Predictions and generations from large language models are increasingly being explored as an aid in limited data regimes, such as in computational social science and human subjects research. While prior technical work has mainly explored the potential to use model-predicted labels for unlabeled data in a principled manner, there is increasing interest in using large language models to generate entirely new synthetic samples (e.g., synthetic simulations), such as in responses to surveys. However, it remains unclear by what means practitioners can combine such data with real data and yet produce statistically valid conclusions upon them. In this paper, we introduce a new estimator based on generalized method of moments, providing a hyperparameter-free solution with strong theoretical guarantees to address this challenge. Intriguingly, we find that interactions between the moment residuals of synthetic data and those of real data (i.e., when they are predictive of each other) can greatly improve estimates of the target parameter.

We consider the parameter estimation problem in logistic regression with Gaussian design: the estimation of a fixed unknown parameter $θ^*\in \mathbb{R}^d$ ($\|θ^*\|_2\ge 1$) from $n$ i.i.d. samples $\{(x_i,y_i)\}_{i=1}^n$, where $x_i\sim N(0,I_d)$ and $y_i|x_i \sim {\rm Bernoulli}(1/(1+\exp(-x_i^\top θ^*)))$. Our main aim is to characterize the finite-sample estimation performance and convergence behavior of gradient descent (GD) on the maximum likelihood objective (i.e., the logistic loss). Under small $O(1)$ stepsize and $0$ initialization, we show that GD linearly converges to a small neighborhood of $θ^*$ achieving an $\ell_2$ error of order $O(\sqrt{\|θ^*\|_2^5d/n})$. This substantially goes beyond existing theoretical results that lack non-asymptotic estimation error rate and exhibit much slower parameter convergence. We also establish a faster local linear convergence to the same statistical error under a large $Θ(\|θ^*\|_2)$ stepsize. The main technical component is to show that the gradient of the logistic loss satisfies a certain approximate invertibility condition (AIC). To that end, we uniformly control the deviation of the gradient from its population counterpart by covering and peeling arguments, and then show that the population GD is a contraction by a delicate analysis based on the eigenvalues of population Hessian matrices. Finally, we build upon the recent work Matsumoto and Mazumdar (2025) and devise a novel efficient estimator that attains a sharper rate in high dimensions. This indicates that the existing non-asymptotic guarantees exhibit sub-optimal dependence on $\|θ^*\|_2$, and that in many regimes $Θ(\sqrt{\|θ^*\|_2d/n})$ is the tight estimation error rate. Numerical examples are provided to corroborate our theoretical results.

We study gradient descent (GD) with a constant stepsize for ℓ2-regularized logistic regression with linearly separable data. Classical theory suggests small stepsizes to ensure monotonic reduction of the optimization objective, achieving exponential convergence in eO(κ) steps with κ being the condition number. Surprisingly, we show that this can be accelerated to eO( κ)by simply using a large stepsize--for which the objective evolves nonmonotonically. The acceleration brought by large stepsizes extends to minimizing the population risk for separable distributions, improving on the best-known upper bounds on the number of steps to reach a nearoptimum. Finally, we characterize the largest stepsize for the local convergence of GD, which also determines the global convergence in special scenarios. Our results extend the analysis of Wu et al. (2024) from convex settings with minimizers at infinity to strongly convex cases with finite minimizers.

Most existing transfer learning algorithms for high-dimensional models employ a two-step regularization framework, whose success heavily hinges on the assumption that the pre-trained model closely resembles the target. To relax this assumption, we propose a co-regularization process to directly exploit beneficial knowledge from the source domain for high-dimensional generalized linear models. The proposed method learns the target parameter by constraining the source parameters to be close to the target one, thereby preventing fine-tuning failures caused by significantly deviated pre-trained parameters. Our theoretical analysis demonstrates that the proposed method accommodates a broader range of sources than existing two-step frameworks, thus being more robust to less similar sources. Its effectiveness is validated through extensive empirical studies.

Direct preference optimization (DPO) is widely used as a simple and stable method for aligning large language models (LLMs) with human preferences. This paper investigates a generalized DPO loss that enables a policy model to match the target policy from a likelihood ratio estimation perspective. The ratio of the target policy provides a unique identification of the policy distribution without relying on reward models or partition functions. This allows the generalized loss to retain both simplicity and theoretical guarantees, which prior work such as f-PO fails to achieve simultaneously. We propose Bregman preference optimization (BPO), a generalized framework for ratio matching that provides a family of objective functions achieving target policy optimality.

Gaussian sketching, which consists of pre-multiplying the data with a random Gaussian matrix, is a widely used technique in data science and machine learning. Beyond computational benefits, this operation also provides differential privacy guarantees due to its inherent randomness. In this work, we revisit this operation through the lens of Rényi Differential Privacy (RDP), providing a refined privacy analysis that yields significantly tighter bounds than prior results. We then demonstrate how this improved analysis leads to performance improvement in different linear regression settings, establishing theoretical utility guarantees. Empirically, our methods improve performance across multiple datasets and, in several cases, reduce runtime.

Electronic health records (EHR) pose large-scale multi-disease modeling problems in which many outcomes are rare and strongly influenced by shared risk factors. While modern approaches achieve strong predictive performance, they often treat diseases independently or rely on black-box architectures, offering limited insight into how risk factors organize disease risk and little principled uncertainty quantification. We introduce a Bayesian hypergraph inference framework that reframes multi-disease modeling around latent, risk-factor-modulated disease pathways. Risk factors act on hyperedges, latent disease subsets with shared risk patterns, allowing diseases to participate in multiple distinct pathways and enabling interpretable, higher-order structure beyond pairwise associations. A repulsion prior encourages parsimonious and identifiable structure, while posterior inference provides calibrated uncertainty over both disease groupings and risk-factor influence. To enable scalable inference on large EHR datasets, we develop a structured variational inference algorithm that preserves logical dependencies among hyperedge existence, disease membership, and pathway-level effects. Experiments on simulated data and UK Biobank demonstrate stable and interpretable disease pathway structure, well-calibrated uncertainty, improved estimation for rare diseases, and competitive predictive performance.

Autonomous spacecraft require rapid, lightweight, and reliable onboard detection of cyber-RF threats. Using the SPARTA attack model, we analyze the latency-accuracy trade-offs of TinyML-compatible classical models -- Random Forest, Logistic Regression, SVM, and MLP -- for detecting uplink jamming, Fake-NR spoofing, payload manipulation, ground-segment compromise, and unauthorized command injection. We present a physics-informed theoretical analysis of each model's computational complexity, VC dimension, Lipschitz continuity, and latency scaling, supported by empirical measurements on adversarial RF spectrograms generated via BandErasure, FakeNR, and NoiseBurst corruption modes. Results show that Logistic Regression achieves microsecond-level inference with only a 1\% accuracy drop relative to Random Forest, making it an effective TinyML baseline for onboard autonomy. The study also identifies opportunities for advancing spacecraft cybersecurity through richer feature encoders and multi-timescale learning architectures, building on recent progress in edge intelligence and trustworthy AI.

Background Childhood Anemia affects an estimated 40% of children aged 6-59 months globally and arises from heterogeneous nutritional, infectious, and socioeconomic factors that vary substantially across settings. This variability challenges the generalizability of predictive machine learning models, which often degrade under cross-population or temporal shifts. We investigated the utility a modern transformer-based tabular foundation model (TabPFN) as a complementatry framework with respect to supervised classical machine learning methods across diverse country contexts, with particular attention to data-scarce settings where surveillance capacity is most limited. Methods We conducted a multi-country prediction study using Demographic and Health Surveys (DHS) children's recode data from 16 countries spanning Africa, Asia, Latin America, the Caucasus, and the Middle East. The harmonized analytic cohort comprised of (n = 68,856)children aged 6-59 months with valid hemoglobin measurements. Anemia was defined using WHO age and altitude-adjusted thresholds and treated as a binary outcome. We trained Logistic Regression, XGBoost, and LightGBM models using standard supervised learning, and evaluated TabPFN v2.6 in an in-context learning setting. Performance was assessed using Area Under the Receiver Operating Characteristic Curve (AUC-ROC) and other standard classification metrics, with calibration evaluated via Brier score and expected calibration error (ECE). Uncertainty in performance estimates was quantified using bootstrap resampling to derive 95% confidence intervals. Robustness was assessed in a few-shot learning setting. Cross-population generalization was examined using leave-one-country-out (LOCO) validation and reverse-LOCO experiments to assess directional transferability. Subgroup analyses were conducted across five demographic strata: child age group, sex, maternal education, residence type, and household wealth quintile. Feature importance was assessed using standard linear and tree-based explainer SHAP values for the three supervised models and an adapted version of SHAP for TabPFN, aggregated across countries and examined at the country level. TabPFN also yielded the best probabilistic calibration across all 16 countries, achieving the lowest mean Brier score (0.203) and Expected Calibration Error (ECE = 0.042) of all models evaluated; LightGBM and Logistic Regression exhibited the greatest miscalibration, particularly at higher predicted probabilities. Under full-data conditions, within-country discrimination was moderate across all models (AUC-ROC 0.59-0.76) Under LOCO validation, performance declined modestly (AUC-ROC 0.58-0.69) Reverse-LOCO analyses revealed asymmetric and directional transferability, with epidemiologically diverse populations serving as more informative training sources and certain target populations remaining persistently difficult to predict regardless of model or training data.

GPUs have significantly accelerated first-order methods for large-scale optimization, especially in continuous optimization. However, this success has not transferred cleanly to problems with discrete variables, combinatorial structure, and nonlinear objectives, such as certifying optimal solutions for cardinality-constrained generalized linear models. Major challenges include the sequential processing of heterogeneous nodes in branch and bound (BnB) and frequent data movement between the CPU and GPU. We propose a simple, generic, and modular CPU--GPU framework that processes multiple BnB nodes in batches on GPUs. The framework is built around a small set of GPU-efficient routines and uses padding together with lightweight custom kernels to handle irregular node data structures. Experiments show one to two orders of magnitude speedups and zero optimality gap on challenging instances. The framework can also be extended to collect the entire Rashomon set, enabling downstream statistical analysis such as variable-importance analysis and model selection under secondary user-specific measures (e.g., AUC in classification).