We develop an anytime-valid framework for optimal policy identification from logged contextual bandit data. In many applied settings, the analyst wants to select the optimal policy from a candidate policy class $Π$, but data are generated by an externally determined logging policy that they do not control. The analyst may also wish to monitor evidence continuously, stopping once the optimal policy is clear rather than committing to a fixed sample size in advance. This paper addresses these challenges by constructing a time-indexed set $S_t$ that retains the true optimal policy set uniformly over time with high probability. The resulting procedure allows the analyst to monitor policy values, eliminate clearly suboptimal policies, and stop at data-dependent times without invalidating inference. When the optimal policy is unique, we define a stopping time for its identification and derive a sample-complexity bound scaling as $O\!\left(\frac{\log |Π|+\log\log(1/Δ_{\min})}{Δ_{\min}^2}\right)$, where $Δ_{\min}$ is the gap between the best and second-best policy values. Simulations demonstrate that the anytime-valid approach can yield substantial sample savings relative to fixed-$N$ designs. An application to a large adaptive experiment on reducing misinformation online illustrates how the method provides a dynamic view as evidence on the optimal policy accumulates.

Response-adaptive randomization (RAR) in clinical trials aims to improve ethical and statistical efficiency by dynamically allocating patients to treatments based on observed outcomes. While RAR based on a target optimal allocation have been extensively studied for two-arms settings, their extension to multi-treatment experiments ($K \geq 2$) remains theoretically fragmented, with most existing methods focusing on specific algorithms or restricted target allocations. In this paper, we introduce a unified framework for response-adaptive targeting, the $α$-Rebalancing Targeting Strategies ($α$RTS), which generalize the ERADE two-armed strategy of Hu et al. [2009]. We prove that all designs in this family share fundamental asymptotic properties: strong consistency, asymptotic normality of allocation proportions and treatment effect estimators, and asymptotic efficiency. To address sparse target regimes (where some treatments are asymptotically eliminated), we further propose $α$RTS with Forced Exploration, a variant that guarantees infinite sampling for all treatments while preserving the asymptotic guarantees. Extensive simulations illustrate the finite-sample behavior of $α$RTS variants in a 3-armed context, highlighting in particular the critical role of forced exploration in sparse settings.

Agentic artificial intelligence systems introduce a new class of model risk. Unlike traditional predictive models, autonomous agents continuously acquire information, form beliefs regarding latent states of the environment, generate forecasts, select actions, and adapt their behavior over time. Existing validation methodologies focus primarily on predictive accuracy and therefore provide limited insight into the quality of the underlying decision process. This paper proposes a model validation framework for agentic AI based on Partially Observable Markov Decision Processes (POMDPs). The framework decomposes autonomous decision making into information, beliefs, forecasts, actions, and utility, allowing each component to be validated independently. Large language models (LLMs) are formalized as approximate Bayesian filtering operators, and a model-risk taxonomy is developed encompassing state-space, filtering, forecast, policy, utility-specification, and parameter risks. The model risk validation methodology is demonstrated through a portfolio-management case study in which an agent infers latent market regimes from market and macroeconomic information, generates belief-conditioned forecasts, and constructs portfolios using a Black--Litterman framework. Empirical validation combines performance analysis, belief calibration diagnostics, coverage tests, ablation studies, and parameter-sensitivity analysis. The results indicate that latent-state inference contributes independently to decision quality and that the principal conclusions remain robust across a broad range of parameter values. The principal contribution of the paper is a practical framework for extending established model risk management concepts to autonomous AI systems and providing a rigorous foundation for their validation, governance, and monitoring.

We study sparse semi-continuous tensor data with excess zeros, heavy right tails, and slice-specific dispersion. Such features arise naturally in monetary-valued multi-way data, such as international trade, where most exporter--importer--product--year cells are zero while positive values are continuous and highly variable. To model these data, we propose a Bayesian hierarchical tensor factorization model that places a low-rank CP structure on a latent Poisson rate tensor and couples it with a conditional Gamma model for positive outcomes, with rate parameters that can vary across slices within a mode. The model therefore separates the occurrence and magnitude of positive observations while borrowing strength across all tensor dimensions through a shared low-rank latent structure. To scale posterior inference to large arrays, we develop a hybrid variational--Monte Carlo algorithm that combines efficient coordinate ascent updates with a partially collapsed augmented-data sampler. Applied to approximately 60 million trade flows, the method surfaces multiway dependence across exporters, importers, products, and years that is difficult to recover from gravity-type or pairwise network analyses, which do not jointly model the product and temporal dimensions.

We propose the data augmented bootstrap (DAB), a framework for constructing confidence intervals from approximately invariant transformations of the data. As special cases, DAB recovers popular methods that rely on exact group symmetries, such as conformal prediction, wild bootstrap for Maximum Mean Discrepancy U-statistics and the recently proposed SymmPI. Meanwhile, DAB also recovers the classical bootstrap method, which exploits the dataset's approximate invariance under uniform sampling of data indices as the dataset size grows. For all DAB methods, we establish theoretical coverage results that interpolate between finite-sample and asymptotic guarantees according to the strength of the invariance, and without assuming a group structure. The approximate invariance is measured in the Kolmogorov distance and, for statistics that satisfy Gaussian universality, reduces to conditional mean and variance matching. This allows us to incorporate data augmentation (DA), a widely used machine learning heuristic based on approximate invariances, into known statistical methods. We empirically test the performance of incorporating DA into bootstrap, wild bootstrap and conformal prediction for simulated settings as well as for image, language and scientific data.

We introduce Martingale Doppelgänger-Eval, a public shadow-market benchmark for auditing whether vision-language models (VLMs) use candlestick evidence rather than extrapolate past trends. The central difficulty is identification: on real market histories, chart evidence and trend are strongly coupled, so an observational score cannot determine whether a fluent technical-analysis narrative is grounded in local visual evidence. We prove this limitation formally: no evaluation functional computed from observational chart--label data can distinguish a grounded responder from a trend-shortcut responder under strong coupling, whereas matched evidence interventions separate the same responders at an exponential rate and trend--label swaps provide an independent shortcut stress test. The benchmark therefore evaluates frozen VLMs on rendered OHLCV charts under four controlled mechanisms: a martingale-null market, injected-alpha counterfactual pairs, trend-confounder swaps, and regime shifts. A structural behavioral model identifies null-market bias, trend sensitivity, evidence sensitivity, prompt/renderer fragility, and evidence faithfulness; the accompanying statistical toolkit provides minimum detectable effects, block-aware sequential testing for metered APIs, and an overlap-weighted artifact check. Across frozen commercial and open VLMs, the identified regression assigns large positive coefficients to past trend but evidence coefficients that are zero or opposite to the rule-implied sign. Matched-pair analyses show that models either ignore injected candlestick semantics or move opposite to the rule-implied direction conditional on responding. The benchmark isolates a failure mode that standard observational chart benchmarks cannot detect and gives a reusable audit template for time-series imagery with controllable label mechanisms.

We study the privacy of releasing posterior sample paths from a Gaussian process (GP) when the entire training set including covariates and responses is private. Unlike standard differential-privacy (DP) mechanisms that add external noise, posterior sampling is random by construction. We show that this intrinsic randomness yields DP guarantees by deriving explicit Rényi-DP bounds for GP posterior sample-path release. The bounds separate posterior-mean leakage from data-dependent posterior-covariance leakage showing that meaningful privacy depends sharply on effective ridge regularisation. We apply membership-inference attacks to show that empirical leakage follows the predicted dependence on regularisation, posterior variance and the number of released posterior sample-paths. Utility experiments on downstream posterior-sampling tasks identify noisy-observation regimes where privacy-compatible regularisation preserves useful decisions with modest utility loss. When stronger privacy is needed, the intrinsic guarantee can be sharpened by adding calibrated GP noise, providing an explicit additional privacy knob.

Existing interpolation methods use pre-trained video diffusion priors to generate intermediate frames between sparsely sampled keyframes. In the absence of 3D geometric guidance, these methods struggle to produce plausible results for complex, articulated human motions and offer limited control over the synthesized dynamics. In this paper, we introduce PoseFuse3DKeyframe Interpolator (PoseFuse3D-KI), a novel framework that integrates 3D human guidance signals into the diffusion process for Controllable Human-centric Keyframe Interpolation (CHKI). To provide rich spatial and structural cues for interpolation, our PoseFuse3D, a 3D-informed control model, features a novel SMPL-X encoder that transforms 3D geometry and shape into the 2D latent conditioning space, alongside a fusion network that integrates these 3D cues with 2D pose embeddings. For evaluation, we build CHKI-Video, a new dataset annotated with both 2D poses and 3DSMPL-X parameters. We show that PoseFuse3D-KI consistently outperforms state-of-the-art baselines on CHKI-Video, achieving a 9% improvement in PSNR and a 38% reduction in LPIPS. Comprehensive ablations demonstrate that our PoseFuse3D model improves interpolation fidelity.

In this paper, we explore semantic clustering properties of deep reinforcement learning (DRL) to improve its interpretability and deepen our understanding of its internal semantic organization. In this context, semantic clustering refers to the ability of neural networks to cluster inputs based on their semantic similarity in the feature space. We propose a DRL architecture that incorporates a novel semantic clustering module that combines feature dimensionality reduction with online clustering.

Existing methods typically rely on heuristic strategies to handle the low-quality training data, which often struggle to produce stable and consistent reconstructions, frequently resulting in visual artifacts. In this work, we propose AsymGS, a novel framework that leverages the stochastic nature of these artifacts: they tend to vary across different training runs due to minor randomness. Specifically, our method trains two 3DGaussian Splatting (3DGS) models in parallel, enforcing a consistency constraint that encourages convergence on reliable scene geometry while suppressing inconsistent artifacts. To prevent the two models from collapsing into similar failure modes due to confirmation bias, we introduce a divergent masking strategy that applies two complementary masks: a multi-cue adaptive mask and a self-supervised soft mask, which leads to an asymmetric training process of the two models, reducing shared error modes. In addition, to improve the efficiency of model training, we introduce a lightweight variant called Dynamic EMAProxy, which replaces one of the two models with a dynamically updated Exponential Moving Average (EMA) proxy, and employs an alternating masking strategy to preserve divergence. Extensive experiments on challenging real-world datasets demonstrate that our method consistently outperforms existing approaches while achieving high efficiency.