In this work, we consider the data-driven assortment optimization problem under the linear multinomial logit (MNL) choice model. We first establish an improved confidence region for the maximum-likelihood-estimator (MLE) of the d-dimensional linear MNL likelihood function that removes the explicit dependency on a problem-dependent parameter κ 1 in previous result [42], which scales exponentially with the radius of the parameter set. Building on the confidence region result, we investigate the data-driven assortment optimization problem in both offline and online settings.

Sample-wise learning curves plot performance versus training set size. They are useful for studying scaling laws and speeding up hyperparameter tuning and model selection. Learning curves are often assumed to be well-behaved: monotone (i.e.

The hippocampus supports spatial navigation by encoding cognitive maps through collective place cell activity. We model the place cell population as non-negative spatial embeddings derived from the spectral decomposition of multi-step random walk transition kernels.

Real-world spatio-temporal forecasting must handle irregular time points, spatially sparse observations, and the need for uncertainty quantification. This setting is often further compounded by nonlocal interactions (long-range spatial coupling). Modeling continuous-space, continuous-time nonlocal dynamics naturally leads to infinite-dimensional integro-differential equations (IDEs), making principled Bayesian inference intractable. We propose the NonLocal Bayesian Spatio-Temporal model (NLBST), a hierarchical Bayesian framework for continuous spatio-temporal fields that learns explicit nonlocal coupling while retaining tractable inference. NLBST represents the latent field via a coordinate-based spatial basis expansion and models the coefficient process with a continuous-time ODE whose learnable linear operator corresponds to a Galerkin reduction of a nonlocal IDE; a Neural ODE residual captures additional nonlinear dynamics. A linear-Gaussian observation model enables Kalman-style sequential updates under missing and irregular observations, while the spatial basis representation enables inductive prediction at unmeasured locations without retraining. Global parameters are learned via variational inference, and uncertainty is handled through a Bayesian hierarchy. Experiments on synthetic and real-world datasets demonstrate strong forecasting and spatial generalization with well-calibrated uncertainty, yielding substantial gains over baselines in strongly nonlocal and partially observed regimes.

Effective modeling of endangered marine mammal species, such as the North Atlantic Right Whale, is critical for balancing marine conservation with the growing blue economy. Passive acoustic monitoring data collected by autonomous underwater vehicles provide new opportunities for localized marine species detection and oceanographic sensing, but introduce complex statistical challenges such as zero inflation, imperfect detection, and intricate dependence structures. In response, we propose the Deep Zero-Inflated Bernoulli (DeepZIB) model--a deep statistical method which jointly models latent species presence and conditional detection probabilities while learning complex habitat relationships from heterogeneous covariate information. We establish theoretical results on the model's structural properties and conduct simulation experiments to demonstrate its ability to recover underlying parameters and latent presence fields. Application to real-world passive acoustic monitoring data on the North Atlantic Right Whale along the U.S. East Coast demonstrates improved model adequacy and predictive performance in capturing the species' dynamic and spatially varying habitat. A key advantage of DeepZIB is its ability to generate high-resolution, spatially and temporally varying presence maps, providing valuable insights for targeted and risk-aware management of blue economy industries, ranging from offshore and marine energy, to fisheries management and maritime transport.

Hidden Markov models are foundational for sequential inference, but their Markovian assumption fails under pathwise constraints such as precedence requirements, visitation cardinalities, or monotonic state progression, which induce long-range dependencies that invalidate standard dynamic programming algorithms. To deal with this, we present Controller-Augmented Hidden Markov Models (CHMMs), a framework that compiles each constraint into a finite-state controller tracking the minimal sufficient history, after which standard forward--backward and Viterbi recursions on the augmented chain compute exact constrained posteriors and maximum a posteriori paths in both discrete and continuous time, the latter through uniformization. We establish four theoretical guarantees: exactness of constrained inference, monotone ascent of constrained EM, inference complexity linear in the controller cardinality, and a total-variation bound under constraint misspecification. A catalog of controller encodings covering 11 constraint families across the ordering, visitation, path, and temporal categories operationalizes the framework. Empirically, we evaluate CHMMs against 6 alternative decoders on 3 real-world sequence-labeling tasks of substantively different character: gene-structure decoding in \emph{Drosophila melanogaster}, free-living activity recognition in CASAS smart-home environments, and protocol-defined human activity recognition from wearable sensors. The results reveal a clean local-versus-cumulative dichotomy in which controller augmentation is uniquely able to recover globally feasible trajectories on cumulative-constraint regimes, whilst simpler decoders are matched in validity on locally-dominated regimes. Together, theory and experiment characterize when exact controller augmentation is necessary and when simpler approaches suffice.

Conformal prediction has been explored as a general and efficient way to provide uncertainty quantification for time series. However, current methods struggle to handle time series data with change points -- sudden shifts in the underlying data-generating process. In this paper, we propose a novel Conformal Prediction for Time-series with Change points (CPTC) algorithm, addressing this gap by integrating a model to predict the underlying state with online conformal prediction to model uncertainties in non-stationary time series. We prove CPTC's validity and improved adaptivity in the time series setting under minimum assumptions, and demonstrate CPTC's practical effectiveness on 6 synthetic and real-world datasets, showing improved validity and adaptivity compared to state-of-the-art baselines.

Behavior cloning has shown promise for robot manipulation, but real-world demonstrations are costly to acquire at scale. While simulated data offers a scalable alternative, particularly with advances in automated demonstration generation, transferring policies to the real world is hampered by various simulation and real domain gaps. In this work, we propose a unified sim-and-real co-training framework for learning generalizable manipulation policies that primarily leverages simulation and only requires a few real-world demonstrations. Central to our approach is learning a domain-invariant, task-relevant feature space. Our key insight is that aligning the joint distributions of observations and their corresponding actions across domains provides a richer signal than aligning observations (marginals) alone. We achieve this by embedding an Optimal Transport (OT)-inspired loss within the co-training framework, and extend this to an Unbalanced OT framework to handle the imbalance between abundant simulation data and limited real-world examples. We validate our method on challenging manipulation tasks, showing it can leverage abundant simulation data to achieve up to a 30% improvement in the real-world success rate and even generalize to scenarios seen only in simulation.

A challenge in human-AI decision-making is to balance three factors: the correctness of predictions, the cost of knowledge and reasoning complexity, and the confidence about whether to abstain from automated answers or escalate to human experts. In this work, we present a cascaded LLM decision framework that adaptively delegates tasks across multiple tiers of expertise - a base model for initial candidate answers, a more capable and knowledgeable (but costlier) large model, and a human expert for when the model cascade abstains.

Generative modeling of non-negative, discrete data, such as symbolic music, remains challenging due to two persistent limitations in existing methods. First, most approaches rely on modeling continuous embeddings, which are not wellsuited for inherently discrete data distributions.