In randomized trials involving multiple treatments, bivariate survival outcomes present significant analytical challenges for making decisions. This paper addresses the problem of deriving optimal individualized treatment rules to maximize the joint survival probability beyond fixed time points $(t_1, t_2)$ through deep neural networks, while accounting for right censoring. We propose a novel approach that models treatment rules via stochastic policies, coupling marginal accelerated failure time models via link function to capture bivariate dependence. To enhance robustness and effectiveness of decision making, we introduce an adaptive prediction-powered method that leverages auxiliary predictions from machine learning models.

Modern Artificial Intelligence achieves remarkable predictive power by optimizing statistical risk functionals over vast corpora. Yet a gap separates this from genuine intelligence: the inability to distinguish correlation from causation. This paper argues that causal inference (identifying mechanisms invariant under intervention) is AI's indispensable statistical conscience. Without causal grounding, AI systems are correlation machines: powerful in familiar domains, brittle under distribution shift, and biased in high-stakes settings. Three contributions develop this argument. First, a Statistical Necessity Theorem for Causal Generalization: any algorithm achieving out-of-distribution generalization must encode causal structure, formalizing the distinction between prediction P(Y|X) and intelligence P(Y|do(X)). Second, a unified framework connects Pearl's do-calculus, the Potential Outcomes framework, Double Machine Learning, and Invariant Risk Minimization as a family of Causal Statistical Estimators, each identifying interventional distributions under different assumptions. Third, three AI failure modes (hallucination in large language models, reward hacking in reinforcement learning from human feedback, and degradation under distribution shift) are manifestations of causal blindness, each admitting a principled statistical remedy. Trustworthy AI is, at its core, a problem of causal statistics. The statistical community is not merely equipped to solve it -- it is the only community with the foundational tools to do so rigorously.

A local specialist LLM, fine-tuned with reinforcement learning from verifiable rewards (RLVR) on operator-local data, is installed in a regulated organization with per-deployment error budget $α$. The operator needs a safety certificate for this deployment's stream at every round: no pooling across deployments, no waiting for a long-run average. Existing wrappers cannot deliver this on adaptive, online-updated streams: offline conformal-risk methods require exchangeability; online-conformal methods bound only long-run averages; non-exchangeable extensions are marginally valid; and the closest anytime wrapper, A-RCPS, controls marginal rather than selective risk. Using a (test statistic, validity guarantee, deployment rule) framework, we identify one empty cell forced by deployment requirements: e-process per threshold, selective risk, anytime-pathwise validity, max-certified-threshold rule. Conformal Selective Acting (CSA) fills it as a per-round wrapper maintaining a Ville-type e-process per threshold on a Bonferroni grid, evaluated against the RLVR filtration. Under predictable updates and isotonic-calibrated monotone risk we prove (i) an anytime-pathwise selective-risk bound $R_T^{\mathrm{act}}\leα+O(N_T^{-1/2})$, (ii) rate-optimal certification matching $Θ(\barη^{-2}\log(1/δ))$, and (iii) a horizon-independent release-rate gap. Across eight specialist benchmarks ($480$ streams), sixteen adversarial distribution-shift cells ($160$ streams), and five live Expert-Iteration RLVR cells with online LoRA over four base models in three architecture families ($10{,}300$ rounds), CSA is the only method among ten compared that satisfies pathwise validity and non-refusing deployment on every cell. We do not propose a new LLM, training algorithm, or policy class; CSA is the deployment-side complement, orthogonal to the model, for operators who cannot use a frontier API.

Panel data, in which multiple units are repeatedly observed over time, arise throughout science and engineering. Quantifying predictive uncertainty in such settings is challenging because conformal prediction, while distribution-free and model-agnostic, classically relies on exchangeability assumptions that fail under temporal dependence and unit heterogeneity. We propose a simple online conformal framework for non-exchangeable panel data. The method exploits a key feature of online panel prediction: when a forecast is required for one unit, contemporaneous outcomes from related units may already be observed and can serve as a calibration panel. At each round, prediction sets are formed using currently observed calibration units together with two adaptive quantities: history-based similarity weights that emphasize calibration units resembling the target, and an adaptive miscoverage level that is updated whenever target feedback is revealed. This two-state design yields a stepwise coverage bound and a long-run coverage guarantee. Empirically, across synthetic and real panel data sets, the method improves coverage on the worst-covered target units through adaptive interval-width allocation rather than uniform inflation. The two states are complementary: similarity weights protect coverage when target feedback is sparse, while the adaptive level further improves coverage as feedback accumulates.

Thompson sampling is a widely used strategy for contextual bandits: at each round, it samples a reward function from a Bayesian posterior and acts greedily under that sample. Prior-data fitted networks (PFNs), such as TabPFN v2+ and TabICL v2, are attractive candidates for this purpose because they approximate Bayesian posterior predictive distributions in a single forward pass. However, PFNs predict noisy future rewards, while Thompson sampling requires uncertainty over the latent mean reward function. We propose PFN-TS, a Thompson sampling algorithm that converts PFN posterior predictives into mean-reward samples using a subsampled predictive central limit theorem. The method estimates posterior variance from a geometric grid of $O(\log n)$ dataset prefixes rather than the full $O(n)$ predictive sequence used in previous predictive-sequence approaches, and reuses TabICL's cached representations across rounds. We prove consistency of the subsampled variance estimator and give a Bayesian regret bound that decomposes PFN-TS regret into exact posterior-sampling regret under the PFN prior plus approximation terms. Empirically, PFN-TS achieves the best average rank across nonlinear synthetic and OpenML classification-to-bandit benchmarks, remains competitive on linear and BART-generated rewards, and attains the highest estimated policy value in an offline mobile-health evaluation. Code is available at https://anonymous.4open.science/r/PFN_TS-36ED/.

Randomized controlled trials typically assume that prognostic covariates are known and available at no cost. In practice, obtaining high-dimensional pretreatment data is costly, forcing a trade-off between covariate-adaptive precision and a measurement budget. We introduce Dynamic Adaptive Rerandomization via Thompson Sampling (DARTS), which treats covariate acquisition as a sequential optimization problem embedded within a design-based causal inference task. A budgeted combinatorial Thompson sampler learns which covariates are most prognostic across successive batches; selected covariates then drive rerandomization and regression adjustment to reduce batch-level average treatment effect variance. Our primary theoretical contribution is a decoupling result: adaptive covariate selection based on past batches preserves batch-level randomization validity, and the cumulative inverse-variance weighted estimator achieves at least nominal asymptotic coverage. We further derive a Bayes risk bound for the acquisition layer that matches the minimax lower bound up to logarithmic factors. Empirically, DARTS systematically concentrates the budget on informative features, significantly closing the efficiency gap to oracle designs while maintaining strict inferential validity.

Conditional Average Treatment Effect (CATE) estimation in practice demands three properties simultaneously: heterogeneous effects τ(x), calibrated uncertainty over them, and robustness to the heavy tails that contaminate real outcome data. Meta-learners (Künzel et al., 2019) give (i); causal forests and BART give (i)-(ii) with Gaussian-tail assumptions; no widely used tool gives all three. We present Bayesian X-Learner, an X-Learner built on cross-fitted doubly robust pseudo-outcomes (Kennedy, 2020) with a full MCMC posterior over τ(x) via a Welsch redescending pseudo-likelihood. On Hill's IHDP benchmark the default configuration attains mean εPEHE = 0.56 on 5 replications (lowest mean; differences from S-/T-/X-learners, full-config Causal BART, and a causal forest baseline are not significant at α = 0.05, and rank ordering is unstable at 10 replications -- IHDP comparisons are competitive rather than dominant). On contaminated "whale" DGPs with up to 20-25% tail density, a one-flag extension (contamination_severity) that selects a Huberδ nuisance loss per Huber's minimax-δ relation recovers RMSE 0.13 with tight credible intervals (single-cross-fit 30-seed coverage 83% [Wilson 66%, 93%] at 20% density; modularBayes pooling with Bayesian-bootstrap nuisance draws restores nominal 95% coverage). We validate on the Hillstrom email-marketing RCT (N = 42,613), demonstrating consistent behaviour on real heavy-tailed outcome data, and report covariate-stratified τ(x) coverage across covariate quintiles to substantiate calibration for heterogeneous effects beyond scalar summaries. We draw a clean distinction between tails-as-contamination (handled by Welsch + Huber nuisance) and tails-as-signal (handled by a tail-aware CATE basis); an empirical probe confirms a tail-aware basis recovers τtail with full subgroup coverage, while the library's Hill-estimator path is contamination-directed and should not be used for heterogeneous τ. We map six empirical boundaries (contamination ceiling, clean-data efficiency cost, basis sensitivity, sample size, treatment type, compute) and show where other tools are preferable. Code and reproducible benchmarks are released.

In online clustering problems, there is often a large amount of uncertainty over possible cluster assignments that cannot be resolved until more data are observed. This difficulty is compounded when clusters follow complex distributions, as is the case with text data. Sequential Monte Carlo (SMC) methods give a natural way of representing and updating this uncertainty over time, but have prohibitive memory requirements for large-scale problems. We propose a novel SMC algorithm that decomposes clustering problems into approximately independent subproblems, allowing a more compact representation of the algorithm state. Our approach is motivated by the knowledge base construction problem, and we show that our method is able to accurately and efficiently solve clustering problems in this setting and others where traditional SMC struggles.

Dynamical systems describe how a physical system evolves over time. Physical processes can evolve faster or slower in different environmental conditions. We use time-warping as rescaling the time in a model of a physical system. This thesis proposes a new method of transfer learning for Recurrent Neural Networks (RNNs) based on time-warping. We prove that for a class of linear, first-order differential equations known as time lag models, an LSTM can approximate these systems with any desired accuracy, and the model can be time-warped while maintaining the approximation accuracy. The Time-Warping method of transfer learning is then evaluated in an applied problem on predicting fuel moisture content (FMC), an important concept in wildfire modeling. An RNN with LSTM recurrent layers is pretrained on fuels with a characteristic time scale of 10 hours, where there are large quantities of data available for training. The RNN is then modified with transfer learning to generate predictions for fuels with characteristic time scales of 1 hour, 100 hours, and 1000 hours. The Time-Warping method is evaluated against several known methods of transfer learning. The Time-Warping method produces predictions with an accuracy level comparable to the established methods, despite modifying only a small fraction of the parameters that the other methods modify.