Importantly,thesuccess ofanymitigation strategystrongly depends on the structure of the shift. Despite this, there has been little discussion of how toempirically assess the structure ofadistribution shift that one isencountering in practice. In this work, we adopt a causal framing to motivate conditional independence tests as akeytool for characterizing distribution shifts. Using our approach in two medical applications, we show that this knowledge can help diagnose failures offairness transfer,including cases where real-world shifts are more complexthanisoften assumed intheliterature.

We propose two novel tricks to tackle this challenge.

We study the problem of offline changepoint localization in a distribution-free setting. One observes a vector of data with a single changepoint, assuming that the data before and after the changepoint are iid (or more generally exchangeable) from arbitrary and unknown distributions. The goal is to produce a finite-sample confidence set for the index at which the change occurs without making any other assumptions. Existing methods often rely on parametric assumptions, tail conditions, or asymptotic approximations, or only produce point estimates. In contrast, our distribution-free algorithm, CONformal CHangepoint localization (CONCH), only leverages exchangeability arguments to construct confidence sets with finite sample coverage. By proving a conformal Neyman-Pearson lemma, we derive principled score functions that yield informative (small) sets. Moreover, with such score functions, the normalized length of the confidence set shrinks to zero under weak assumptions. We also establish a universality result showing that any distribution-free changepoint localization method must be an instance of CONCH. Experiments suggest that CONCH delivers precise confidence sets even in challenging settings involving images or text.

Shoe print evidence recovered from crime scenes plays a key role in forensic investigations. By examining shoe prints, investigators can determine details of the footwear worn by suspects. However, establishing that a suspect's shoes match the make and model of a crime scene print may not be sufficient. Typically, thousands of shoes of the same size, make, and model are manufactured, any of which could be responsible for the print. Accordingly, a popular approach used by investigators is to examine the print for signs of ``accidentals,'' i.e., cuts, scrapes, and other features that accumulate on shoe soles after purchase due to wear. While some patterns of accidentals are common on certain types of shoes, others are highly distinctive, potentially distinguishing the suspect's shoe from all others. Quantifying the rarity of a pattern is thus essential to accurately measuring the strength of forensic evidence. In this study, we address this task by developing a hierarchical Bayesian model. Our improvement over existing methods primarily stems from two advancements. First, we frame our approach in terms of a latent Gaussian model, thus enabling inference to be efficiently scaled to large collections of annotated shoe prints via integrated nested Laplace approximations. Second, we incorporate spatially varying coefficients to model the relationship between shoes' tread patterns and accidental locations. We demonstrate these improvements through superior performance on held-out data, which enhances accuracy and reliability in forensic shoe print analysis.

Contextual bandits are a core technology for personalized mobile health interventions, where decision-making requires adapting to complex, non-linear user behaviors. While Thompson Sampling (TS) is a preferred strategy for these problems, its performance hinges on the quality of the underlying reward model. Standard linear models suffer from high bias, while neural network approaches are often brittle and difficult to tune in online settings. Conversely, tree ensembles dominate tabular data prediction but typically rely on heuristic uncertainty quantification, lacking a principled probabilistic basis for TS. We propose Bayesian Forest Thompson Sampling (BFTS), the first contextual bandit algorithm to integrate Bayesian Additive Regression Trees (BART), a fully probabilistic sum-of-trees model, directly into the exploration loop. We prove that BFTS is theoretically sound, deriving an information-theoretic Bayesian regret bound of $\tilde{O}(\sqrt{T})$. As a complementary result, we establish frequentist minimax optimality for a "feel-good" variant, confirming the structural suitability of BART priors for non-parametric bandits. Empirically, BFTS achieves state-of-the-art regret on tabular benchmarks with near-nominal uncertainty calibration. Furthermore, in an offline policy evaluation on the Drink Less micro-randomized trial, BFTS improves engagement rates by over 30% compared to the deployed policy, demonstrating its practical effectiveness for behavioral interventions.

Constraint-based causal discovery methods require a large number of conditional independence (CI) tests, which severely limits their practical applicability due to high computational complexity. Therefore, it is crucial to design an algorithm that accelerates each individual test. To this end, we propose the Flow Matching-based Conditional Independence Test (FMCIT). The proposed test leverages the high computational efficiency of flow matching and requires the model to be trained only once throughout the entire causal discovery procedure, substantially accelerating causal discovery. According to numerical experiments, FMCIT effectively controls type-I error and maintains high testing power under the alternative hypothesis, even in the presence of high-dimensional conditioning sets. In addition, we further integrate FMCIT into a two-stage guided PC skeleton learning framework, termed GPC-FMCIT, which combines fast screening with guided, budgeted refinement using FMCIT. This design yields explicit bounds on the number of CI queries while maintaining high statistical power. Experiments on synthetic and real-world causal discovery tasks demonstrate favorable accuracy-efficiency trade-offs over existing CI testing methods and PC variants.