Feature Selection

Efficient selection among multiple generative models is increasingly important in modern generative AI, where sampling from suboptimal models is costly. This problem can be viewed as a multi-armed bandit (MAB) task. Under diversity-aware evaluation scores, a non-degenerate mixture of generators can outperform any individual model, distinguishing this MAB setting from classical best-arm identification. Prior approaches incorporate an Upper Confidence Bound (UCB) exploration bonus into the mixture objective. However, across multiple datasets and evaluation metrics, we observe that the UCB term consistently slows convergence and reduces sample efficiency. In contrast, a simple Mixture-Greedy strategy without explicit UCB-type optimism converges faster and achieves even better performance, particularly for widely used metrics such as FID and Vendi where tight confidence bounds are difficult to construct. We provide theoretical insight explaining this behavior: under structural conditions, diversity-aware objectives induce implicit exploration by favoring interior mixtures, leading to sampling of all arms and sublinear regret guarantees for diversity-based objectives. These results suggest that in diversity-aware multi-armed bandits, e.g., for generative model selection, exploration can arise intrinsically from the objective's geometry.

We study model-order selection and component-mean estimation for multidimensional Gaussian mixture models with a known common covariance matrix. Using empirical characteristic-function measurements, we construct Fourier covariance matrices whose population counterparts have rank equal to the number of mixture components. We establish a minimax lower bound showing that distinguishing a separated $k$-component mixture from the class of $(k-1)$-component mixtures requires $Ω(Δ^{-(4k-4)})$ samples. We then develop an oracle spectral-thresholding estimator with a sufficient sample size of order $Δ^{-(8k-8)}$ for fixed $k$, together with a practical singular-value-ratio estimator. Given the model order, we estimate the component means by score-initialized gradient descent on a MUSIC-type projection objective. Under an explicit sample-size condition, a qualifying sample initialization lies in a certified attraction region with high probability, after which the iterates converge linearly. For fixed positive component separation, the resulting mean estimates achieve the parametric rate $\mathcal{O}_p(n^{-1/2})$. Numerical experiments demonstrate competitive accuracy and lower computational cost than expectation-maximization across a range of multidimensional settings.

Symbolic regression (SR) has gained recent traction in AI-driven scientific discovery for learning closed-form physical laws. Yet existing methods are dominated by heuristic search or data-intensive approaches that often assume low-noise regimes and lack principled uncertainty quantification, while fully probabilistic SR formulations remain scarce. We introduce a scalable probabilistic framework for SR, VaSST, based on variational inference. VaSST uses soft symbolic trees, a continuous relaxation of symbolic expression trees in which discrete operator and feature assignments are replaced by probability distributions over allowable components. This transforms combinatorial symbolic search through an astronomically large expression space into efficient gradient-based optimization while preserving a coherent probabilistic interpretation. The learned soft representations induce posterior distributions over symbolic structures, enabling uncertainty quantification across plausible symbolic forms through posterior-aware symbolic model selection. On simulated experiments and the Feynman Symbolic Regression Database, VaSST achieves strong structural recovery and predictive accuracy compared to state-of-the-art competing SR methods.

Demand forecasting is critical for inventory planning, procurement, replenishment, production, and capacity decisions in heterogeneous supply chains. However, selecting the most appropriate model for each demand series remains challenging because performance varies across datasets, demand structures, horizons, and evaluation metrics. This study proposes the Adaptive Hybrid Selector (AHS), an automatic model-selection rule that combines observed predictive performance with structural demand information. AHS uses demand frequency and series variability to activate a hierarchical logic based on RMSSE, MAE, sMAPE, and BIAS. The proposed selector is compared with Overall Weighted Average (OWA), a benchmark-relative criterion based on sMAPE and MASE, and Equilibrium Ranking Aggregation (ERA), a comparator based on MAE, RMSE, and R^2 rankings. The empirical evaluation uses the Walmart, M3, M4, and M5 datasets, three training-testing partitions, 22 forecasting models, and horizons of up to 12 cycles. Selector performance is assessed ex post using Global Relative Accuracy (GRA), interpreted as an indicator of volumetric coherence between accumulated forecasted demand and observed demand. Results show that AHS provides the most robust overall behavior, especially in M5, while OWA remains competitive in more regular datasets. ERA shows lower volumetric coherence in most configurations. These findings suggest that automatic model selection should account for demand structure and be evaluated using ex post indicators of volumetric coherence.

While open sourced Vision-Language Models (VLMs) have proliferated, selecting the optimal pretrained model for a specific downstream task remains challenging. Exhaustive evaluation is often infeasible due to computational constraints and data limitations in few shot scenarios. Existing selection methods fail to fully address this: they either rely on data-intensive proxies or use symmetric textual descriptors that neglect the inherently directional and model-specific nature of transferability. To address this problem, we propose a framework that grounds model selection in the internal functional dynamics of the visual encoder. Our approach represents each task via layer wise conductance and derives a target-conditioned block importance distribution through entropy regularized alignment. Building on this, we introduce Directional Conductance Divergence (DCD), an asymmetric metric that quantifies how effectively a source task covers the target's salient functional blocks. This allows for predicting target model rankings by aggregating source task ranks without direct inference. Experimental results on 48 VLMs across 21 datasets demonstrate that our method outperforms state-of-the-art baselines, achieving a 14.7% improvement in NDCG@5 over SWAB.

Feature selection (FS) is essential for biomarker discovery and clinical predictive modeling. Over the past decades, methodological literature on FS has become rich and mature, offering a wide spectrum of algorithmic approaches. However, much of this methodological progress has not fully translated into applied biomedical research. Moreover, challenges inherent in biomedical data, such as high-dimensional feature space, low sample size, multicollinearity, and missing values, make FS non-trivial. To help bridge this gap between methodological development and practical application, we propose ROOFS (RObust biOmarker Feature Selection), a Python package available at https://gitlab.inria.fr/compo/roofs, designed to help researchers in the choice of FS method adapted to their problem. ROOFS benchmarks multiple FS methods on the user's data and generates reports summarizing a comprehensive set of evaluation metrics, including downstream predictive performance estimated using optimism correction, stability, robustness of individual features, and true positive and false positive rates assessed on semi-synthetic data with a simulated outcome. We demonstrate the utility of ROOFS on data from the PIONeeR clinical trial, aimed at identifying predictors of resistance to anti-PD-(L)1 immunotherapy in lung cancer. Of the 34 FS methods gathered in ROOFS, we evaluated 23 in combination with 11 classifiers (253 models) and identified a filter based on the union of Benjamini-Hochberg false discovery rate-adjusted p-values from t-test and logistic regression as the optimal approach, outperforming other methods including widely used LASSO. We conclude that comprehensive benchmarking with ROOFS has the potential to improve the reproducibility of FS discoveries and increase the translational value of clinical models.

In many machine learning problems, there may exist multiple models that achieve nearly identical predictive performance while relying on fundamentally different internal logic. However, standard training procedures produce a single model, offering no practical way to explore alternatives that may better suit downstream needs. The set of these equally accurate models is known as the Rashomon set. Exploring the Rashomon set is particularly challenging in large and complex hypothesis spaces, such as Concept Bottleneck Models (CBMs), which are widely used in computer vision to make predictions through intermediate, human-understandable concepts. In this paper, we provide a method for efficiently exploring the Rashomon set of CBMs. Our framework introduces a specialized parallel parameter-efficient adaptation module, combined with a checkpointing scheme and a concept diversity objective, to generate multiple equally accurate CBMs from a single training process. Empirical results show that our method finds models with better diversity than baselines while using much less memory. We further demonstrate that access to these diverse yet accurate CBMs enables trustworthy model selection, resolution of inter-class confusion, and reliable abstention in decision-making.

Assessing the importance of individual features in Machine Learning is critical to understand the model's decision-making process. While numerous methods exist, the lack of a definitive ground truth for comparison highlights the need for alternative, well-founded measures. This paper introduces a novel post-hoc local feature importance method called Counterfactual Importance Distribution (CID). We generate two sets of positive and negative counterfactuals, model their distributions using Kernel Density Estimation, and rank features based on a distributional dissimilarity measure. This measure, grounded in a rigorous mathematical framework, satisfies key properties required to function as a valid metric. We showcase the effectiveness of our method by comparing with well-established local feature importance explainers. Our method not only offers complementary perspectives to existing approaches, but also improves performance on faithfulness metrics (both for comprehensiveness and sufficiency), resulting in more faithful explanations of the system. These results highlight its potential as a valuable tool for model analysis. Link to repository: https://github.com/EddieConti/CID

We revisit Cox's proportional hazards model to improve variable selection in survival analysis. A square-root transformation of the partial likelihood renders the selection of the regularization parameter pivotal, free of the unknown baseline hazard and censoring mechanism. The resulting criterion borrows from information criteria such as BIC and from penalized regression methods such as the lasso, taking the best of both. On simulated and real data, our method substantially improves upon state-of-the-art approaches used daily in support recovery.

We study the problem of fair cohort selection under uncertainty, motivated by university admissions where applicant outcomes are only partially observed. We consider both a one-shot setting, where a fixed policy is applied to a population, and a sequential setting, where policies are updated over time using data from previous admission years. We propose a policy optimization framework that combines probabilistic modeling of outcomes with policy gradient methods, supporting both logistic and neural network policies. In the sequential setting, the approach jointly updates the policy and the underlying models to adapt to evolving applicant populations. Experiments on a simulator grounded in real admission data show that adaptive policies substantially outperform static baselines in term of expected utility, especially under higher admission costs. Neural policies consistently achieve higher utility and adapt more effectively than simpler models, while maintaining favorable fairness properties over time. Our results demonstrate the importance of adaptivity and model expressiveness for decision-making under uncertainty.

Unsupervised feature selection is critical for improving clustering performance in high-dimensional data, where irrelevant features can obscure meaningful structure. In this work, we propose the Minkowski weighted $k$-means++, a novel initialisation strategy for the Minkowski Weighted $k$-means. Our initialisation selects centroids probabilistically using feature relevance estimates derived from the data itself. Building on this, we propose two new feature selection algorithms, FS-MWK++, which aggregates feature weights across a range of Minkowski exponents identifying stable and informative features, and SFS-MWK++, a scalable variant based on subsampling. We support our approach with a theoretical analysis, demonstrating that, under explicit assumptions on noise features and cluster structure, relevant features are assigned consistently higher weights than noise features across a range of Minkowski exponents. Our software can be found at https://github.com/xzhang4-ops1/FSMWK.

In this paper, we study the problem of learning one-dimensional Gaussian mixture models (GMMs) with a specific focus on estimating both the model order and the mixing distribution from independent and identically distributed (i.i.d.) samples. This paper establishes the optimal sampling complexity for model order estimation in one-dimensional Gaussian mixture models. We prove a fundamental lower bound on the number of samples required to correctly identify the number of components with high probability, showing that this limit depends critically on the separation between component means and the total number of components. We then propose a Fourier-based approach to estimate both the model order and the mixing distribution. Our algorithm utilizes Fourier measurements constructed from the samples, and our analysis demonstrates that its sample complexity matches the established lower bound, thereby confirming its optimality. Numerical experiments further show that our method outperforms conventional techniques in terms of efficiency and accuracy.

Fetal health classification is a critical task in obstetrics, enabling early identification and management of potential health problems. However, it remains challenging due to data complexity and limited labeled samples. This research paper presents a novel machine-learning approach for fetal health classification, leveraging a LightGBM classifier trained on a comprehensive dataset. The proposed model achieves an impressive accuracy of 98.31% on a test set. Our findings demonstrate the potential of machine learning in enhancing fetal health classification, offering a more objective and accurate assessment. Notably, our approach combines various features, such as fetal heart rate, uterine contractions, and maternal blood pressure, to provide a comprehensive evaluation. This methodology holds promise for improving early detection and treatment of fetal health issues, ensuring better outcomes for both mothers and babies. Beyond the high accuracy achieved, the novelty of our approach lies in its comprehensive feature selection and assessment methodology. By incorporating multiple data points, our model offers a more holistic and reliable evaluation compared to traditional methods. This research has significant implications in the field of obstetrics, paving the way for advancements in early detection and intervention of fetal health concerns. Future work involves validating the model on a larger dataset and developing a clinical application. Ultimately, we anticipate that our research will revolutionize the assessment and management of fetal health, contributing to improved healthcare outcomes for expectant mothers and their babies.

Cross-validation is one of the most widely used tools for risk estimation and model selection in statistics and machine learning, yet its theoretical properties when embedded in a learning procedure remain insufficiently understood. This paper develops a general, distribution-free framework for learning via model selection with cross-validation risk estimation within classical statistical learning theory. We establish VC dimension-based deviation bounds for the entire learning pipeline, providing detailed proofs for both bounded and unbounded loss functions, the latter requiring a novel extension of existing results. A central focus of the analysis is how the structure of the collection of candidate models influences generalization. To this end, we introduce Learning Spaces as collections of candidate models equipped with a partial order whose inclusion structure reflects increasing model complexity. We show how Learning Spaces can be constructed from domain knowledge and analyze how such structural information increases generalization. The framework is illustrated through case studies and a simulation study in high-dimensional linear regression, comparing learning via model selection in two distinct Learning Spaces against ordinary least squares, LASSO, and ridge regression across scenarios of varying alignment between prior knowledge and the true target. The results demonstrate that, when the Learning Space is well-adapted to the target and an efficient search algorithm is employed, learning via model selection can outperform standard methods by orders of magnitude. Through theoretical insights and concrete examples, we provide guidance on selecting the family of candidate models based on domain knowledge to enhance the performance of model selection with cross-validation.

Mixtures of experts (MoE) are conditional mixture models in which both the mixing proportions and the component densities depend on the predictors, and are widely used for regression, classification and model-based clustering of heterogeneous data. Fitting MoE by maximum likelihood becomes unstable, and sometimes infeasible, when the predictors are numerous or correlated. We propose a regularized maximum likelihood framework for simultaneous parameter estimation and feature selection in MoE whose experts belong to the generalized linear model family, covering Gaussian, Poisson and multinomial responses within a single formulation. Sparsity is induced in both the gating network and the experts through $\ell_1$ penalties, and the penalized log-likelihood is maximized by a proximal Newton-EM algorithm whose M-step reduces to weighted Lasso problems with closed-form coordinate-ascent updates. Unlike existing penalized MoE procedures, the algorithm requires neither a local quadratic approximation of the penalty nor any matrix inversion, it returns exactly sparse estimates without thresholding, and a proximal Newton-type variant guarantees a monotone increase of the penalized objective at every iteration. On simulated data and five real data sets, the method recovers the actual sparsity support and delivers prediction and clustering accuracy that is competitive with, and often better than, state-of-the-art regularized MoE. The source codes of our developed algorithms and their documentation are publicly available on Github at https://github.com/nv-thin/GLM-RMoE.

There is growing interest in using machine learning (ML) to support clinical diagnosis, but most approaches rely on static, fully observed datasets and fail to reflect the sequential, resource-aware reasoning clinicians use in practice. Diagnosis remains complex and error prone, especially in high-pressure or resource-limited settings, underscoring the need for frameworks that help clinicians make timely and cost-effective decisions. We propose ACTMED (Adaptive Clinical Test selection via Model-based Experimental Design), a diagnostic framework that integrates Bayesian Experimental Design (BED) with large language models (LLMs) to better emulate real-world diagnostic reasoning. At each step, ACTMED selects the test expected to yield the greatest reduction in diagnostic uncertainty for a given patient. LLMs act as flexible simulators, generating plausible patient state distributions and supporting belief updates without requiring structured, task-specific training data. Clinicians can remain in the loop; reviewing test suggestions, interpreting intermediate outputs, and applying clinical judgment throughout. We evaluate ACTMED on real-world datasets and show it can optimize test selection to improve diagnostic accuracy, interpretability, and resource use. This represents a step toward transparent, adaptive, and clinician-aligned diagnostic systems that generalize across settings with reduced reliance on domain-specific data.