arXiv:2507. 06637v2 Announce Type: replace-cross Abstract: We propose Path Signatures Logistic Regression (PSLR), a semi-parametric framework for classifying vector-valued functional data with scalar covariates.
arXiv:2303. 08777v3 Announce Type: replace-cross Abstract: Cross-validation is one of the most widely used tools for risk estimation and model selection in statistics and machine learning, yet its theoretical properties when embedded in a learning procedure remain insufficiently understood.
arXiv:2607. 28567v1 Announce Type: cross Abstract: Longitudinal causal studies often record histories as irregular functional fragments: laboratory values, physiologic signals, sensor streams, and image-derived summaries measured at unequal and informative times.
arXiv:2605. 25826v2 Announce Type: replace-cross Abstract: We develop a branched signature kernel solver for linear and nonlinear ordinary differential equations driven by a \emph{single observed trajectory} of a possibly rough forcing signal--a setting common within earthquake engineering, finance, biology, and structural health monitoring, where only one forcing realization is available, and the solver must respect the underlying physical law without an ensemble of realizations.
arXiv:2606. 15332v1 Announce Type: new Abstract: The signature transform is a principled feature map for continuous-time paths, valued for its uniqueness and universality.
arXiv:2507. 00260v3 Announce Type: replace-cross Abstract: When predictors are statistically dependent, the appropriate definition of feature importance depends on the operational goal.
arXiv:2509. 09371v2 Announce Type: replace-cross Abstract: Distributionally robust optimization (DRO) protects statistical learning against distributional shifts by optimizing the worst-case performance over a set of perturbed distributions.
arXiv:2606. 18650v1 Announce Type: new Abstract: As Large Language Model (LLM) datasets scale to trillions of tokens, data selection has emerged as a critical frontier to filter out uninformative noise and construct adaptive learning trajectories.
arXiv:2606. 03885v1 Announce Type: new Abstract: Feature attribution methods explain predictions by assigning importance scores to input features.
arXiv:2602. 22083v2 Announce Type: replace-cross Abstract: Causal identification functionals often require integration over conditional densities of continuous variables, such as those arising in nonparametric identification theory of total and mediated causal effects in DAGs with hidden variables.
arXiv:2604. 27742v2 Announce Type: replace Abstract: A fundamental dichotomy in the theory of classification sets smoothness against statistical efficiency: smooth surrogate losses such as the logistic loss enable fast $O(1/T)$ optimization but yield slow square-root $H$-consistency bounds, while piecewise-linear losses like the Hinge loss achieve optimal linear $H$-consistency rates but are non-differentiable.
arXiv:2607. 21773v1 Announce Type: new Abstract: In this paper, we propose and study a robust variant of the smart predict-then-optimize approach that accounts for prediction shifts due to disturbance in the covariate feature space.
arXiv:2510. 12744v2 Announce Type: replace-cross Abstract: We develop a unified statistical framework for softmax-gated Gaussian mixture of experts (SGMoE) that addresses three long-standing obstacles in parameter estimation and model selection: (i) non-identifiability of gating parameters up to common translations, (ii) intrinsic gate-expert interactions that induce coupled differential relations in the likelihood, and (iii) the tight numerator-denominator coupling in the softmax-induced conditional density.