In many business settings, task-specific labeled data are scarce or costly to obtain, which limits supervised learning on a specific task. To address this challenge, we study sample sharing in the case of ridge regression: leveraging an auxiliary data set while explicitly protecting against negative transfer. We introduce a principled, data-driven rule that decides how many samples from an auxiliary dataset to add to the target training set. The rule is based on an estimate of the transfer gain i.e. the marginal reduction in the predictive error. Building on this estimator, we derive finite-sample guaranties: under standard conditions, the procedure borrows when it improves parameter estimation and abstains otherwise. In the Gaussian feature setting, we analyze which data set properties ensure that borrowing samples reduces the predictive error. We validate the approach in synthetic and real datasets, observing consistent gains over strong baselines and single-task training while avoiding negative transfer.

In social sciences, small- to medium-scale datasets are common and linear regression (LR) is canonical. In privacy-aware settings, much work has focused on differentially private (DP) LR, but mostly on point estimation with limited attention to uncertainty quantification. Meanwhile, synthetic data generation (SDG) is increasingly important for reproducibility studies, yet current DP LR methods do not readily support it. Mainstream SDG approaches are either tailored to discretized data, making them less suitable for continuous regression, or rely on deep models that require large datasets, limiting their use for the smaller, continuous data typical in social science. We propose a method for LR with valid inference under Gaussian DP: a DP bias-corrected estimator with asymptotic confidence intervals (CIs) and a general SDG procedure in which regression on the synthetic data matches our DP regression. Our binning-aggregation strategy is effective in small- to moderate-dimensional settings. Experiments show our method (1) improves accuracy over existing methods, (2) provides valid CIs, and (3) produces more reliable synthetic data for downstream ML tasks than current DP SDGs.

We develop a framework for dualizing the Kolmogorov structure function $h_x(α)$, which then allows using computable complexity proxies. We establish a mathematical analogy between information-theoretic constructs and statistical mechanics, introducing a suitable partition function and free energy functional. We explicitly prove the Legendre-Fenchel duality between the structure function and free energy, showing detailed balance of the Metropolis kernel, and interpret acceptance probabilities as information-theoretic scattering amplitudes. A susceptibility-like variance of model complexity is shown to peak precisely at loss-complexity trade-offs interpreted as phase transitions. Practical experiments with linear and tree-based regression models verify these theoretical predictions, explicitly demonstrating the interplay between the model complexity, generalization, and overfitting threshold.

Cardiovascular disease and chronic kidney disease are major complications of diabetes, leading to high morbidity and mortality. Early detection of these conditions is critical, yet traditional diagnostic markers often lack sensitivity in the initial stages. This study integrates conventional statistical methods with machine learning approaches to improve early diagnosis of CKD and CVD in diabetic patients. Descriptive and inferential statistics were computed in SPSS to explore associations between diseases and clinical or demographic factors. Patients were categorized into four groups: Group A both CKD and CVD, Group B CKD only, Group C CVD only, and Group D no disease. Statistical analysis revealed significant correlations: Serum Creatinine and Hypertension with CKD, and Cholesterol, Triglycerides, Myocardial Infarction, Stroke, and Hypertension with CVD. These results guided the selection of predictive features for machine learning models. Logistic Regression, Support Vector Machine, and Random Forest algorithms were implemented, with Random Forest showing the highest accuracy, particularly for CKD prediction. Ensemble models outperformed single classifiers in identifying high-risk diabetic patients. SPSS results further validated the significance of the key parameters integrated into the models. While challenges such as interpretability and class imbalance remain, this hybrid statistical machine learning framework offers a promising advancement toward early detection and risk stratification of diabetic complications compared to conventional diagnostic approaches.

Survival analysis is central in many applications across medicine, engineering, economics and finance. It concerns time-to-event modeling: given a process that can generate an event of interest (e.g., death from disease, failure due to wear), the goal is to estimate the probability that an event occurs at any time t > 0 for an individual described by some input variables (or features, or covariates). Unlike standard regression settings, survival data are characterized by censoring, which means that for some instances, the exact event time is not observed (for example, when individuals remain event-free at the end of the study), and only the last recorded follow-up time is available. Traditional approaches to survival modeling rely on strong statistical assumptions linking input variables and risk. The Cox proportional hazards (CoxPH) model [1] remains the most widely used and best established method. The proportional hazards assumption implies that the instantaneous risk of event for two individuals differs by a constant factor over time. The CoxPH model is also linear, making it clear how each single input variable affects the outcome, but at the expense of missing interactions between features. In its original form, this relation is modeled through a linear regression on the features, though many extensions have been developed to relax linearity and improve performance in high-dimensional settings [2-4]. Despite its success, Cox regression is limited by the proportional hazards (PH) assumption, which is often unrealistic.

Contrary to common belief, we show that gradient ascent-based unconstrained optimization methods frequently fail to perform machine unlearning, a phenomenon we attribute to the inherent statistical dependence between the forget and retain data sets. This dependence, which can manifest itself even as simple correlations, undermines the misconception that these sets can be independently manipulated during unlearning. We provide empirical and theoretical evidence showing these methods often fail precisely due to this overlooked relationship. For random forget sets, this dependence means that degrading forget set metrics (which, for a retrained model, should mirror test set metrics) inevitably harms overall test performance. Going beyond random sets, we consider logistic regression as an instructive example where a critical failure mode emerges: inter-set dependence causes gradient descent-ascent iterations to progressively diverge from the ideal retrained model. Strikingly, these methods can converge to solutions that are not only far from the retrained ideal but are potentially even further from it than the original model itself, rendering the unlearning process actively detrimental. A toy example further illustrates how this dependence can trap models in inferior local minima, inescapable via finetuning. Our findings highlight that the presence of such statistical dependencies, even when manifest only as correlations, can be sufficient for ascent-based unlearning to fail. Our theoretical insights are corroborated by experiments on complex neural networks, demonstrating that these methods do not perform as expected in practice due to this unaddressed statistical interplay.

Transfer learning is a key component of modern machine learning, enhancing the performance of target tasks by leveraging diverse data sources. Simultaneously, overparameterized models such as the minimum-$\ell_2$-norm interpolator (MNI) in high-dimensional linear regression have garnered significant attention for their remarkable generalization capabilities, a property known as benign overfitting. Despite their individual importance, the intersection of transfer learning and MNI remains largely unexplored. Our research bridges this gap by proposing a novel two-step Transfer MNI approach and analyzing its trade-offs. We characterize its non-asymptotic excess risk and identify conditions under which it outperforms the target-only MNI. Our analysis reveals free-lunch covariate shift regimes, where leveraging heterogeneous data yields the benefit of knowledge transfer at limited cost. To operationalize our findings, we develop a data-driven procedure to detect informative sources and introduce an ensemble method incorporating multiple informative Transfer MNIs. Finite-sample experiments demonstrate the robustness of our methods to model and data heterogeneity, confirming their advantage.

Consider two sets of entities and their members' mutual affinity values, say drug-target affinities (DTA). Drugs and targets are said to interact in their effects on DTAs if drug's effect on it depends on the target. Presence of interaction implies that assigning a drug to a target and another drug to another target does not provide the same aggregate DTA as the reversed assignment would provide. Accordingly, correctly capturing interactions enables better decision-making, for example, in allocation of limited numbers of drug doses to their best matching targets. Learning to predict DTAs is popularly done from either solely from known DTAs or together with side information on the entities, such as chemical structures of drugs and targets. In this paper, we introduce interaction directions' prediction performance estimator we call interaction concordance index (IC-index), for both fixed predictors and machine learning algorithms aimed for inferring them. IC-index complements the popularly used DTA prediction performance estimators by evaluating the ratio of correctly predicted directions of interaction effects in data. First, we show the invariance of IC-index on predictors unable to capture interactions. Secondly, we show that learning algorithm's permutation equivariance regarding drug and target identities implies its inability to capture interactions when either drug, target or both are unseen during training. In practical applications, this equivariance is remedied via incorporation of appropriate side information on drugs and targets. We make a comprehensive empirical evaluation over several biomedical interaction data sets with various state-of-the-art machine learning algorithms. The experiments demonstrate how different types of affinity strength prediction methods perform in terms of IC-index complementing existing prediction performance estimators.

Microwell microfluidics has been utilized for single-cell analysis to reveal heterogeneity in gene expression, signaling pathways, and phenotypic responses for identifying rare cell types, understanding disease progression, and developing more precise therapeutic strategies. However, designing microwell microfluidics is a considerably complex task, requiring knowledge, experience, and CAD software, as well as manual intervention, which often fails initial designs, demanding multiple costly and time-consuming iterations. In this study, we establish an autonomous large language model (LLM)-driven microwell design framework to generate code-based computer-aided design (CAD) scripts, that enables the rapid and reproducible creation of microwells with diverse geometries and imaging-based analysis. We propose a multimodal large language model (MLLM)-logistic regression framework based on integrating high-level semantic descriptions generated by MLLMs with image embeddings for image classification tasks, aiming to identify microwell occupancy and microwell shape. The fused multimodal representation is input to a logistic regression model, which is both interpretable and computationally efficient. We achieved significant improvements, exceeding 0.92 for occupancy classification and 0.99 for shape classification, across all evaluated MLLMs, compared with 0.50 and 0.55, respectively, when relying solely on direct classification. The MLLM-logistic regression framework is a scalable, efficient solution for high-throughput microwell image analysis. Our study demonstrates an autonomous design microwell platform by translating natural language prompts into optimized device geometries, CAD scripts and image analysis, facilitating the development of next-generation digital discovery by integration of literature mining, autonomous design and experimental data analysis.

In a mixture of linear regression model, the regression coefficients are treated as random vectors that may follow either a continuous or discrete distribution. We propose two Expectation-Maximization (EM) algorithms to estimate this prior distribution. The first algorithm solves a kernelized version of the nonparametric maximum likelihood estimation (NPMLE). This method not only recovers continuous prior distributions but also accurately estimates the number of clusters when the prior is discrete. The second algorithm, designed to approximate the NPMLE, targets prior distributions with a density. It also performs well for discrete priors when combined with a post-processing step. We study the convergence properties of both algorithms and demonstrate their effectiveness through simulations and applications to real datasets.