With the rapid development of the big data era, Vertical Federated Learning (VFL) has been widely applied to enable data collaboration while ensuring privacy protection. However, the ultrahigh dimensionality of features and the sparse data structures inherent in large-scale datasets introduce significant computational complexity. In this paper, we propose the Vertical Federated Feature Screening (VFS) algorithm, which effectively reduces computational, communication, and encryption costs. VFS is a two-stage feature screening procedure that proceeds from coarse to fine: the first stage quickly filters out irrelevant feature groups, followed by a more refined screening of individual features. It significantly reduces the resource demands of downstream tasks such as secure joint modeling or federated feature selection. This efficiency is particularly beneficial in scenarios with ultrahigh feature dimensionality or severe class imbalance in the response variable. The statistical and computational properties of VFS are rigorously established. Numerical simulations and real-world applications demonstrate its superior performance.

Label prototype learning has emerged as an effective paradigm in Partial MultiLabel Learning (PML), providing a distinctive framework for modeling structured representations of label semantics while naturally filtering noise through prototypebased label confidence estimation. However, existing prototype-based methods face a critical limitation: class prototypes are the biased estimates due to noisy candidate labels, particularly when positive samples are scarce. To this end, we first propose a mutually class prototype alignment strategy bypassing noise interference by introducing two different transformation matrices, which makes the class prototypes learned by the fuzzy clustering and candidate label set mutually alignment for correcting themselves. Such alignment is also passed on to the fuzzy memberships label in turn. In addition, to eliminate noise interference in the candidate label set during the classifier learning, we use the learned permutation matrix to transform the fuzzy memberships label for learning a label reliability indicator matrix accompanied by the candidate label set. This makes the label reliability indicator matrix absolutely prevent the occurrence of numerical values located in non-label and simultaneously eliminate the introduction of incorrect label as much as possible.

Recent advances in false discovery rate (FDR)-controlled feature selection methods have improved reliability by effectively limiting false positives, making them wellsuited for complex applications. A popular FDR-controlled framework called data splitting uses the "mirror statistics" to select features. However, we find that the unit variance assumption on mirror statistics could potentially limit the feature selection power. To address this, we generalize the mirror statistics in the Gaussian mirror framework and introduce a new approach called "generalized Gaussian mirror" (G2M), which adaptively learns the variance and forms new test statistics. We demonstrate both theoretically and empirically that the proposed test statistics achieve higher power than those of Gaussian mirror and data splitting. Comparisons with other FDR-controlled frameworks on synthetic, semi-synthetic, and real datasets highlight the superior performance of the G2M method in achieving higher power while maintaining FDR control. These findings suggest the potential for the G2M method for practical applications in real-world problems. Code is available at: https://github.com/skyve2012/G2M.

When algorithmic predictors inform resource allocation in high-stakes domains such as healthcare, these predictors must account for strategic manipulation of input features. The typical solution is to redesign the predictor itself to explicitly account for strategic interactions. In practice, however, decision makers are often constrained to adjusting coarser levers within existing prediction pipelines. For example, healthcare organizations often select which features to exclude based on perceived manipulability, while using standard regularization procedures to shrink the coefficients of retained features. In this work, we initiate a formal study of strategic classification through feature selection and its interaction with ridge regularization. Our main finding is that excluding individual features based on their manipulability alone is generally suboptimal. We provide a fine-grained characterization of the performance of a feature subset under optimal regularization, yielding new insights for policy design. Motivated by this characterization, we develop a practical algorithm for jointly choosing the feature set and the level of ridge regularization. Through a real-world case study on a healthcare payments benchmark, we illustrate how our algorithm can guide the design of coarse policy levers in practice. Our results provide a principled, practical framework for mitigating the effects of strategic behavior in algorithmic decision-making systems.

We study the problem of selecting limited features to observe such that models trained on them can perform well simultaneously across multiple subpopulations. This problem has applications in settings where collecting each feature is costly, e.g.

Non-alcoholic fatty liver disease (NAFLD) affects roughly 25% of global adults, posing substantial hepatic and cardiovascular risks. Yet, population-level screening tools remain inadequate. We present Method, a machine-learning framework for NAFLD risk prediction coupling gradient-boosted decision trees with conformal prediction to yield calibrated, distribution-free coverage guarantees on individual risk estimates. It integrates a mutual-information-based stability selection procedure to identify a compact, clinically interpretable feature subset via bootstrap resampling, constructing prediction sets whose marginal coverage provably exceeds a user-specified confidence level. We evaluated Method on a multicenter cohort from Guangzhou, China (primary n=2,187; external validation n=412) using 78 candidate features across demographics, metabolic biomarkers, and lifestyle factors. Method achieves an AUROC of 0.912 internally and 0.891 externally, outperforming deep neural networks, TabNet, support vector machines, and logistic regression. Conformal prediction sets achieve 91.3% empirical coverage at the 90% nominal level. A three-tier risk stratification derived from these scores separates the population into distinct groups, with the high-risk subgroup showing a 12-month progression rate 4.7 times that of the low-risk tier. The selected features -- notably waist circumference, ALT, GGT, triglycerides, fasting glucose, and BMI -- align with established metabolic risk factors, providing biological plausibility.

Sparse optimization refers to an optimization problem involving the zero-norm in objective or constraints. In this paper, nonconvex approximation approaches for sparse optimization have been studied with a unifying point of view in DC (Difference of Convex functions) programming framework. Considering a common DC approximation of the zero-norm including all standard sparse inducing penalty functions, we studied the consistency between global minimums (resp. local minimums) of approximate and original problems. We showed that, in several cases, some global minimizers (resp. local minimizers) of the approximate problem are also those of the original problem. Using exact penalty techniques in DC programming, we proved stronger results for some particular approximations, namely, the approximate problem, with suitable parameters, is equivalent to the original problem. The efficiency of several sparse inducing penalty functions have been fully analyzed. Four DCA (DC Algorithm) schemes were developed that cover all standard algorithms in nonconvex sparse approximation approaches as special versions. They can be viewed as, an $\ell _{1}$-perturbed algorithm / reweighted-$\ell _{1}$ algorithm / reweighted-$\ell _{1}$ algorithm. We offer a unifying nonconvex approximation approach, with solid theoretical tools as well as efficient algorithms based on DC programming and DCA, to tackle the zero-norm and sparse optimization. As an application, we implemented our methods for the feature selection in SVM (Support Vector Machine) problem and performed empirical comparative numerical experiments on the proposed algorithms with various approximation functions.

Under standard graphical assumptions, the Markov boundary of a target variable is the smallest set of features that renders every other feature redundant. Once the boundary is observed, the target is conditionally independent of the rest of the table. This is a tempting object for tabular prediction, since it names exactly the columns a model should need. Yet modern regressors are still trained on the full feature set. We ask whether the Markov boundary is genuinely useful for prediction on SCM3K, a 3,450-task synthetic SCM benchmark with feature counts from 40 to 1000 and six SCM families, evaluated with six regressors. The answer is more nuanced than the theory suggests. Restricting a regressor to the oracle boundary often improves prediction substantially, and the improvement grows as the feature space becomes larger and sparser. But the natural pipeline of recovering the boundary with causal discovery and training on the recovered mask does not deliver. Existing estimators exhaust the compute budget before reaching the regime where the boundary helps most, and even where they run they rarely beat the full feature set. We trace this to three causes. Discovery optimizes structural recovery rather than prediction. False negatives and false positives carry sharply asymmetric predictive cost. The exact boundary is only one of many feature sets that beat all features. We then develop what these facts imply for prediction-aligned feature selection and for tabular models that learn to use causal structure.

Scientific observations may consist of a large number of variables (features). Selecting a subset of meaningful features is often crucial for identifying patterns hidden in the ambient space. In this paper, we present a method for unsupervised feature selection, and we demonstrate its advantage in clustering, a common unsupervised task. We propose a differentiable loss that combines a graph Laplacian-based score that favors low-frequency features with a gating mechanism for removing nuisance features. Our method improves upon the naive graph Laplacian score by replacing it with a gated variant computed on a subset of low-frequency features. We identify this subset by learning the parameters of continuously relaxed Bernoulli variables, which gate the entire feature space. We mathematically motivate the proposed approach and demonstrate that it is crucial to compute the graph Laplacian on the gated inputs rather than on the full feature space in the high noise regime. Using several real-world examples, we demonstrate the efficacy and advantage of the proposed approach over leading baselines.