Explainable machine learning aims to strike a balance between prediction accuracy and model transparency, particularly in settings where black-box predictive models, such as deep neural networks or kernel-based methods, achieve strong empirical performance but remain difficult to interpret. This work introduces a mixture of generalized additive models (GAMs) in which random Fourier feature (RFF) representations are leveraged to uncover locally adaptive structure in the data. In the proposed method, an RFF-based embedding is first learned and then compressed via principal component analysis. The resulting low-dimensional representations are used to perform soft clustering of the data through a Gaussian mixture model. These cluster assignments are then applied to construct a mixture-of-GAMs framework, where each local GAM captures nonlinear effects through interpretable univariate smooth functions. Numerical experiments on real-world regression benchmarks, including the California Housing, NASA Airfoil Self-Noise, and Bike Sharing datasets, demonstrate improved predictive performance relative to classical interpretable models. Overall, this construction provides a principled approach for integrating representation learning with transparent statistical modeling.

We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{á}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions obtained as level sets of a real-valued function. This loss function allows optimal trade-offs between conditional probabilistic coverage and the ''size'' of the set, measured by a non-decreasing submodular function. We also propose several extensions that mimic loss functions and criteria for binary classification with asymmetric losses, and show how to naturally obtain sets with optimized conditional coverage. We derive efficient optimization algorithms, either based on stochastic gradient descent or reweighted least-squares formulations, and illustrate our findings with a series of experiments on synthetic datasets for classification and regression tasks, showing improvements over approaches that aim for marginal coverage.

Effective feature selection is essential for high-dimensional data analysis and machine learning. Unsupervised feature selection (UFS) aims to simultaneously cluster data and identify the most discriminative features. Most existing UFS methods linearly project features into a pseudo-label space for clustering, but they suffer from two critical limitations: (1) an oversimplified linear mapping that fails to capture complex feature relationships, and (2) an assumption of uniform cluster distributions, ignoring outliers prevalent in real-world data. To address these issues, we propose the Robust Autoencoder-based Unsupervised Feature Selection (RAEUFS) model, which leverages a deep autoencoder to learn nonlinear feature representations while inherently improving robustness to outliers. We further develop an efficient optimization algorithm for RAEUFS. Extensive experiments demonstrate that our method outperforms state-of-the-art UFS approaches in both clean and outlier-contaminated data settings.

Transformers can implement both generalizable algorithms (e.g., induction heads) and simple positional shortcuts (e.g., memorizing fixed output positions). In this work, we study how the choice of pretraining data distribution steers a shallow transformer toward one behavior or the other. Focusing on a minimal trigger-output prediction task -- copying the token immediately following a special trigger upon its second occurrence -- we present a rigorous analysis of gradient-based training of a single-layer transformer. In both the infinite and finite sample regimes, we prove a transition in the learned mechanism: if input sequences exhibit sufficient diversity, measured by a low ``max-sum'' ratio of trigger-to-trigger distances, the trained model implements an induction head and generalizes to unseen contexts; by contrast, when this ratio is large, the model resorts to a positional shortcut and fails to generalize out-of-distribution (OOD). We also reveal a trade-off between the pretraining context length and OOD generalization, and derive the optimal pretraining distribution that minimizes computational cost per sample. Finally, we validate our theoretical predictions with controlled synthetic experiments, demonstrating that broadening context distributions robustly induces induction heads and enables OOD generalization. Our results shed light on the algorithmic biases of pretrained transformers and offer conceptual guidelines for data-driven control of their learned behaviors.

We study the problem of deciding whether, and when an organization should replace a trained incumbent model with a challenger relying on newly available features. We develop a unified economic and statistical framework that links learning-curve dynamics, data-acquisition and retraining costs, and discounting of future gains. First, we characterize the optimal switching time in stylized settings and derive closed-form expressions that quantify how horizon length, learning-curve curvature, and cost differentials shape the optimal decision. Second, we propose three practical algorithms--a one-shot baseline, a greedy sequential method, and a look-ahead sequential method. Using a real-world credit-scoring dataset with gradually arriving alternative data, we show that (i) optimal switching times vary systematically with cost parameters and learning-curve behavior, and (ii) the look-ahead sequential method outperforms other methods and is able to approach in value an oracle with full foresight. Finally, we establish finite-sample guarantees, including conditions under which the sequential look-ahead method achieve sublinear regret relative to that oracle. Our results provide an operational blueprint for economically sound model transitions as new data sources become available.

Survival analysis is a critical tool for modeling time-to-event data. Recent deep learning-based models have reduced various modeling assumptions including proportional hazard and linearity. However, a persistent challenge remains in incorporating longitudinal covariates, with prior work largely focusing on cross-sectional features, and in assessing calibration of these models, with research primarily focusing on discrimination during evaluation. We introduce TraCeR, a transformer-based survival analysis framework for incorporating longitudinal covariates. Based on a factorized self-attention architecture, TraCeR estimates the hazard function from a sequence of measurements, naturally capturing temporal covariate interactions without assumptions about the underlying data-generating process. The framework is inherently designed to handle censored data and competing events. Experiments on multiple real-world datasets demonstrate that TraCeR achieves substantial and statistically significant performance improvements over state-of-the-art methods. Furthermore, our evaluation extends beyond discrimination metrics and assesses model calibration, addressing a key oversight in literature.

Learned time-series models, whether continuous-or discrete-time, are widely used to forecast the states of a dynamical system. Such models generate multi-step forecasts either directly, by predicting the full horizon at once, or iteratively, by feeding back their own predictions at each step. In both cases, the multi-step forecasts are prone to errors. To address this, we propose a Predictor-Corrector mechanism where the Predictor is any learned time-series model and the Corrector is a neural controlled differential equation. The Predictor forecasts, and the Corrector predicts the errors of the forecasts. Adding these errors to the forecasts improves forecast performance. The proposed Corrector works with irregularly sampled time series and continuous-and discrete-time Predictors. Additionally, we introduce two regularization strategies to improve the extrapolation performance of the Corrector with accelerated training. We evaluate our Corrector with diverse Predictors, e.g., neural ordinary differential equations, Contiformer, and DLinear, on synthetic, physics simulation, and real-world forecasting datasets. The experiments demonstrate that the Predictor-Corrector mechanism consistently improves the performance compared to Predictor alone. Learning time-series models from such datasets has applications ranging from energy demand forecasting, traffic and mobility prediction, weather prediction, anomaly detection, and decision-making in robotics (Zeng et al., 2022; Li et al., 2017; Stankeviciute et al., 2021; Xu et al., 2021; Chua et al., 2018). Several works focused on learning time-series models from data. There are at least two ways to train such models. Early studies focused on training the model to predict one step ahead (Basharat & Shah, 2009; Khansari-Zadeh & Billard, 2011).

Conformal prediction (CP) provides distribution-free, finite-sample coverage guarantees but critically relies on exchangeability, a condition often violated under distribution shift. We study the robustness of split conformal prediction under adversarial perturbations at test time, focusing on both coverage validity and the resulting prediction set size. Our theoretical analysis characterizes how the strength of adversarial perturbations during calibration affects coverage guarantees under adversarial test conditions. We further examine the impact of adversarial training at the model-training stage. Extensive experiments support our theory: (i) Prediction coverage varies monotonically with the calibration-time attack strength, enabling the use of nonzero calibration-time attack to predictably control coverage under adversarial tests; (ii) target coverage can hold over a range of test-time attacks: with a suitable calibration attack, coverage stays within any chosen tolerance band across a contiguous set of perturbation levels; and (iii) adversarial training at the training stage produces tighter prediction sets that retain high informativeness.

Novo Nordisk's semaglutide will soon be available in a daily pill Americans can take for weight loss. The US Food and Drug Administration today approved a pill version of the blockbuster anti-obesity drug Wegovy. Made by Novo Nordisk, the pill is taken once a day. The company's original version of Wegovy is a weekly injection. Both drugs contain the same active ingredient, semaglutide.

Vince Zampella, who co-created the widely-popular video game Call of Duty, has died in a single-vehicle Ferrari crash in California, aged 55. Zampella's death was confirmed by Electronic Arts, which owns Respawn Entertainment, a game studio he co-founded. This is an unimaginable loss, and our hearts are with Vince's family, his loved ones, and all those touched by his work, a spokesperson for Electronic Arts told the BBC. Officials said the person on the vehicle's passenger seat was ejected while the driver remained trapped. It is unclear if Zampella was driving the car.