arXiv subjects

Reuben Adams

Publications and source records attributed to Reuben Adams.

2 recordsLinked to original sources

arXiv2023

E-values for k-Sample Tests With Exponential Families

We develop and compare e-variables for testing whether $k$ samples of data are drawn from the same distribution, the alternative being that they come from different elements of an exponential family. We consider the GRO (growth-rate optimal) e-variables for (1) a `small' null inside the same exponential family, and (2) a `large' nonparametric null, as well as (3) an e-variable arrived at by conditioning on the sum of the sufficient statistics. (2) and (3) are efficiently computable, and extend ideas from Turner et al. [2021] and Wald [1947] respectively from Bernoulli to general exponential families. We provide theoretical and simulation-based comparisons of these e-variables in terms of their logarithmic growth rate, and find that for small effects all four e-variables behave surprisingly similarly; for the Gaussian location and Poisson families, e-variables (1) and (3) coincide; for Bernoulli, (1) and (2) coincide; but in general, whether (2) or (3) grows faster under the alternative is family-dependent. We furthermore discuss algorithms for numerically approximating (1).

stat.ME↗

arXiv2022

Controlling Multiple Errors Simultaneously with a PAC-Bayes Bound

Current PAC-Bayes generalisation bounds are restricted to scalar metrics of performance, such as the loss or error rate. However, one ideally wants more information-rich certificates that control the entire distribution of possible outcomes, such as the distribution of the test loss in regression, or the probabilities of different mis-classifications. We provide the first PAC-Bayes bound capable of providing such rich information by bounding the Kullback-Leibler divergence between the empirical and true probabilities of a set of $M$ error types, which can either be discretized loss values for regression, or the elements of the confusion matrix (or a partition thereof) for classification. We transform our bound into a differentiable training objective. Our bound is especially useful in cases where the severity of different mis-classifications may change over time; existing PAC-Bayes bounds can only bound a particular pre-decided weighting of the error types. In contrast our bound implicitly controls all uncountably many weightings simultaneously.

stat.ML↗