The UK government is facing calls to cancel a sprawling health care contract with Palantir. The region of Greater Manchester insists it can do a better job itself. The UK government has six months to decide whether to terminate a deal worth more than $400 million between the country's National Health Service and American software company Palantir . If one part of the NHS is already doing without Palantir, politicians are asking, why can't the rest of the country? In 2023, the UK commissioned Palantir to develop a " federated data platform " (FDP) that could ingest and organize the tangle of health data produced across the country.

Conformal selection (CS) uses calibration data to identify test inputs whose unobserved outcomes are likely to satisfy a pre-specified minimal quality requirement, while controlling the false discovery rate (FDR). Existing methods fix the target FDR level before observing data, which prevents the user from adapting the balance between number of selected test inputs and FDR to downstream needs and constraints based on the available data. For example, in genomics or neuroimaging, researchers often inspect the distribution of test statistics, and decide how aggressively to pursue candidates based on observed evidence strength and available follow-up resources. To address this limitation, we introduce {post-hoc CS} (PH-CS), which generates a path of candidate selection sets, each paired with a data-driven false discovery proportion (FDP) estimate. PH-CS lets the user select any operating point on this path by maximizing a user-specified utility, arbitrarily balancing selection size and FDR. Building on conformal e-variables and the e-Benjamini-Hochberg (e-BH) procedure, PH-CS is proved to provide a finite-sample post-hoc reliability guarantee whereby the ratio between estimated FDP level and true FDP is, on average, upper bounded by $1$, so that the average estimated FDP is, to first order, a valid upper bound on the true FDR. PH-CS is extended to control quality defined in terms of a general risk. Experiments on synthetic and real-world datasets demonstrate that, unlike CS, PH-CS can consistently satisfy user-imposed utility constraints while producing reliable FDP estimates and maintaining competitive FDR control.

Controlling the false discovery rate (FDR) in high-dimensional variable selection requires balancing rigorous error control with statistical power. Existing methods with provable guarantees are often overly conservative, creating a persistent gap between the realized false discovery proportion (FDP) and the target FDR level. We introduce a learning-augmented enhancement of the T-Rex Selector framework that narrows this gap. Our approach replaces the analytical FDP estimator with a neural network trained solely on diverse synthetic datasets, enabling a substantially tighter and more accurate approximation of the FDP. This refinement allows the procedure to operate much closer to the desired FDR level, thereby increasing discovery power while maintaining effective approximate control. Through extensive simulations and a challenging synthetic genome-wide association study (GWAS), we demonstrate that our method achieves superior detection of true variables compared to existing approaches.

As datasets grow richer, an important challenge is to leverage the full features in the data to maximize the number of useful discoveries while controlling for false positives. We address this problem in the context of multiple hypotheses testing, where for each hypothesis, we observe a p-value along with a set of features specific to that hypothesis. For example, in genetic association studies, each hypothesis tests the correlation between a variant and the trait.

Diffusion models have been extensively leveraged for learning robot skills from demonstrations. These policies are conditioned on several observational modalities such as proprioception, vision and tactile. However, observational modalities have varying levels of influence for different tasks that diffusion polices fail to capture. In this work, we propose 'Factorized Diffusion Policies' abbreviated as FDP, a novel policy formulation that enables observational modalities to have differing influence on the action diffusion process by design. This results in learning policies where certain observations modalities can be prioritized over the others such as $\texttt{vision>tactile}$ or $\texttt{proprioception>vision}$. FDP achieves modality prioritization by factorizing the observational conditioning for diffusion process, resulting in more performant and robust policies. Our factored approach shows strong performance improvements in low-data regimes with $15\%$ absolute improvement in success rate on several simulated benchmarks when compared to a standard diffusion policy that jointly conditions on all input modalities. Moreover, our benchmark and real-world experiments show that factored policies are naturally more robust with $40\%$ higher absolute success rate across several visuomotor tasks under distribution shifts such as visual distractors or camera occlusions, where existing diffusion policies fail catastrophically. FDP thus offers a safer and more robust alternative to standard diffusion policies for real-world deployment. Videos are available at https://fdp-policy.github.io/fdp-policy/ .

Given an unsupervised novelty detection task on a new dataset, how can we automatically select a "best" detection model while simultaneously controlling the

We introduce a novel privatization framework for high-dimensional controlled variable selection. Our framework enables rigorous False Discovery Rate (FDR) control under differential privacy constraints. While the Model-X knockoff procedure provides FDR guarantees by constructing provably exchangeable ``negative control" features, existing privacy mechanisms like Laplace or Gaussian noise injection disrupt its core exchangeability conditions. Our key innovation lies in privatizing the data knockoff matrix through the Gaussian Johnson-Lindenstrauss Transformation (JLT), a dimension reduction technique that simultaneously preserves covariate relationships through approximate isometry for $(ε,δ)$-differential privacy. We theoretically characterize both FDR and the power of the proposed private variable selection procedure, in an asymptotic regime. Our theoretical analysis characterizes the role of different factors, such as the JLT's dimension reduction ratio, signal-to-noise ratio, differential privacy parameters, sample size and feature dimension, in shaping the privacy-power trade-off. Our analysis is based on a novel `debiasing technique' for high-dimensional private knockoff procedure. We further establish sufficient conditions under which the power of the proposed procedure converges to one. This work bridges two critical paradigms -- knockoff-based FDR control and private data release -- enabling reliable variable selection in sensitive domains. Our analysis demonstrates that structural privacy preservation through random projections outperforms the classical noise addition mechanism, maintaining statistical power even under strict privacy budgets.