In real-world data analysis, missingness distributional shifts between training and test input datasets frequently occur, posing a significant challenge to achieving robust prediction performance. In this study, we propose a novel deep learning framework designed to address such shifts in missingness distributions. We begin by introducing a set of mutual information-based conditions, called MI robustness conditions, which guide a prediction model to extract label-relevant information while remaining invariant to diverse missingness patterns, thereby enhancing robustness to unseen missingness scenarios at test-time. To make these conditions practical, we propose simple yet effective techniques to derive loss terms corresponding to each and formulate a final objective function, termed MIRRAMS(Mutual Information Regularization for Robustness Against Missingness Shifts). As a by-product, our analysis provides a theoretical interpretation of the principles underlying consistency regularization-based semi-supervised learning methods, such as FixMatch. Extensive experiments across various benchmark datasets show that MIRRAMS consistently outperforms existing baselines and maintains stable performance across diverse missingness scenarios. Moreover, our approach achieves state-of-the-art performance even without missing data and can be naturally extended to address semi-supervised learning tasks, highlighting MIRRAMS as a powerful, off-the-shelf framework for general-purpose learning.

Data depths are score functions that quantify in an unsupervised fashion how central is a point inside a distribution, with numerous applications such as anomaly detection, multivariate or functional data analysis, arising across various fields. The halfspace depth was the first depth to aim at generalising the notion of quantile beyond the univariate case. Among the existing variety of depth definitions, it remains one of the most used notions of data depth. Taking a different angle from the quantile point of view, we show that the halfspace depth can also be regarded as the minimum loss of a set of classifiers for a specific labelling of the points. By changing the loss or the set of classifiers considered, this new angle naturally leads to a family of "loss depths", extending to well-studied classifiers such as, e.g., SVM or logistic regression, among others. This framework directly inherits computational efficiency of existing machine learning algorithms as well as their fast statistical convergence rates, and opens the data depth realm to the high-dimensional setting. Furthermore, the new loss depths highlight a connection between the dataset and the right amount of complexity or simplicity of the classifiers. The simplicity of classifiers as well as the interpretation as a risk makes our new kind of data depth easy to explain, yet efficient for anomaly detection, as is shown by experiments.

Accurate uncertainty quantification is critical for reliable predictive modeling, especially in regression tasks. Existing methods typically address either aleatoric uncertainty from measurement noise or epistemic uncertainty from limited data, but not necessarily both in a balanced way. We propose CLEAR, a calibration method with two distinct parameters, $γ_1$ and $γ_2$, to combine the two uncertainty components for improved conditional coverage. CLEAR is compatible with any pair of aleatoric and epistemic estimators; we show how it can be used with (i) quantile regression for aleatoric uncertainty and (ii) ensembles drawn from the Predictability-Computability-Stability (PCS) framework for epistemic uncertainty. Across 17 diverse real-world datasets, CLEAR achieves an average improvement of 28.2% and 17.4% in the interval width compared to the two individually calibrated baselines while maintaining nominal coverage. This improvement can be particularly evident in scenarios dominated by either high epistemic or high aleatoric uncertainty.

We introduce Galerkin-ARIMA, a novel time-series forecasting framework that integrates Galerkin projection techniques with the classical ARIMA model to capture potentially nonlinear dependencies in lagged observations. By replacing the fixed linear autoregressive component with a spline-based basis expansion, Galerkin-ARIMA flexibly approximates the underlying relationship among past values via ordinary least squares, while retaining the moving-average structure and Gaussian innovation assumptions of ARIMA. We derive closed-form solutions for both the AR and MA components using two-stage Galerkin projections, establish conditions for asymptotic unbiasedness and consistency, and analyze the bias-variance trade-off under basis-size growth. Complexity analysis reveals that, for moderate basis dimensions, our approach can substantially reduce computational cost compared to maximum-likelihood ARIMA estimation. Through extensive simulations on four synthetic processes-including noisy ARMA, seasonal, trend-AR, and nonlinear recursion series-we demonstrate that Galerkin-ARIMA matches or closely approximates ARIMA's forecasting accuracy while achieving orders-of-magnitude speedups in rolling forecasting tasks. These results suggest that Galerkin-ARIMA offers a powerful, efficient alternative for modeling complex time series dynamics in high-volume or real-time applications.

This paper considers the projection-free sparse convex optimization problem for the vector domain and the matrix domain, which covers a large number of important applications in machine learning and data science. For the vector domain $\mathcal{D} \subset \mathbb{R}^d$, we propose two quantum algorithms for sparse constraints that finds a $\varepsilon$-optimal solution with the query complexity of $O(\sqrt{d}/\varepsilon)$ and $O(1/\varepsilon)$ by using the function value oracle, reducing a factor of $O(\sqrt{d})$ and $O(d)$ over the best classical algorithm, respectively, where $d$ is the dimension. For the matrix domain $\mathcal{D} \subset \mathbb{R}^{d\times d}$, we propose two quantum algorithms for nuclear norm constraints that improve the time complexity to $\tilde{O}(rd/\varepsilon^2)$ and $\tilde{O}(\sqrt{r}d/\varepsilon^3)$ for computing the update step, reducing at least a factor of $O(\sqrt{d})$ over the best classical algorithm, where $r$ is the rank of the gradient matrix. Our algorithms show quantum advantages in projection-free sparse convex optimization problems as they outperform the optimal classical methods in dependence on the dimension $d$.

Emotion detection in older adults is crucial for understanding their cognitive and emotional well-being, especially in hospital and assisted living environments. In this work, we investigate an edge-based, non-obtrusive approach to emotion identification that uses only physiological signals obtained via wearable sensors. Our dataset includes data from 40 older individuals. Emotional states were obtained using physiological signals from the Empatica E4 and Shimmer3 GSR+ wristband and facial expressions were recorded using camera-based emotion recognition with the iMotion's Facial Expression Analysis (FEA) module. The dataset also contains twelve emotion categories in terms of relative intensities. We aim to study how well emotion recognition can be accomplished using simply physiological sensor data, without the requirement for cameras or intrusive facial analysis. By leveraging classical machine learning models, we predict the intensity of emotional responses based on physiological signals. We achieved the highest 0.782 r2 score with the lowest 0.0006 MSE on the regression task. This method has significant implications for individuals with Alzheimer's Disease and Related Dementia (ADRD), as well as veterans coping with Post-Traumatic Stress Disorder (PTSD) or other cognitive impairments. Our results across multiple classical regression models validate the feasibility of this method, paving the way for privacy-preserving and efficient emotion recognition systems in real-world settings.

Matching theoretical predictions to experimental data remains a central challenge in hadron spectroscopy. In particular, the identification of new hadronic states is difficult, as exotic signals near threshold can arise from a variety of physical mechanisms. A key diagnostic in this context is the pole structure of the scattering amplitude, but different configurations can produce similar signatures. The mapping between pole configurations and line shapes is especially ambiguous near the mass threshold, where analytic control is limited. In this work, we introduce an uncertainty-aware machine learning approach for classifying pole structures in $S$-matrix elements. Our method is based on an ensemble of classifier chains that provide both epistemic and aleatoric uncertainty estimates. We apply a rejection criterion based on predictive uncertainty, achieving a validation accuracy of nearly $95\%$ while discarding only a small fraction of high-uncertainty predictions. Trained on synthetic data with known pole structures, the model generalizes to previously unseen experimental data, including enhancements associated with the $P_{c\bar{c}}(4312)^+$ state observed by LHCb. In this, we infer a four-pole structure, representing the presence of a genuine compact pentaquark in the presence of a higher channel virtual state pole with non-vanishing width. While evaluated on this particular state, our framework is broadly applicable to other candidate hadronic states and offers a scalable tool for pole structure inference in scattering amplitudes.

While Prover-Verifier Games (PVGs) offer a promising path toward verifiability in nonlinear classification models, they have not yet been applied to complex inputs such as high-dimensional images. Conversely, Concept Bottleneck Models (CBMs) effectively translate such data into interpretable concepts but are limited by their reliance on low-capacity linear predictors. In this work, we introduce the Neural Concept Verifier (NCV), a unified framework combining PVGs with concept encodings for interpretable, nonlinear classification in high-dimensional settings. NCV achieves this by utilizing recent minimally supervised concept discovery models to extract structured concept encodings from raw inputs. A prover then selects a subset of these encodings, which a verifier -- implemented as a nonlinear predictor -- uses exclusively for decision-making. Our evaluations show that NCV outperforms CBM and pixel-based PVG classifier baselines on high-dimensional, logically complex datasets and also helps mitigate shortcut behavior. Overall, we demonstrate NCV as a promising step toward performative, verifiable AI.

Algorithms are the engine for reproducible problem-solving. We present a framework automating algorithm discovery by conceptualizing them as sequences of operations, represented as tokens. These computational tokens are chained using a grammar, enabling the formation of increasingly sophisticated procedures. Our ensemble Monte Carlo tree search (MCTS) guided by reinforcement learning (RL) explores token chaining and drives the creation of new tokens. This methodology rediscovers, improves, and generates new algorithms that substantially outperform existing methods for strongly NP-hard combinatorial optimization problems and foundational quantum computing approaches such as Grover's and Quantum Approximate Optimization Algorithm. Operating at the computational rather than code-generation level, our framework produces algorithms that can be tailored specifically to problem instances, not merely classes.

The primary objective of human activity recognition (HAR) is to infer ongoing human actions from sensor data, a task that finds broad applications in health monitoring, safety protection, and sports analysis. Despite proliferating research, HAR still faces key challenges, including the scarcity of labeled samples for rare activities, insufficient extraction of high-level features, and suboptimal model performance on lightweight devices. To address these issues, this paper proposes a comprehensive optimization approach centered on multi-attention interaction mechanisms. First, an unsupervised, statistics-guided diffusion model is employed to perform data augmentation, thereby alleviating the problems of labeled data scarcity and severe class imbalance. Second, a multi-branch spatio-temporal interaction network is designed, which captures multi-scale features of sequential data through parallel residual branches with 3*3, 5*5, and 7*7 convolutional kernels. Simultaneously, temporal attention mechanisms are incorporated to identify critical time points, while spatial attention enhances inter-sensor interactions. A cross-branch feature fusion unit is further introduced to improve the overall feature representation capability. Finally, an adaptive multi-loss function fusion strategy is integrated, allowing for dynamic adjustment of loss weights and overall model optimization. Experimental results on three public datasets, WISDM, PAMAP2, and OPPORTUNITY, demonstrate that the proposed unsupervised data augmentation spatio-temporal attention diffusion network (USAD) achieves accuracies of 98.84%, 93.81%, and 80.92% respectively, significantly outperforming existing approaches. Furthermore, practical deployment on embedded devices verifies the efficiency and feasibility of the proposed method.