TabPFN: One Model to Rule Them All?

Hollmann et al. (Nature 637 (2025) 319-326) recently introduced TabPFN, a transformer-based deep learning model for regression and classification on tabular data, which they claim "outperforms all previous methods on datasets with up to 10,000 samples by a wide margin, using substantially less training time." Furthermore, they have called TabPFN a "foundation model" for tabular data, as it can support "data generation, density estimation, learning reusable embeddings and fine-tuning". If these statements are well-supported, TabPFN may have the potential to supersede existing modeling approaches on a wide range of statistical tasks, mirroring a similar revolution in other areas of artificial intelligence that began with the advent of large language models. In this paper, we provide a tailored explanation of how TabPFN works for a statistics audience, by emphasizing its interpretation as approximate Bayesian inference. We also provide more evidence of TabPFN's "foundation model" capabilities: We show that an out-of-the-box application of TabPFN vastly outperforms specialized state-of-the-art methods for semi-supervised parameter estimation, prediction under covariate shift, and heterogeneous treatment effect estimation. We further show that TabPFN can outperform LASSO at sparse regression and can break a robustness-efficiency trade-off in classification. All experiments can be reproduced using the code provided at https://github.com/qinglong-tian/tabpfn_study (https://github.com/qinglong-tian/tabpfn_study).

Positive and Unlabeled Data: Model, Estimation, Inference, and Classification

This study introduces a new approach to addressing positive and unlabeled (PU) data through the double exponential tilting model (DETM). Traditional methods often fall short because they only apply to selected completely at random (SCAR) PU data, where the labeled positive and unlabeled positive data are assumed to be from the same distribution. In contrast, our DETM's dual structure effectively accommodates the more complex and underexplored selected at random PU data, where the labeled and unlabeled positive data can be from different distributions. We rigorously establish the theoretical foundations of DETM, including identifiability, parameter estimation, and asymptotic properties. Additionally, we move forward to statistical inference by developing a goodness-of-fit test for the SCAR condition and constructing confidence intervals for the proportion of positive instances in the target domain. We leverage an approximated Bayes classifier for classification tasks, demonstrating DETM's robust performance in prediction. Through theoretical insights and practical applications, this study highlights DETM as a comprehensive framework for addressing the challenges of PU data.

ReTaSA: A Nonparametric Functional Estimation Approach for Addressing Continuous Target Shift

The presence of distribution shifts poses a significant challenge for deploying modern machine learning models in real-world applications. This work focuses on the target shift problem in a regression setting (Zhang et al., 2013; Nguyen et al., 2016). More specifically, the target variable y (also known as the response variable), which is continuous, has different marginal distributions in the training source and testing domain, while the conditional distribution of features x given y remains the same. While most literature focuses on classification tasks with finite target space, the regression problem has an infinite dimensional target space, which makes many of the existing methods inapplicable. In this work, we show that the continuous target shift problem can be addressed by estimating the importance weight function from an ill-posed integral equation. We propose a nonparametric regularized approach named ReTaSA to solve the ill-posed integral equation and provide theoretical justification for the estimated importance weight function. The effectiveness of the proposed method has been demonstrated with extensive numerical studies on synthetic and real-world datasets.

ELSA: Efficient Label Shift Adaptation through the Lens of Semiparametric Models

We study the domain adaptation problem with label shift in this work. Under the label shift context, the marginal distribution of the label varies across the training and testing datasets, while the conditional distribution of features given the label is the same. Traditional label shift adaptation methods either suffer from large estimation errors or require cumbersome post-prediction calibrations. To address these issues, we first propose a moment-matching framework for adapting the label shift based on the geometry of the influence function. Under such a framework, we propose a novel method named \underline{E}fficient \underline{L}abel \underline{S}hift \underline{A}daptation (ELSA), in which the adaptation weights can be estimated by solving linear systems. Theoretically, the ELSA estimator is $\sqrt{n}$-consistent ($n$ is the sample size of the source data) and asymptotically normal. Empirically, we show that ELSA can achieve state-of-the-art estimation performances without post-prediction calibrations, thus, gaining computational efficiency.