Time-varying dependence is often modeled with dynamic correlations or Gaussian graphical models, but multivariate systems can change through tail behavior, asymmetry, or conditional structure even when correlations are nearly stable. We introduce Dynamic Vine Copulas (DVC), a temporal vine-copula framework for estimating and diagnosing sequence-wide non-Gaussian dependence. DVC fixes a chosen vine factorization for comparability; the framework applies to C-, D-, and R-vines, and our experiments use fixed-root-order C-vines. Pair-copula states evolve through smooth parameter trajectories or temporally regularized family-switching paths. The main diagnostic is a held-out comparison between a full vine and its matched 1-truncated version, which separates flexible first-tree pairwise dependence from evidence contributed by higher-tree conditional terms. At the population level, under a correct fixed vine and the simplifying assumption, this contrast equals the higher-tree component of a vine total-correlation decomposition; in finite samples, it is a predictive diagnostic. In controlled benchmarks, DVC detects Student-t degrees-of-freedom changes, Clayton-to-Gumbel switches, and recurrent conditional-interaction episodes missed or conflated by Gaussian dynamic baselines. The higher-tree score remains near zero in pairwise-only regimes and rises during conditional-interaction regimes. On Allen Visual Behavior Neuropixels data, DVC identifies a reproducible time-indexed higher-tree signal that is positive across held-out splits and vanishes under a decorrelated null, indicating simultaneous cross-area dependence. DVC therefore provides a flexible temporal copula model and an interpretable test of whether temporal dependence changes are pairwise or conditional.

Factorial Hidden Markov Models (FHMMs) are powerful models for sequential data but they do not scale well with long sequences. We propose a scalable inference and learning algorithm for FHMMs that draws on ideas from the stochastic variational inference, neural network and copula literatures. Unlike existing approaches, the proposed algorithm requires no message passing procedure among latent variables and can be distributed to a network of computers to speed up learning. Our experiments corroborate that the proposed algorithm does not introduce further approximation bias compared to the proven structured mean-field algorithm, and achieves better performance with long sequences and large FHMMs.

Minimising a spectral risk objective, defined as a convex combination of expected cost and Conditional Value-at-Risk (CVaR), is challenging when the uncertainty distribution is decision-dependent, making both surrogate modelling and simulation-based ranking sensitive to tail estimation error. We propose Adaptive Conditional Forest Sampling (ACFS), a four-phase simulation-optimisation framework that integrates Generalised Random Forests for decision-conditional distribution approximation, CEM-guided global exploration, rank-weighted focused augmentation, and surrogate-to-oracle two-stage reranking before multi-start gradient-based refinement. We evaluate ACFS on two structurally distinct data-generating processes: a decision-dependent Student-t copula and a Gaussian copula with log-normal marginals, across three penalty-weight configurations and 100 replications per setting. ACFS achieves the lowest median oracle spectral risk on the second benchmark in every configuration, with median gaps over GP-BO ranging from 6.0% to 20.0%. On the first benchmark, ACFS and GP-BO are statistically indistinguishable in median objective, but ACFS reduces cross-replication dispersion by approximately 1.8 to 1.9 times on the first benchmark and 1.7 to 2.0 times on the second, indicating materially improved run-to-run reliability. ACFS also outperforms CEM-SO, SGD-CVaR, and KDE-SO in nearly all settings, while ablation and sensitivity analyses support the contribution and robustness of the proposed design.

Neural Information Processing Systems http://nips.cc/

Social survey datasets, for example, are typically mixed because they include variables like age (continuous), demographic group (categorical), and Likert scales (ordinal) measuring how strongly a respondent agrees with certain stated opinions. Continuous variables are encoded as real numbers and sometimes called numeric. We refer to variables that admit a total order (e.g.

Clinical and genomic models are both used to predict breast cancer outcomes, but they are often combined using simple linear rules that do not account for how their risk scores relate, especially at the extremes. Using the METABRIC breast cancer cohort, we studied whether directly modeling the joint relationship between clinical and genomic machine learning risk scores could improve risk stratification for 5-year cancer-specific mortality. We created a binary 5-year cancer-death outcome and defined two sets of predictors: a clinical set (demographic, tumor, and treatment variables) and a genomic set (gene-expression $z$-scores). We trained several supervised classifiers, such as Random Forest and XGBoost, and used 5-fold cross-validated predicted probabilities as unbiased risk scores. These scores were converted to pseudo-observations on $(0,1)^2$ to fit Gaussian, Clayton, and Gumbel copulas. Clinical models showed good discrimination (AUC 0.783), while genomic models had moderate performance (AUC 0.681). The joint distribution was best captured by a Gaussian copula (bootstrap $p=0.997$), which suggests a symmetric, moderately strong positive relationship. When we grouped patients based on this relationship, Kaplan-Meier curves showed clear differences: patients who were high-risk in both clinical and genomic scores had much poorer survival than those high-risk in only one set. These results show that copula-based fusion works in real-world cohorts and that considering dependencies between scores can better identify patient subgroups with the worst prognosis.

Estimating mutual information (MI) is a fundamental task in data science and machine learning. Existing estimators mainly rely on either highly flexible models (e.g., neural networks), which require large amounts of data, or overly simplified models (e.g., Gaussian copula), which fail to capture complex distributions. Drawing upon recent vector copula theory, we propose a principled interpolation between these two extremes to achieve a better trade-off between complexity and capacity. Experiments on state-of-the-art synthetic benchmarks and real-world data with diverse modalities demonstrate the advantages of the proposed estimator.