A common task arising in various domains is that of ranking items based on the outcomes of pairwise comparisons, from ranking players and teams in sports to ranking products or brands in marketing studies and recommendation systems. Statistical inference-based methods such as the Bradley-Terry model, which extract rankings based on an underlying generative model of the comparison outcomes, have emerged as flexible and powerful tools to tackle the task of ranking in empirical data. In situations with limited and/or noisy comparisons, it is often challenging to confidently distinguish the performance of different items based on the evidence available in the data. However, existing inference-based ranking methods overwhelmingly choose to assign each item to a unique rank or score, suggesting a meaningful distinction when there is none. Here, we address this problem by developing a principled Bayesian methodology for learning partial rankings -- rankings with ties -- that distinguishes among the ranks of different items only when there is sufficient evidence available in the data. Our framework is adaptable to any statistical ranking method in which the outcomes of pairwise observations depend on the ranks or scores of the items being compared. We develop a fast agglomerative algorithm to perform Maximum A Posteriori (MAP) inference of partial rankings under our framework and examine the performance of our method on a variety of real and synthetic network datasets, finding that it frequently gives a more parsimonious summary of the data than traditional ranking, particularly when observations are sparse.

Eating disorders (ED) are critical psychiatric problems that have alarmed the mental health community. Mental health professionals are increasingly recognizing the utility of data derived from social media platforms such as Twitter. However, high dimensionality and extensive feature sets of Twitter data present remarkable challenges for ED classification. To overcome these hurdles, we introduce a novel method, an informed branch and bound search technique known as ED-Filter. This strategy significantly improves the drawbacks of conventional feature selection algorithms such as filters and wrappers. ED-Filter iteratively identifies an optimal set of promising features that maximize the eating disorder classification accuracy. In order to adapt to the dynamic nature of Twitter ED data, we enhance the ED-Filter with a hybrid greedy-based deep learning algorithm. This algorithm swiftly identifies sub-optimal features to accommodate the ever-evolving data landscape. Experimental results on Twitter eating disorder data affirm the effectiveness and efficiency of ED-Filter. The method demonstrates significant improvements in classification accuracy and proves its value in eating disorder detection on social media platforms.

This study is motivated by optimal control applications that exhibit high complexity, high uncertainty, and very limited data [Wang et al., 2024, Zheng et al., 2023, Plotkin et al., 2017, Mirasol, 2017]. In particular, all of these challenges are present in the domain of biopharmaceutical manufacturing, used for production of essential life-saving treatments for severe and chronic diseases, including cancers, autoimmune disorders, metabolic diseases, genetic disorders, and infectious diseases such as COVID-19 [Zahavi and Weiner, 2020, Teo, 2022]. Using cells as factories, biomanufacturing involves hundreds of biological, physical, and chemical factors dynamically interacting with each other at molecular, cellular, and macroscopic levels and impacting production outcomes. Due to the complexity of these mechanisms, it is quite difficult to control production safely and effectively, especially in the presence of very limited data. Digital twins have proven very useful in guiding the control of complex physical systems [Tao et al., 2018].

In this work, we study the weighted empirical risk minimization (weighted ERM) schema, in which an additional data-dependent weight function is incorporated when the empirical risk function is being minimized. We show that under a general ``balanceable" Bernstein condition, one can design a weighted ERM estimator to achieve superior performance in certain sub-regions over the one obtained from standard ERM, and the superiority manifests itself through a data-dependent constant term in the error bound. These sub-regions correspond to large-margin ones in classification settings and low-variance ones in heteroscedastic regression settings, respectively. Our findings are supported by evidence from synthetic data experiments.

Based on limited observations, machine learning discerns a dependence which is expected to hold in the future. What makes it possible? Statistical learning theory imagines indefinitely increasing training sample to justify its approach. In reality, there is no infinite time or even infinite general population for learning. Here I argue that practical machine learning is based on an implicit assumption that underlying dependence is relatively ``smooth" : likely, there are no abrupt differences in feedback between cases with close data points. From this point of view learning shall involve selection of the hypothesis ``smoothly" approximating the training set. I formalize this as Practical learning paradigm. The paradigm includes terminology and rules for description of learners. Popular learners (local smoothing, k-NN, decision trees, Naive Bayes, SVM for classification and for regression) are shown here to be implementations of this paradigm.

Here, we present the outcomes from the second Large Language Model (LLM) Hackathon for Applications in Materials Science and Chemistry, which engaged participants across global hybrid locations, resulting in 34 team submissions. The submissions spanned seven key application areas and demonstrated the diverse utility of LLMs for applications in (1) molecular and material property prediction; (2) molecular and material design; (3) automation and novel interfaces; (4) scientific communication and education; (5) research data management and automation; (6) hypothesis generation and evaluation; and (7) knowledge extraction and reasoning from scientific literature. Each team submission is presented in a summary table with links to the code and as brief papers in the appendix. Beyond team results, we discuss the hackathon event and its hybrid format, which included physical hubs in Toronto, Montreal, San Francisco, Berlin, Lausanne, and Tokyo, alongside a global online hub to enable local and virtual collaboration. Overall, the event highlighted significant improvements in LLM capabilities since the previous year's hackathon, suggesting continued expansion of LLMs for applications in materials science and chemistry research. These outcomes demonstrate the dual utility of LLMs as both multipurpose models for diverse machine learning tasks and platforms for rapid prototyping custom applications in scientific research.

The PAC-Bayesian framework has significantly advanced the understanding of statistical learning, particularly for majority voting methods. Despite its successes, its application to multi-view learning -- a setting with multiple complementary data representations -- remains underexplored. In this work, we extend PAC-Bayesian theory to multi-view learning, introducing novel generalization bounds based on R\'enyi divergence. These bounds provide an alternative to traditional Kullback-Leibler divergence-based counterparts, leveraging the flexibility of R\'enyi divergence. Furthermore, we propose first- and second-order oracle PAC-Bayesian bounds and extend the C-bound to multi-view settings. To bridge theory and practice, we design efficient self-bounding optimization algorithms that align with our theoretical results.

Existing methods to summarize posterior inference for mixture models focus on identifying a point estimate of the implied random partition for clustering, with density estimation as a secondary goal (Wade and Ghahramani, 2018; Dahl et al., 2022). We propose a novel approach for summarizing posterior inference in nonparametric Bayesian mixture models, prioritizing density estimation of the mixing measure (or mixture) as an inference target. One of the key features is the model-agnostic nature of the approach, which remains valid under arbitrarily complex dependence structures in the underlying sampling model. Using a decision-theoretic framework, our method identifies a point estimate by minimizing posterior expected loss. A loss function is defined as a discrepancy between mixing measures. Estimating the mixing measure implies inference on the mixture density and the random partition. Exploiting the discrete nature of the mixing measure, we use a version of sliced Wasserstein distance. We introduce two specific variants for Gaussian mixtures. The first, mixed sliced Wasserstein, applies generalized geodesic projections on the product of the Euclidean space and the manifold of symmetric positive definite matrices. The second, sliced mixture Wasserstein, leverages the linearity of Gaussian mixture measures for efficient projection.

Marketing mix modeling (MMM) is a widely used method to assess the effectiveness of marketing campaigns and optimize marketing strategies. Bayesian MMM is an advanced approach that allows for the incorporation of prior information, uncertainty quantification, and probabilistic predictions (1). In this paper, we describe the process of building a Bayesian MMM model for the online insurance company Lemonade. We first collected data on Lemonade's marketing activities, such as online advertising, social media, and brand marketing, as well as performance data. We then used a Bayesian framework to estimate the contribution of each marketing channel on total performance, while accounting for various factors such as seasonality, market trends, and macroeconomic indicators. To validate the model, we compared its predictions with the actual performance data from A/B-testing and sliding window holdout data (2). The results showed that the predicted contribution of each marketing channel is aligned with A/B test performance and is actionable. Furthermore, we conducted several scenario analyses using convex optimization to test the sensitivity of the model to different assumptions and to evaluate the impact of changes in the marketing mix on sales. The insights gained from the model allowed Lemonade to adjust their marketing strategy and allocate their budget more effectively. Our case study demonstrates the benefits of using Bayesian MMM for marketing attribution and optimization in a data-driven company like Lemonade. The approach is flexible, interpretable, and can provide valuable insights for decision-making.

The ever growing need for data for machine learning science and applications has fueled a long history of Active Learning (AL) research, as it is able to reduce the amount of annotations necessary to train strong models. However, most research was done for classification problems, as it is generally easier to derive uncertainty quantification (UC) from classification output without changing the model or training procedure. This feat is a lot less common for regression models, with few historic exceptions like Gaussian Processes. This leads to regression problems being under-researched in AL literature. In this paper, we are focusing specifically on the area of regression and recent models with uncertainty quantification (UC) in the architecture. Recently, two main approaches of UC for regression problems have been researched: Firstly, Gaussian neural networks (GNN) [6, 14], which use a neural network to parametrize µ and σ parameters and build a Gaussian predictive distribution and secondly, Normalizing Flows [16, 4], which are parametrizing a free-form predictive distribution with invertible transformations to be able to model more complex target distributions. Their predictive distributions allow these models to not only be trained via Negative Log Likelihood (NLL), but also to draw samples from the predictive distribution as well as to compute the log likelihood of any given point y. Recent works [2, 1] have investigated the potential of uncertainty quantification with normalizing flows by experimenting on synthetic experiments with a known ground-truth uncertainty. Intuitively, a predictive distribution should inertly allow for a good uncertainty quantification (e.g.