Degeneracy is an inherent feature of the loss landscape of neural networks, but it is not well understood how stochastic gradient MCMC (SGMCMC) algorithms interact with this degeneracy. In particular, current global convergence guarantees for common SGMCMC algorithms rely on assumptions which are likely incompatible with degenerate loss landscapes. In this paper, we argue that this gap requires a shift in focus from global to local posterior sampling, and, as a first step, we introduce a novel scalable benchmark for evaluating the local sampling performance of SGMCMC algorithms. We evaluate a number of common algorithms, and find that RMSProp-preconditioned SGLD is most effective at faithfully representing the local geometry of the posterior distribution. Although we lack theoretical guarantees about global sampler convergence, our empirical results show that we are able to extract non-trivial local information in models with up to O(100M) parameters.

Tree ensembles are non-parametric methods widely recognized for their accuracy and ability to capture complex interactions. While these models excel at prediction, they are difficult to interpret and may fail to uncover useful relationships in the data. We propose an estimator to extract compact sets of decision rules from tree ensembles. The extracted models are accurate and can be manually examined to reveal relationships between the predictors and the response. A key novelty of our estimator is the flexibility to jointly control the number of rules extracted and the interaction depth of each rule, which improves accuracy. We develop a tailored exact algorithm to efficiently solve optimization problems underlying our estimator and an approximate algorithm for computing regularization paths, sequences of solutions that correspond to varying model sizes. We also establish novel non-asymptotic prediction error bounds for our proposed approach, comparing it to an oracle that chooses the best data-dependent linear combination of the rules in the ensemble subject to the same complexity constraint as our estimator. The bounds illustrate that the large-sample predictive performance of our estimator is on par with that of the oracle. Through experiments, we demonstrate that our estimator outperforms existing algorithms for rule extraction.

We demonstrate how Quantum Cognition Machine Learning (QCML) encodes data as quantum geometry. In QCML, features of the data are represented by learned Hermitian matrices, and data points are mapped to states in Hilbert space. The quantum geometry description endows the dataset with rich geometric and topological structure - including intrinsic dimension, quantum metric, and Berry curvature - derived directly from the data. QCML captures global properties of data, while avoiding the curse of dimensionality inherent in local methods. We illustrate this on a number of synthetic and real-world examples. Quantum geometric representation of QCML could advance our understanding of cognitive phenomena within the framework of quantum cognition.

We develop a unified Data Processing Inequality PAC-Bayesian framework -- abbreviated DPI-PAC-Bayesian -- for deriving generalization error bounds in the supervised learning setting. By embedding the Data Processing Inequality (DPI) into the change-of-measure technique, we obtain explicit bounds on the binary Kullback-Leibler generalization gap for both Rényi divergence and any $f$-divergence measured between a data-independent prior distribution and an algorithm-dependent posterior distribution. We present three bounds derived under our framework using Rényi, Hellinger \(p\) and Chi-Squared divergences. Additionally, our framework also demonstrates a close connection with other well-known bounds. When the prior distribution is chosen to be uniform, our bounds recover the classical Occam's Razor bound and, crucially, eliminate the extraneous \(\log(2\sqrt{n})/n\) slack present in the PAC-Bayes bound, thereby achieving tighter results. The framework thus bridges data-processing and PAC-Bayesian perspectives, providing a flexible, information-theoretic tool to construct generalization guarantees.

This paper proposes a machine learning-based approach for identifying honey floral and geographical sources using mineral element profiles. The proposed method comprises two steps: preprocessing and classification. The preprocessing phase involves missing-value treatment and data normalization. In the classification phase, we employ various supervised classification models for discriminating between six botanical sources and 13 geographical origins of honey. We test the classifiers' performance on a publicly available honey mineral element dataset. The dataset contains mineral element profiles of honeys from various floral and geographical origins. Results show that mineral element content in honey provides discriminative information useful for classifying honey botanical and geographical sources. Results also show that the Random Forests (RF) classifier obtains the best performance on this dataset, achieving a cross-validation accuracy of 99.30% for classifying honey botanical origins and 98.01% for classifying honey geographical origins.

We introduce new methods of staining and locking computer vision models, to protect their owners' intellectual property. Staining, also known as watermarking, embeds secret behaviour into a model which can later be used to identify it, while locking aims to make a model unusable unless a secret trigger is inserted into input images. Unlike existing methods, our algorithms can be used to stain and lock pre-trained models without requiring fine-tuning or retraining, and come with provable, computable guarantees bounding their worst-case false positive rates. The stain and lock are implemented by directly modifying a small number of the model's weights and have minimal impact on the (unlocked) model's performance. Locked models are unlocked by inserting a small `trigger patch' into the corner of the input image. We present experimental results showing the efficacy of our methods and demonstrating their practical performance on a variety of computer vision models.

-- Cardiovascular diseases (CVDs) are a main cause of mortality globally, accounting for 31% of all deaths. This study involves a cardiovascular disease (CVD) dataset comprising 68,119 records to explore the influence of numerical (age, height, weight, blood pressure, BMI) and categorical gender, cholesterol, glucose, smoking, alcohol, activity) factors on CVD occurrence. We have performed statistical analyses, including t - tests, Chi - square tests, and ANOVA, to identify strong associations between CVD and elde rly people, hypertension, higher weight, and abnormal cholesterol levels, while physical activity (a protective factor). A logistic regression model highlights age, blood pressure, and cholesterol as primary risk factors, with unexpected negative associati ons for smoking and alcohol, suggesting potential data issues. Model performance comparisons reveal CatBoost as the top performer with an accuracy of 0.734 and an ECE of 0.0064 and excels in probabilistic prediction (Brier score = 0.1824). Data challenges, including outliers and skewed distributions, indicate a need for improved preprocessing to enhance predictive reliability. Cardiovascular diseases (CVDs) encompass a range of conditions affecting the heart and blood vessels, including coronary heart disease, stroke, and heart failure.

The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often result in models that lack physical meaning and interpretability, let alone represent the true physics of the system. We propose an unsupervised parameter estimation methodology that first finds an approximate general solution, followed by a spline transformation to linearly estimate the coefficients of the governing ordinary differential equation (ODE). The approximate general solution is postulated using the same functional form as the analytical solution of a general homogeneous, linear, constant-coefficient ODE. An added advantage is its ability to produce a high-fidelity, smooth functional form even in the presence of noisy data. The spline approximation obtains gradient information from the functional form which are linearly independent and creates the basis of the gradient matrix. This gradient matrix is used in a linear system to find the coefficients of the ODEs. From the case studies, we observed that our modeling approach discovers ODEs with high accuracy and also promotes sparsity in the solution without using any regularization techniques. The methodology is also robust to noisy data and thus allows the integration of data-driven techniques into real experimental setting for data-driven learning of physical phenomena.

The empirical success of deep learning has spurred its application to the radio-frequency (RF) domain, leading to significant advances in Deep Wireless Sensing (DWS). However, most existing DWS models function as black boxes with limited interpretability, which hampers their generalizability and raises concerns in security-sensitive physical applications. In this work, inspired by the remarkable advances of white-box transformers, we present RF-CRATE, the first mathematically interpretable deep network architecture for RF sensing, grounded in the principles of complex sparse rate reduction. To accommodate the unique RF signals, we conduct non-trivial theoretical derivations that extend the original real-valued white-box transformer to the complex domain. By leveraging the CR-Calculus framework, we successfully construct a fully complex-valued white-box transformer with theoretically derived self-attention and residual multi-layer perceptron modules. Furthermore, to improve the model's ability to extract discriminative features from limited wireless data, we introduce Subspace Regularization, a novel regularization strategy that enhances feature diversity, resulting in an average performance improvement of 19.98% across multiple sensing tasks. We extensively evaluate RF-CRATE against seven baselines with multiple public and self-collected datasets involving different RF signals. The results show that RF-CRATE achieves performance on par with thoroughly engineered black-box models, while offering full mathematical interpretability. More importantly, by extending CRATE to the complex domain, RF-CRATE yields substantial improvements, achieving an average classification gain of 5.08% and reducing regression error by 10.34% across diverse sensing tasks compared to CRATE. RF-CRATE is fully open-sourced at: https://github.com/rfcrate/RF_CRATE.

The performance of predictive models in clinical settings often degrades when deployed in new hospitals due to distribution shifts. This paper presents a large-scale study of causality-inspired domain generalization on heterogeneous multi-center intensive care unit (ICU) data. We apply anchor regression and introduce anchor boosting, a novel, tree-based nonlinear extension, to a large dataset comprising 400,000 patients from nine distinct ICU databases. The anchor regularization consistently improves out-of-distribution performance, particularly for the most dissimilar target domains. The methods appear robust to violations of theoretical assumptions, such as anchor exogeneity. Furthermore, we propose a novel conceptual framework to quantify the utility of large external data datasets. By evaluating performance as a function of available target-domain data, we identify three regimes: (i) a domain generalization regime, where only the external model should be used, (ii) a domain adaptation regime, where refitting the external model is optimal, and (iii) a data-rich regime, where external data provides no additional value.