We describe HypotheSAEs, a general method to hypothesize interpretable relationships between text data (e.g., headlines) and a target variable (e.g., clicks). HypotheSAEs has three steps: (1) train a sparse autoencoder on text embeddings to produce interpretable features describing the data distribution, (2) select features that predict the target variable, and (3) generate a natural language interpretation of each feature (e.g., "mentions being surprised or shocked") using an LLM. Each interpretation serves as a hypothesis about what predicts the target variable. Compared to baselines, our method better identifies reference hypotheses on synthetic datasets (at least +0.06 in F1) and produces more predictive hypotheses on real datasets (~twice as many significant findings), despite requiring 1-2 orders of magnitude less compute than recent LLM-based methods. HypotheSAEs also produces novel discoveries on two well-studied tasks: explaining partisan differences in Congressional speeches and identifying drivers of engagement with online headlines.

Despite the generative model's groundbreaking success, the need to study its implications for privacy and utility becomes more urgent. Although many studies have demonstrated the privacy threats brought by GANs, no existing survey has systematically categorized the privacy and utility perspectives of GANs and VAEs. In this article, we comprehensively study privacy-preserving generative models, articulating the novel taxonomies for both privacy and utility metrics by analyzing 100 research publications. Finally, we discuss the current challenges and future research directions that help new researchers gain insight into the underlying concepts.

In many practical applications, regression models are employed to uncover relationships between predictors and a response variable, yet the common assumption of constant error variance is frequently violated. This issue is further compounded in high-dimensional settings where the number of predictors exceeds the sample size, necessitating regularization for effective estimation and variable selection. To address this problem, we propose the Heteroscedastic Double Bayesian Elastic Net (HDBEN), a novel framework that jointly models the mean and log-variance using hierarchical Bayesian priors incorporating both $\ell_1$ and $\ell_2$ penalties. Our approach simultaneously induces sparsity and grouping in the regression coefficients and variance parameters, capturing complex variance structures in the data. Theoretical results demonstrate that proposed HDBEN achieves posterior concentration, variable selection consistency, and asymptotic normality under mild conditions which justifying its behavior. Simulation studies further illustrate that HDBEN outperforms existing methods, particularly in scenarios characterized by heteroscedasticity and high dimensionality.

This paper focuses on linear regression models with non-conjugate sparsity-inducing regularizers such as lasso and group lasso. Although empirical Bayes approach enables us to estimate the regularization parameter, little is known on the properties of the estimators. In particular, there are many unexplained aspects regarding the specific conditions under which the mechanism of automatic relevance determination (ARD) occurs. In this paper, we derive the empirical Bayes estimators for the group lasso regularized linear regression models with a limited number of parameters. It is shown that the estimators diverge under a certain condition, giving rise to the ARD mechanism. We also prove that empirical Bayes methods can produce ARD mechanism in general regularized linear regression models and clarify the conditions under which models such as ridge, lasso, and group lasso can produce ARD mechanism.

Prediction-powered inference (PPI) enables valid statistical inference by combining experimental data with machine learning predictions. When a sufficient number of high-quality predictions is available, PPI results in more accurate estimates and tighter confidence intervals than traditional methods. In this paper, we propose to inform the PPI framework with prior knowledge on the quality of the predictions. The resulting method, which we call frequentist, assisted by Bayes, PPI (FAB-PPI), improves over PPI when the observed prediction quality is likely under the prior, while maintaining its frequentist guarantees. Furthermore, when using heavy-tailed priors, FAB-PPI adaptively reverts to standard PPI in low prior probability regions. We demonstrate the benefits of FAB-PPI in real and synthetic examples.

Personalization in machine learning involves tailoring models to individual users by incorporating personal attributes such as demographic or medical data. While personalization can improve prediction accuracy, it may also amplify biases and reduce explainability. This work introduces a unified framework to evaluate the impact of personalization on both prediction accuracy and explanation quality across classification and regression tasks. We derive novel upper bounds for the number of personal attributes that can be used to reliably validate benefits of personalization. Our analysis uncovers key trade-offs. We show that regression models can potentially utilize more personal attributes than classification models. We also demonstrate that improvements in prediction accuracy due to personalization do not necessarily translate to enhanced explainability -- underpinning the importance to evaluate both metrics when personalizing machine learning models in critical settings such as healthcare. Validated with a real-world dataset, this framework offers practical guidance for balancing accuracy, fairness, and interpretability in personalized models.

The prevalence of drawing causal conclusions from observational studies has raised concerns about potential exaggeration in science communication. While some believe causal language should only apply to randomized controlled trials, others argue that rigorous methods can justify causal claims in observational studies. Ideally, causal language should align with the strength of the evidence. However, through the analysis of over 80,000 observational study abstracts using computational linguistic and regression methods, we found that causal language is more frequently used by less experienced authors, smaller research teams, male last authors, and authors from countries with higher uncertainty avoidance indices. These findings suggest that the use of causal language may be influenced by external factors such as the sociocultural backgrounds of authors and the dynamics of research collaboration. This newly identified link deepens our understanding of how such factors help shape scientific conclusions in causal inference and science communication.

Fr\'echet regression extends classical regression methods to non-Euclidean metric spaces, enabling the analysis of data relationships on complex structures such as manifolds and graphs. This work establishes a rigorous theoretical analysis for Fr\'echet regression through the lens of comparison geometry which leads to important considerations for its use in practice. The analysis provides key results on the existence, uniqueness, and stability of the Fr\'echet mean, along with statistical guarantees for nonparametric regression, including exponential concentration bounds and convergence rates. Additionally, insights into angle stability reveal the interplay between curvature of the manifold and the behavior of the regression estimator in these non-Euclidean contexts. Empirical experiments validate the theoretical findings, demonstrating the effectiveness of proposed hyperbolic mappings, particularly for data with heteroscedasticity, and highlighting the practical usefulness of these results.

The machine learning (ML) training over disparate data sources traditionally involves materialization, which can impose substantial time and space overhead due to data movement and replication. Factorized learning, which leverages direct computation on disparate sources through linear algebra (LA) rewriting, has emerged as a viable alternative to improve computational efficiency. However, the adaptation of factorized learning to leverage the full capabilities of modern LA-friendly hardware like GPUs has been limited, often requiring manual intervention for algorithm compatibility. This paper introduces Ilargi, a novel factorized learning framework that utilizes matrix-represented data integration (DI) metadata to facilitate automatic factorization across CPU and GPU environments without the need for costly relational joins. Ilargi incorporates an ML-based cost estimator to intelligently selects between factorization and materialization based on data properties, algorithm complexity, hardware environments, and their interactions. This strategy ensures up to 8.9x speedups on GPUs and achieves over 20% acceleration in batch ML training workloads, thereby enhancing the practicability of ML training across diverse data integration scenarios and hardware platforms. To our knowledge, this work is the very first effort in GPU-compatible factorized learning.

Learning models have been shown to rely on spurious correlations between non-predictive features and the associated labels in the training data, with negative implications on robustness, bias and fairness. In this work, we provide a statistical characterization of this phenomenon for high-dimensional regression, when the data contains a predictive core feature $x$ and a spurious feature $y$. Specifically, we quantify the amount of spurious correlations $C$ learned via linear regression, in terms of the data covariance and the strength $\lambda$ of the ridge regularization. As a consequence, we first capture the simplicity of $y$ through the spectrum of its covariance, and its correlation with $x$ through the Schur complement of the full data covariance. Next, we prove a trade-off between $C$ and the in-distribution test loss $L$, by showing that the value of $\lambda$ that minimizes $L$ lies in an interval where $C$ is increasing. Finally, we investigate the effects of over-parameterization via the random features model, by showing its equivalence to regularized linear regression. Our theoretical results are supported by numerical experiments on Gaussian, Color-MNIST, and CIFAR-10 datasets.