Papers

We propose a robust deep mixture model based on a pathway-wise shared scale-mixture construction. Layer-specific component indicators are independently distributed according to their corresponding mixing proportions and jointly define a complete pathway through the latent hierarchy. Conditional on the selected pathway, a single gamma-distributed latent precision variable is shared across the deepest latent distribution, every intermediate latent transition, and the observation model. Integrating out this shared precision yields an exact multivariate Student-$t$ distribution for each complete pathway, allowing robustness to propagate coherently throughout the entire latent hierarchy rather than being introduced separately within individual latent layers. Model parameters are estimated using a stochastic expectation–maximisation algorithm. Complete-pathway responsibilities are evaluated analytically, whereas the shared latent precision variables and latent Gaussian variables are generated from their conditional distributions before updating the model parameters. The pathway-specific degrees-of-freedom parameters are estimated by one-dimensional numerical optimisation. Simulation studies demonstrate accurate recovery of the pathway-specific degrees-of-freedom parameters together with consistently improved clustering performance relative to the deep Gaussian mixture model under heavy-tailed and contaminated settings. Real-data applications further illustrate the ability of the proposed model to identify heterogeneous latent structures while reducing the influence of atypical observations. The proposed framework retains the hierarchical representation and parsimonious parameter-sharing structure of the deep Gaussian mixture model while providing coherent pathway-wise robustness.

We propose method-of-moments estimators for the eigenvalues of variance component covariance matrices in multivariate mixed effects models. Assuming a parametric form for the eigenvalue distribution, we focus on the high-dimensional regime where the number of predictors is large and comparable to the number of realizations of each random effect. In this setting, we show that the empirical moments of sum-of-squares matrices (e.g., MANOVA estimators of the covariance matrices) can be closely approximated by deterministic functions of the underlying parameters. This relationship enables the construction of consistent and asymptotically normal estimators via moment matching. Our approach is motivated by applications in quantitative genetics, where estimating genetic covariance components across multiple phenotypic traits is of central interest. We implement our method in a new python package mlmm-mom, and demonstrate how our method adapts to several common experimental designs in this domain.

In recent years, numerous open-source software libraries have been developed for computing sets of features from univariate time series. The type and number of features vary across these feature sets, which have been constructed with varying disciplinary perspectives on quantifying structure in time-series data. To date, the relative strengths and weaknesses of these feature sets on time-series classification problems remains largely unexplored. Here we aimed to understand the relative performance of six open-source feature sets and three baseline feature sets (based on distributional and/or basic spectral structure) across 124 univariate time-series classification problems using a normalization-based approach to problem-level benchmarking that better indexes the relative strengths and weaknesses of different algorithms compared to prior rank-based approaches. Despite their dramatic differences in size, composition, and computation time, we found that feature sets performed relatively similarly overall (85.3% of pairwise comparisons resulted in ties), with the largest feature set, tsfresh, exhibiting the strongest overall performance (29.03% wins across all pairwise comparisons against other feature sets). We also highlighted specific problems on which the specific composition of a given feature set gave it a substantial performance advantage or disadvantage, and problems where simple baselines comprised of Fourier coefficients and quantiles were sufficient to achieve strong performance. Our results demonstrate the need to consider problem-level performance when benchmarking time-series feature sets, and highlight the importance of feature make-up in driving relative classification performance.