependence are particularly challenging to detect, as they are often less pronounced than shifts in marginal statistics such as the mean or variance. Existing methods detect changes using reconstruction error, which provides only an indirect measure of dynamical change, or rely on scalar functionals that may be too coarse to capture global structure. We introduce CHASM, an online nonparametric method that monitors the truncated eigenvalue sequence of the recursively estimated dynamic mode decomposition operator. Designing such an approach raises two challenges: the permutation invariance of eigendecompositions, resolved via optimal linear assignment, and the lack of online changepoint methods for multivariate complex-valued time series, addressed through a novel augmented monitoring scheme. We study the theoretical properties of the dynamics estimator under the canonical vector autoregressive model, which directly motivates our algorithmic design. The proposed method achieves competitive or superior performance to modern competitors across synthetic and real-world data sets, including challenging settings in video and text data. It is unsupervised, depends on a small number of interpretable parameters, and requires no distributional assumptions beyond finite moments, making it readily deployable across scientific domains.

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arXiv2025

Scale two-sample testing with arbitrarily missing data

This work proposes a novel rank-based scale two-sample testing method for univariate, distinct data when a subset of the data may be missing. Our approach is based on mathematically tight bounds of the Ansari-Bradley test statistic in the presence of missing data, and rejects the null hypothesis if the test statistic is significant regardless of the missing values. This proposed scale testing method is then combined with the location testing method proposed by Zeng et al. (2024) using the Holm-Bonferroni correction for location-scale testing. We show that our methods control the Type I error regardless of the values of the missing data. Simulation results demonstrate that our methods have good statistical power, typically when less than 10% of the data are missing, while other missing data methods, such as case deletion or imputation methods, fail to control the Type I error when the data are missing not at random. We illustrate the proposed location-scale testing method on hepatitis C virus dataset where a subset of values is unobserved.

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arXiv2025

Exact Bounds of Spearman's footrule in the Presence of Missing Data with Applications to Independence Testing

This work studies exact bounds of Spearman's footrule between two partially observed $n$-dimensional distinct real-valued vectors $X$ and $Y$. The lower bound is obtained by sequentially constructing imputations of the partially observed vectors, each with a non-increasing value of Spearman's footrule. The upper bound is found by first considering the set of all possible values of Spearman's footrule for imputations of $X$ and $Y$, and then the size of this set is gradually reduced using several constraints. Algorithms with computational complexities $O(n^2)$ and $O(n^3)$ are provided for computing the lower and upper bound of Spearman's footrule for $X$ and $Y$, respectively. As an application of the bounds, we propose a novel two-sample independence testing method for data with missing values. Improving on all existing approaches, our method controls the Type I error under arbitrary missingness. Simulation results demonstrate our method has good power, typically when the proportion of pairs containing missing data is below $15\%$.

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arXiv2024

MMD Two-sample Testing in the Presence of Arbitrarily Missing Data

In many real-world applications, it is common that a proportion of the data may be missing or only partially observed. We develop a novel two-sample testing method based on the Maximum Mean Discrepancy (MMD) which accounts for missing data in both samples, without making assumptions about the missingness mechanism. Our approach is based on deriving the mathematically precise bounds of the MMD test statistic after accounting for all possible missing values. To the best of our knowledge, it is the only two-sample testing method that is guaranteed to control the Type I error for both univariate and multivariate data where data may be arbitrarily missing. Simulation results show that our method has good statistical power, typically for cases where 5% to 10% of the data are missing. We highlight the value of our approach when the data are missing not at random, a context in which either ignoring the missing values or using common imputation methods may not control the Type I error.

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arXiv2024

Online Changepoint Detection via Dynamic Mode Decomposition

Detecting changes in data streams is a vital task in many applications. There is increasing interest in changepoint detection in the online setting, to enable real-time monitoring and support prompt responses and informed decision-making. Many approaches assume stationary sequences before encountering an abrupt change in the mean or variance. Notably less attention has focused on the challenging case where the monitored sequences exhibit trend, periodicity and seasonality. Dynamic mode decomposition is a data-driven dimensionality reduction technique that extracts the essential components of a dynamical system. We propose a changepoint detection method that leverages this technique to sequentially model the dynamics of a moving window of data and produce a low-rank reconstruction. A change is identified when there is a significant difference between this reconstruction and the observed data, and we provide theoretical justification for this approach. Extensive simulations demonstrate that our approach has superior detection performance compared to other methods for detecting small changes in mean, variance, periodicity, and second-order structure, among others, in data that exhibits seasonality. Results on real-world datasets also show excellent performance compared to contemporary approaches.

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arXiv2024

On two-sample testing for data with arbitrarily missing values

We develop a new rank-based approach for univariate two-sample testing in the presence of missing data which makes no assumptions about the missingness mechanism. This approach is a theoretical extension of the Wilcoxon-Mann-Whitney test that controls the Type I error by providing exact bounds for the test statistic after accounting for the number of missing values. Greater statistical power is shown when the method is extended to account for a bounded domain. Furthermore, exact bounds are provided on the proportions of data that can be missing in the two samples while yielding a significant result. Simulations demonstrate that our method has good power, typically for cases of $10\%$ to $20\%$ missing data, while standard imputation approaches fail to control the Type I error. We illustrate our method on complex clinical trial data in which patients' withdrawal from the trial lead to missing values.

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