The rise of large-scale pretrained models has made it feasible to generate predictive or synthetic features at low cost, raising the question of how to incorporate such surrogate predictions into downstream decision-making. We study this problem in the setting of online linear contextual bandits, where contexts may be complex, nonstationary, and only partially observed. In addition to bandit data, we assume access to an auxiliary dataset containing fully observed contexts--common in practice since such data are collected without adaptive interventions. We propose PULSE-UCB, an algorithm that leverages pretrained models trained on the auxiliary data to impute missing features during online decision-making. We establish regret guarantees that decompose into a standard bandit term plus an additional component reflecting pretrained model quality. In the i.i.d. context case with Hölder-smooth missing features, PULSE-UCB achieves near-optimal performance, supported by matching lower bounds. Our results quantify how uncertainty in predicted contexts affects decision quality and how much historical data is needed to improve downstream learning.

We present CuMPerLay, a novel differentiable vectorization layer that enables the integration of Cubical Multiparameter Persistence (CMP) into deep learning pipelines. While CMP presents a natural and powerful way to topologically work with images, its use is hindered by the complexity of multifiltration structures as well as the vectorization of CMP. In face of these challenges, we introduce a new algorithm for vectorizing MP homologies of cubical complexes. Our CuMPerLay decomposes the CMP into a combination of individual, learnable single-parameter persistence, where the bifiltration functions are jointly learned. Thanks to the differentiability, its robust topological feature vectors can be seamlessly used within state-of-the-art architectures such as Swin Transformers. We establish theoretical guarantees for the stability of our vectorization under generalized Wasserstein metrics. Our experiments on benchmark medical imaging and computer vision datasets show the benefit CuMPerLay on classification and segmentation performance, particularly in limited-data scenarios. Overall, CuMPerLay offers a promising direction for integrating global structural information into deep networks for structured image analysis.

We study neural network compressibility by using singular learning theory to extend the minimum description length (MDL) principle to singular models like neural networks. Through extensive experiments on the Pythia suite with quantization, factorization, and other compression techniques, we find that complexity estimates based on the local learning coefficient (LLC) are closely, and in some cases, linearly correlated with compressibility. Our results provide a path toward rigorously evaluating the limits of model compression.

Nonlinear and delayed effects of covariates often render time series forecasting challenging. To this end, we propose a novel forecasting framework based on ridge regression with signature features calculated on sliding windows. These features capture complex temporal dynamics without relying on learned or hand-crafted representations. Focusing on the discrete-time setting, we establish theoretical guarantees, namely universality of approximation and stationarity of signatures. We introduce an efficient sequential algorithm for computing signatures on sliding windows. The method is evaluated on both synthetic and real electricity demand data. Results show that signature features effectively encode temporal and nonlinear dependencies, yielding accurate forecasts competitive with those based on expert knowledge.

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. Our approach introduces Voronoi-type loss functions aligned with the gate-partition geometry and establishes finite-sample convergence rates for the maximum likelihood estimator (MLE). In over-specified models, we reveal a link between the MLE's convergence rate and the solvability of an associated system of polynomial equations characterizing near-nonidentifiable directions. For model selection, we adapt dendrograms of mixing measures to SGMoE, yielding a consistent, sweep-free selector of the number of experts that attains pointwise-optimal parameter rates under overfitting while avoiding multi-size training. Simulations on synthetic data corroborate the theory, accurately recovering the expert count and achieving the predicted rates for parameter estimation while closely approximating the regression function. Under model misspecification (e.g., $ε$-contamination), the dendrogram selection criterion is robust, recovering the true number of mixture components, while the Akaike information criterion, the Bayesian information criterion, and the integrated completed likelihood tend to overselect as sample size grows. On a maize proteomics dataset of drought-responsive traits, our dendrogram-guided SGMoE selects two experts, exposes a clear mixing-measure hierarchy, stabilizes the likelihood early, and yields interpretable genotype-phenotype maps, outperforming standard criteria without multi-size training.

We introduce a novel high-frequency daily panel dataset of both markets and news-based indicators -- including Geopolitical Risk, Economic Policy Uncertainty, Trade Policy Uncertainty, and Political Sentiment -- for 42 countries across both emerging and developed markets. Using this dataset, we study how sentiment dynamics shape sovereign risk, measured by Credit Default Swap (CDS) spreads, and evaluate their forecasting value relative to traditional drivers such as global monetary policy and market volatility. Our horse-race analysis of forecasting models demonstrates that incorporating news-based indicators significantly enhances predictive accuracy and enriches the analysis, with non-linear machine learning methods -- particularly Random Forests -- delivering the largest gains. Our analysis reveals that while global financial variables remain the dominant drivers of sovereign risk, geopolitical risk and economic policy uncertainty also play a meaningful role. Crucially, their effects are amplified through non-linear interactions with global financial conditions. Finally, we document pronounced regional heterogeneity, as certain asset classes and emerging markets exhibit heightened sensitivity to shocks in policy rates, global financial volatility, and geopolitical risk.

We develop interacting particle algorithms for learning latent variable models with energy-based priors. To do so, we leverage recent developments in particle-based methods for solving maximum marginal likelihood estimation (MMLE) problems. Specifically, we provide a continuous-time framework for learning latent energy-based models, by defining stochastic differential equations (SDEs) that provably solve the MMLE problem. We obtain a practical algorithm as a discretisation of these SDEs and provide theoretical guarantees for the convergence of the proposed algorithm. Finally, we demonstrate the empirical effectiveness of our method on synthetic and image datasets.

Stochastic Gradient Descent (SGD) and its Ruppert-Polyak averaged variant (ASGD) lie at the heart of modern large-scale learning, yet their theoretical properties in high-dimensional settings are rarely understood. In this paper, we provide rigorous statistical guarantees for constant learning-rate SGD and ASGD in high-dimensional regimes. Our key innovation is to transfer powerful tools from high-dimensional time series to online learning. Specifically, by viewing SGD as a nonlinear autoregressive process and adapting existing coupling techniques, we prove the geometric-moment contraction of high-dimensional SGD for constant learning rates, thereby establishing asymptotic stationarity of the iterates. Building on this, we derive the $q$-th moment convergence of SGD and ASGD for any $q\ge2$ in general $\ell^s$-norms, and, in particular, the $\ell^{\infty}$-norm that is frequently adopted in high-dimensional sparse or structured models. Furthermore, we provide sharp high-probability concentration analysis which entails the probabilistic bound of high-dimensional ASGD. Beyond closing a critical gap in SGD theory, our proposed framework offers a novel toolkit for analyzing a broad class of high-dimensional learning algorithms.

In Bayesian Optimization (BO), additive assumptions can mitigate the twin difficulties of modeling and searching a complex function in high dimension. However, common acquisition functions, like the Additive Lower Confidence Bound, ignore pairwise covariances between dimensions, which we'll call \textit{bilateral uncertainty} (BU), imposing a second layer of approximations. While theoretical results indicate that asymptotically not much is lost in doing so, little is known about the practical effects of this assumption in small budgets. In this article, we show that by exploiting conditional independence, Thompson Sampling respecting BU can be efficiently conducted. We use this fact to execute an empirical investigation into the loss incurred by ignoring BU, finding that the additive approximation to Thompson Sampling does indeed have, on balance, worse performance than the exact method, but that this difference is of little practical significance. This buttresses the theoretical understanding and suggests that the BU-ignoring approximation is sufficient for BO in practice, even in the non-asymptotic regime.

We developed a task-oriented dialogue framework structured as a Directed Acyclic Graph (DAG) of medical questions. The system integrates: (1) a systematic pipeline for transforming medical algorithms and guidelines into a clinical question corpus; (2) a cold-start mechanism based on hierarchical clustering to generate efficient initial questioning without prior patient information; (3) an expand-and-prune mechanism enabling adaptive branching and backtracking based on patient responses; (4) a termination logic to ensure interviews end once sufficient information is gathered; and (5) automated synthesis of doctor-friendly structured reports aligned with clinical workflows. Human-computer interaction principles guided the design of both the patient and physician applications. Preliminary evaluation involved five physicians using standardized instruments: NASA-TLX (cognitive workload), the System Usability Scale (SUS), and the Questionnaire for User Interface Satisfaction (QUIS). The patient application achieved low workload scores (NASA-TLX = 15.6), high usability (SUS = 86), and strong satisfaction (QUIS = 8.1/9), with particularly high ratings for ease of learning and interface design. The physician application yielded moderate workload (NASA-TLX = 26) and excellent usability (SUS = 88.5), with satisfaction scores of 8.3/9. Both applications demonstrated effective integration into clinical workflows, reducing cognitive demand and supporting efficient report generation. Limitations included occasional system latency and a small, non-diverse evaluation sample.