Selecting high-quality candidates from large datasets is critical in applications such as drug discovery, precision medicine, and alignment of large language models (LLMs). While Conformal Selection (CS) provides rigorous uncertainty quantification, it is limited to univariate responses and scalar criteria. To address this, we propose Multivariate Conformal Selection (mCS), a generalization of CS designed for multivariate response settings. Our method introduces regional monotonicity and employs multivariate nonconformity scores to construct conformal $p$-values, enabling finite-sample False Discovery Rate (FDR) control. We present two variants: $\texttt{mCS-dist}$, using distance-based scores, and $\texttt{mCS-learn}$, which learns optimal scores via differentiable optimization. Experiments on simulated and real-world datasets demonstrate that mCS significantly improves selection power while maintaining FDR control, establishing it as a robust framework for multivariate selection tasks.

We propose a computationally efficient alternative to generalized random forests (GRFs) for estimating heterogeneous effects in large dimensions. While GRFs rely on a gradient-based splitting criterion, which in large dimensions is computationally expensive and unstable, our method introduces a fixed-point approximation that eliminates the need for Jacobian estimation. This gradient-free approach preserves GRF’s theoretical guarantees of consistency and asymptotic normality while significantly improving computational efficiency. We demonstrate that our method achieves a speedup of multiple times over standard GRFs without compromising statistical accuracy. Experiments on both simulated and real-world data validate our approach. Our findings suggest that the proposed method is a scalable alternative for localized effect estimation in machine learning and causal inference applications.

High-dimensional data often conceal low-dimensional signals beneath structured background noise, limiting standard PCA. Motivated by contrastive learning, we address the problem of recovering shared signal subspaces from positive pairs--paired observations sharing the same signal but differing in background. Our baseline, PCA+, uses alignment-only contrastive learning and succeeds when background variation is mild, but fails under strong noise or high-dimensional regimes. To address this, we introduce PCA++, a hard uniformity-constrained contrastive PCA that enforces identity covariance on projected features. PCA++ has a closed-form solution via a generalized eigenproblem, remains stable in high dimensions, and provably regularizes against background interference. We provide exact high-dimensional asymptotics in both fixed-aspect-ratio and growing-spike regimes, showing uniformity’s role in robust signal recovery. Empirically, PCA++ outperforms standard PCA and alignment-only PCA+ on simulations, corrupted-MNIST, and single-cell transcriptomics, reliably recovering condition-invariant structure. More broadly, we clarify uniformity’s role in contrastive learning—showing that explicit feature dispersion defends against structured noise and enhances robustness.

Survival models can help medical practitioners to evaluate the prognostic importance of clinical variables to patient outcomes such as mortality or hospital readmission and subsequently design personalized treatment regimes. Electronic Health Records (EHRs) hold the promise for large-scale survival analysis based on systematically recorded clinical features for each patient. However, existing survival models either do not scale to high dimensional and multi-modal EHR data or are difficult to interpret. In this study, we present a supervised topic model called MixEHR-SurG to simultaneously integrate heterogeneous EHR data and model survival hazard. Our contributions are three-folds: (1) integrating EHR topic inference with Cox proportional hazards likelihood; (2) integrating patient-specific topic hyperparameters using the PheCode concepts such that each topic can be identified with exactly one PheCode-associated phenotype; (3) multi-modal survival topic inference. This leads to a highly interpretable survival topic model that can infer PheCode-specific phenotype topics associated with patient mortality. We evaluated MixEHR-SurG using a simulated dataset and two real-world EHR datasets: the Quebec Congenital Heart Disease (CHD) data consisting of 8211 subjects with 75,187 outpatient claim records of 1767 unique ICD codes; the MIMIC-III consisting of 1458 subjects with multi-modal EHR records. Compared to the baselines, MixEHR-SurG achieved a superior dynamic AUROC for mortality prediction, with a mean AUROC score of 0.89 in the simulation dataset and a mean AUROC of 0.645 on the CHD dataset. Qualitatively, MixEHR-SurG associates severe cardiac conditions with high mortality risk among the CHD patients after the first heart failure hospitalization and critical brain injuries with increased mortality among the MIMIC-III patients after their ICU discharge. Together, the integration of the Cox proportional hazards model and EHR topic inference in MixEHR-SurG not only leads to competitive mortality prediction but also meaningful phenotype topics for in-depth survival analysis. The software is available at GitHub: https://github.com/li-lab-mcgill/MixEHR-SurG.

We propose a consolidated cross-validation (CV) algorithm for training and tuning the support vector machines (SVM) on reproducing kernel Hilbert spaces. Our consolidated CV algorithm utilizes a recently proposed exact leave-one-out formula for the SVM and accelerates the SVM computation via a data reduction strategy. In addition, to compute the SVM with the bias term (intercept), which is not handled by the existing data reduction methods, we propose a novel two-stage consolidated CV algorithm. With numerical studies, we demonstrate that our algorithm is about an order of magnitude faster than the two mainstream SVM solvers, kernlab and LIBSVM, with almost the same accuracy.