While most ML models expect independent and identically distributed data, this assumption is often violated in real-world scenarios due to distribution shifts, resulting in the degradation of machine learning model performance. Until now, no tabular method has consistently outperformed classical supervised learning, which ignores these shifts. To address temporal distribution shifts, we present Drift-Resilient TabPFN, a fresh approach based on In-Context Learning with a Prior-Data Fitted Network that learns the learning algorithm itself: it accepts the entire training dataset as input and makes predictions on the test set in a single forward pass. Specifically, it learns to approximate Bayesian inference on synthetic datasets drawn from a prior that specifies the model's inductive bias. This prior is based on structural causal models (SCM), which gradually shift over time. To model shifts of these causal models, we use a secondary SCM, that specifies changes in the primary model parameters. The resulting Drift-Resilient TabPFN can be applied to unseen data, runs in seconds on small to moderately sized datasets and needs no hyperparameter tuning. Comprehensive evaluations across 18 synthetic and real-world datasets demonstrate large performance improvements over a wide range of baselines, such as XGB, CatBoost, TabPFN, and applicable methods featured in the Wild-Time benchmark. Compared to the strongest baselines, it improves accuracy from 0.688 to 0.744 and ROC AUC from 0.786 to 0.832 while maintaining stronger calibration. This approach could serve as significant groundwork for further research on out-of-distribution prediction.

Current causal discovery approaches require restrictive model assumptions or assume access to interventional data to ensure structure identifiability. These assumptions often do not hold in real-world applications leading to a loss of guarantees and poor accuracy in practice. Recent work has shown that, in the bivariate case, Bayesian model selection can greatly improve accuracy by exchanging restrictive modelling for more flexible assumptions, at the cost of a small probability of error. We extend the Bayesian model selection approach to the important multivariate setting by making the large discrete selection problem scalable through a continuous relaxation. We demonstrate how for our choice of Bayesian non-parametric model, the Causal Gaussian Process Conditional Density Estimator (CGP-CDE), an adjacency matrix can be constructed from the model hyperparameters. This adjacency matrix is then optimised using the marginal likelihood and an acyclicity regulariser, outputting the maximum a posteriori causal graph. We demonstrate the competitiveness of our approach on both synthetic and real-world datasets, showing it is possible to perform multivariate causal discovery without infeasible assumptions using Bayesian model selection.

Accurately characterizing migration velocity models is crucial for a wide range of geophysical applications, from hydrocarbon exploration to monitoring of CO2 sequestration projects. Traditional velocity model building methods such as Full-Waveform Inversion (FWI) are powerful but often struggle with the inherent complexities of the inverse problem, including noise, limited bandwidth, receiver aperture and computational constraints. To address these challenges, we propose a scalable methodology that integrates generative modeling, in the form of Diffusion networks, with physics-informed summary statistics, making it suitable for complicated imaging problems including field datasets. By defining these summary statistics in terms of subsurface-offset image volumes for poor initial velocity models, our approach allows for computationally efficient generation of Bayesian posterior samples for migration velocity models that offer a useful assessment of uncertainty. To validate our approach, we introduce a battery of tests that measure the quality of the inferred velocity models, as well as the quality of the inferred uncertainties. With modern synthetic datasets, we reconfirm gains from using subsurface-image gathers as the conditioning observable. For complex velocity model building involving salt, we propose a new iterative workflow that refines amortized posterior approximations with salt flooding and demonstrate how the uncertainty in the velocity model can be propagated to the final product reverse time migrated images. Finally, we present a proof of concept on field datasets to show that our method can scale to industry-sized problems.

Environmental and individualistic variables affect the rate of human decomposition in complex ways. These effects complicate the estimation of the postmortem interval (PMI) based on observed decomposition characteristics. In this work, we develop a generative probabilistic model for decomposing human remains based on PMI and a wide range of environmental and individualistic variables. This model explicitly represents the effect of each variable, including PMI, on the appearance of each decomposition characteristic, allowing for direct interpretation of model effects and enabling the use of the model for PMI inference and optimal experimental design. In addition, the probabilistic nature of the model allows for the integration of expert knowledge in the form of prior distributions. We fit this model to a diverse set of 2,529 cases from the GeoFOR dataset. We demonstrate that the model accurately predicts 24 decomposition characteristics with an ROC AUC score of 0.85. Using Bayesian inference techniques, we invert the decomposition model to predict PMI as a function of the observed decomposition characteristics and environmental and individualistic variables, producing an R-squared measure of 71%. Finally, we demonstrate how to use the fitted model to design future experiments that maximize the expected amount of new information about the mechanisms of decomposition using the Expected Information Gain formalism.

The proliferation of Machine Learning (ML) models and their open-source implementations has transformed Artificial Intelligence research and applications. Platforms like Hugging Face (HF) enable the development, sharing, and deployment of these models, fostering an evolving ecosystem. While previous studies have examined aspects of models hosted on platforms like HF, a comprehensive longitudinal study of how these models change remains underexplored. This study addresses this gap by utilizing both repository mining and longitudinal analysis methods to examine over 200,000 commits and 1,200 releases from over 50,000 models on HF. We replicate and extend an ML change taxonomy for classifying commits and utilize Bayesian networks to uncover patterns in commit and release activities over time. Our findings indicate that commit activities align with established data science methodologies, such as CRISP-DM, emphasizing iterative refinement and continuous improvement. Additionally, release patterns tend to consolidate significant updates, particularly in documentation, distinguishing between granular changes and milestone-based releases. Furthermore, projects with higher popularity prioritize infrastructure enhancements early in their lifecycle, and those with intensive collaboration practices exhibit improved documentation standards. These and other insights enhance the understanding of model changes on community platforms and provide valuable guidance for best practices in model maintenance.

Several statistical models for regression of a function $F$ on $\mathbb{R}^d$ without the statistical and computational curse of dimensionality exist, for example by imposing and exploiting geometric assumptions on the distribution of the data (e.g. that its support is low-dimensional), or strong smoothness assumptions on $F$, or a special structure $F$. Among the latter, compositional models assume $F=f\circ g$ with $g$ mapping to $\mathbb{R}^r$ with $r\ll d$, have been studied, and include classical single- and multi-index models and recent works on neural networks. While the case where $g$ is linear is rather well-understood, much less is known when $g$ is nonlinear, and in particular for which $g$'s the curse of dimensionality in estimating $F$, or both $f$ and $g$, may be circumvented. In this paper, we consider a model $F(X):=f(\Pi_\gamma X) $ where $\Pi_\gamma:\mathbb{R}^d\to[0,\rm{len}_\gamma]$ is the closest-point projection onto the parameter of a regular curve $\gamma: [0,\rm{len}_\gamma]\to\mathbb{R}^d$ and $f:[0,\rm{len}_\gamma]\to\mathbb{R}^1$. The input data $X$ is not low-dimensional, far from $\gamma$, conditioned on $\Pi_\gamma(X)$ being well-defined. The distribution of the data, $\gamma$ and $f$ are unknown. This model is a natural nonlinear generalization of the single-index model, which corresponds to $\gamma$ being a line. We propose a nonparametric estimator, based on conditional regression, and show that under suitable assumptions, the strongest of which being that $f$ is coarsely monotone, it can achieve the $one$-$dimensional$ optimal min-max rate for non-parametric regression, up to the level of noise in the observations, and be constructed in time $\mathcal{O}(d^2n\log n)$. All the constants in the learning bounds, in the minimal number of samples required for our bounds to hold, and in the computational complexity are at most low-order polynomials in $d$.

This work addresses the fundamental linear inverse problem in compressive sensing (CS) by introducing a new type of regularizing generative prior. Our proposed method utilizes ideas from classical dictionary-based CS and, in particular, sparse Bayesian learning (SBL), to integrate a strong regularization towards sparse solutions. At the same time, by leveraging the notion of conditional Gaussianity, it also incorporates the adaptability from generative models to training data. However, unlike most state-of-the-art generative models, it is able to learn from a few compressed and noisy data samples and requires no optimization algorithm for solving the inverse problem. Additionally, similar to Dirichlet prior networks, our model parameterizes a conjugate prior enabling its application for uncertainty quantification. We support our approach theoretically through the concept of variational inference and validate it empirically using different types of compressible signals.

This paper presents a variant of the Multinomial mixture model tailored for the unsupervised classification of short text data. Traditionally, the Multinomial probability vector in this hierarchical model is assigned a Dirichlet prior distribution. Here, however, we explore an alternative prior--the Beta-Liouville distribution--which offers a more flexible correlation structure than the Dirichlet. We examine the theoretical properties of the Beta-Liouville distribution, focusing on its conjugacy with the Multinomial likelihood. This property enables the derivation of update equations for a CAVI (Coordinate Ascent Variational Inference) variational algorithm, facilitating the approximate posterior estimation of model parameters. Additionally, we propose a stochastic variant of the CAVI algorithm that enhances scalability. The paper concludes with data examples that demonstrate effective strategies for setting the Beta-Liouville hyperparameters.

An important problem on social information sites is the recovery of ground truth from individual reports when the experts are in the minority. The wisdom of the crowd, i.e. the collective opinion of a group of individuals fails in such a scenario. However, the surprisingly popular (SP) algorithm~\cite{prelec2017solution} can recover the ground truth even when the experts are in the minority, by asking the individuals to report additional prediction reports--their beliefs about the reports of others. Several recent works have extended the surprisingly popular algorithm to an equivalent voting rule (SP-voting) to recover the ground truth ranking over a set of $m$ alternatives. However, we are yet to fully understand when SP-voting can recover the ground truth ranking, and if so, how many samples (votes and predictions) it needs. We answer this question by proposing two rank-order models and analyzing the sample complexity of SP-voting under these models. In particular, we propose concentric mixtures of Mallows and Plackett-Luce models with $G (\ge 2)$ groups. Our models generalize previously proposed concentric mixtures of Mallows models with $2$ groups, and we highlight the importance of $G > 2$ groups by identifying three distinct groups (expert, intermediate, and non-expert) from existing datasets. Next, we provide conditions on the parameters of the underlying models so that SP-voting can recover ground-truth rankings with high probability, and also derive sample complexities under the same. We complement the theoretical results by evaluating SP-voting on simulated and real datasets.

The inherent complexity of biological agents often leads to motility behavior that appears to have random components. Robust stochastic inference methods are therefore required to understand and predict the motion patterns from time discrete trajectory data provided by experiments. In many cases second order Langevin models are needed to adequately capture the motility. Additionally, population heterogeneity needs to be taken into account when analyzing data from several individual organisms. In this work, we describe a maximum likelihood approach to infer dynamical, stochastic models and, simultaneously, estimate the heterogeneity in a population of motile active particles from discretely sampled, stochastic trajectories. To this end we propose a new method to approximate the likelihood for non-linear second order Langevin models. We show that this maximum likelihood ansatz outperforms alternative approaches especially for short trajectories. Additionally, we demonstrate how a measure of uncertainty for the heterogeneity estimate can be derived. We thereby pave the way for the systematic, data-driven inference of dynamical models for actively driven entities based on trajectory data, deciphering temporal fluctuations and inter-particle variability.