Some of the simplest, yet most frequently used predictors in statistics and machine learning use weighted linear combinations of features. Such linear predictors can model non-linear relationships between features by adding interaction terms corresponding to the products of all pairs of features. We consider the problem of accurately estimating coefficients for interaction terms in linear predictors. We hypothesize that the coefficients for different interaction terms have an approximate low-dimensional structure and represent each feature by a latent vector in a low-dimensional space. This low-dimensional representation can be viewed as a structured regularization approach that further mitigates overfitting in high-dimensional settings beyond standard regularizers such as the lasso and elastic net. We demonstrate that our approach, called LIT-LVM, achieves superior prediction accuracy compared to elastic net and factorization machines on a wide variety of simulated and real data, particularly when the number of interaction terms is high compared to the number of samples. LIT-LVM also provides low-dimensional latent representations for features that are useful for visualizing and analyzing their relationships.

Theoretically understanding stochastic gradient descent (SGD) in overparameterized models has led to the development of several optimization algorithms that are widely used in practice today. Recent work by Zou et al. [2021] provides sharp rates for SGD optimization in linear regression using constant learning rate, both with and without tail iterate averaging, based on a bias-variance decomposition of the risk. In our work, we provide a simplified analysis recovering the same bias and variance bounds provided in [Zou et al., 2021] based on simple linear algebra tools, bypassing the requirement to manipulate operators on positive semi-definite (PSD) matrices. We believe our work makes the analysis of SGD on linear regression very accessible and will be helpful in further analyzing mini-batching and learning rate scheduling, leading to improvements in the training of realistic models. We use bolded small letters for vectors and bolded capital letters for matrices, and we use 1 for a vector of ones.

Clinical laboratory results are ubiquitous in any diagnosis making. Predicting abnormal values of not prescribed tests based on the results of performed tests looks intriguing, as it would be possible to make early diagnosis available to everyone. The special place is taken by the Common Blood Count (CBC) test, as it is the most widely used clinical procedure. Combining routine biochemical panels with CBC presents a set of test-value pairs that varies from patient to patient, or, in common settings, a table with missing values. Here we formulate a tabular modeling problem as a set translation problem where the source set comprises pairs of GPT-like label column embedding and its corresponding value while the target set consists of the same type embeddings only. The proposed approach can effectively deal with missing values without implicitly estimating them and bridges the world of LLM with the tabular domain. Applying this method to clinical laboratory data, we achieve an improvement up to 8% AUC for joint predictions of high uric acid, glucose, cholesterol, and low ferritin levels.

Accurate prediction of anthropometric body composition variables, such as Appendicular Lean Mass (ALM), Body Fat Percentage (BFP), and Bone Mineral Density (BMD), is essential for early diagnosis of several chronic diseases. Currently, researchers rely on Dual-Energy X-ray Absorptiometry (DXA) scans to measure these metrics; however, DXA scans are costly and time-consuming. This work proposes an alternative to DXA scans by applying statistical and machine learning models on biomarkers (height, volume, left calf circumference, etc) obtained from 3D optical images. The dataset consists of 847 patients and was sourced from Pennington Biomedical Research Center. Extracting patients' data in healthcare faces many technical challenges and legal restrictions. However, most supervised machine learning algorithms are inherently data-intensive, requiring a large amount of training data. To overcome these limitations, we implemented a semi-supervised model, the $p$-Laplacian regression model. This paper is the first to demonstrate the application of a $p$-Laplacian model for regression. Our $p$-Laplacian model yielded errors of $\sim13\%$ for ALM, $\sim10\%$ for BMD, and $\sim20\%$ for BFP when the training data accounted for 10 percent of all data. Among the supervised algorithms we implemented, Support Vector Regression (SVR) performed the best for ALM and BMD, yielding errors of $\sim 8\%$ for both, while Least Squares SVR performed the best for BFP with $\sim 11\%$ error when trained on 80 percent of the data. Our findings position the $p$-Laplacian model as a promising tool for healthcare applications, particularly in a data-constrained environment.

Patent claims define the scope of protection for an invention. If there are ambiguities in a claim, it is rejected by the patent office. In the US, this is referred to as indefiniteness (35 U.S.C § 112(b)) and is among the most frequent reasons for patent application rejection. The development of automatic methods for patent definiteness examination has the potential to make patent drafting and examination more efficient, but no annotated dataset has been published to date. We introduce PEDANTIC (Patent Definiteness Examination Corpus), a novel dataset of 14k US patent claims from patent applications relating to Natural Language Processing (NLP), annotated with reasons for indefiniteness. We construct PEDANTIC using a fully automatic pipeline that retrieves office action documents from the USPTO and uses Large Language Models (LLMs) to extract the reasons for indefiniteness. A human validation study confirms the pipeline's accuracy in generating high-quality annotations. To gain insight beyond binary classification metrics, we implement an LLM-as-Judge evaluation that compares the free-form reasoning of every model-cited reason with every examiner-cited reason. We show that LLM agents based on Qwen 2.5 32B and 72B struggle to outperform logistic regression baselines on definiteness prediction, even though they often correctly identify the underlying reasons. PEDANTIC provides a valuable resource for patent AI researchers, enabling the development of advanced examination models. We will publicly release the dataset and code.

Existing analysis of Local (Stochastic) Gradient Descent for heterogeneous objectives requires stepsizes $η\leq 1/K$ where $K$ is the communication interval, which ensures monotonic decrease of the objective. In contrast, we analyze Local Gradient Descent for logistic regression with separable, heterogeneous data using any stepsize $η> 0$. With $R$ communication rounds and $M$ clients, we show convergence at a rate $\mathcal{O}(1/ηK R)$ after an initial unstable phase lasting for $\widetilde{\mathcal{O}}(ηK M)$ rounds. This improves upon the existing $\mathcal{O}(1/R)$ rate for general smooth, convex objectives. Our analysis parallels the single machine analysis of~\cite{wu2024large} in which instability is caused by extremely large stepsizes, but in our setting another source of instability is large local updates with heterogeneous objectives.

Gallstone disease is a complex, multifactorial condition with significant global health burdens. Identifying underlying risk factors and their interactions is crucial for early diagnosis, targeted prevention, and effective clinical management. Although logistic regression remains a standard tool for assessing associations between predictors and gallstone status, it often underperforms in high-dimensional settings and may fail to capture intricate relationships among variables. To address these limitations, we propose a hybrid machine learning framework that integrates robust variable selection with advanced interaction detection. Specifically, Adaptive LASSO is employed to identify a sparse and interpretable subset of influential features, followed by Bayesian Additive Regression Trees (BART) to model nonlinear effects and uncover key interactions. Selected interactions are further characterized by physiological knowledge through differential equation-informed interaction terms, grounding the model in biologically plausible mechanisms. The insights gained from these steps are then integrated into a final logistic regression model within a Bayesian framework, providing a balance between predictive accuracy and clinical interpretability. This proposed framework not only enhances prediction but also yields actionable insights, offering a valuable support tool for medical research and decision-making.

There is growing interest in extending average treatment effect (ATE) estimation to incorporate non-tabular data, such as images and text, which may act as sources of confounding. Neglecting these effects risks biased results and flawed scientific conclusions. However, incorporating non-tabular data necessitates sophisticated feature extractors, often in combination with ideas of transfer learning. In this work, we investigate how latent features from pre-trained neural networks can be leveraged to adjust for sources of confounding. We formalize conditions under which these latent features enable valid adjustment and statistical inference in ATE estimation, demonstrating results along the example of double machine learning. We discuss critical challenges inherent to latent feature learning and downstream parameter estimation arising from the high dimensionality and non-identifiability of representations. Common structural assumptions for obtaining fast convergence rates with additive or sparse linear models are shown to be unrealistic for latent features. We argue, however, that neural networks are largely insensitive to these issues. In particular, we show that neural networks can achieve fast convergence rates by adapting to intrinsic notions of sparsity and dimension of the learning problem.

We address the regression problem under the constraint of demographic parity, a commonly used fairness definition. Recent studies have revealed fair minimax optimal regression algorithms, the most accurate algorithms that adhere to the fairness constraint. However, these analyses are tightly coupled with specific data generation models. In this paper, we provide meta-theorems that can be applied to various situations to validate the fair minimax optimality of the corresponding regression algorithms. Furthermore, we demonstrate that fair minimax optimal regression can be achieved through post-processing methods, allowing researchers and practitioners to focus on improving conventional regression techniques, which can then be efficiently adapted for fair regression.

Diabetes is a chronic metabolic disease characterized by elevated blood glucose levels, leading to complications like heart disease, kidney failure, and nerve damage. Accurate state-level predictions are vital for effective healthcare planning and targeted interventions, but in many cases, data for necessary analyses are incomplete. This study begins with a data engineering process to integrate diabetes-related datasets from 2011 to 2021 to create a comprehensive feature set. We then introduce an enhanced bagging ensemble regression model (EBMBag+) for time series forecasting to predict diabetes prevalence across U.S. cities. Several baseline models, including SVMReg, BDTree, LSBoost, NN, LSTM, and ERMBag, were evaluated for comparison with our EBMBag+ algorithm. The experimental results demonstrate that EBMBag+ achieved the best performance, with an MAE of 0.41, RMSE of 0.53, MAPE of 4.01, and an R2 of 0.9.