Causal abstractions allow us to relate causal models on different levels of granularity. To ensure that the models agree on cause and effect, frameworks for causal abstractions define notions of consistency. Two distinct methods for causal abstraction are common in the literature: (i) graphical abstractions, such as Cluster DAGs, which relate models on a structural level, and (ii) functional abstractions, like $\alpha$-abstractions, which relate models by maps between variables and their ranges. In this paper we will align the notions of graphical and functional consistency and show an equivalence between the class of Cluster DAGs, consistent $\alpha$-abstractions, and constructive $\tau$-abstractions. Furthermore, we extend this alignment and the expressivity of graphical abstractions by introducing Partial Cluster DAGs. Our results provide a rigorous bridge between the functional and graphical frameworks and allow for adoption and transfer of results between them.

Classical information design models (e.g., Bayesian persuasion and cheap talk) require players to have perfect knowledge of the prior distribution of the state of the world. Our paper studies repeated persuasion problems in which the information designer does not know the prior. The information designer learns to design signaling schemes from repeated interactions with the receiver. We design learning algorithms for the information designer to achieve no regret compared to using the optimal signaling scheme with known prior, under two models of the receiver's decision-making. (1) The first model assumes that the receiver knows the prior and can perform posterior update and best respond to signals. In this model, we design a learning algorithm for the information designer with $O(\log T)$ regret in the general case, and another algorithm with $\Theta(\log \log T)$ regret in the case where the receiver has only two actions. (2) The second model assumes that the receiver does not know the prior and employs a no-regret learning algorithm to take actions. We show that the information designer can achieve regret $O(\sqrt{\mathrm{rReg}(T) T})$, where $\mathrm{rReg}(T)=o(T)$ is an upper bound on the receiver's learning regret. Our work thus provides a learning foundation for the problem of information design with unknown prior.

We propose a novel deep neural network methodology for density estimation on product Riemannian manifold domains. In our approach, the network directly parameterizes the unknown density function and is trained using a penalized maximum likelihood framework, with a penalty term formed using manifold differential operators. The network architecture and estimation algorithm are carefully designed to handle the challenges of high-dimensional product manifold domains, effectively mitigating the curse of dimensionality that limits traditional kernel and basis expansion estimators, as well as overcoming the convergence issues encountered by non-specialized neural network methods. Extensive simulations and a real-world application to brain structural connectivity data highlight the clear advantages of our method over the competing alternatives.

This paper proposes an extension of standard mixture stochastic models, by replacing the constant mixture weights with functional weights defined using a classifier. Classifier Weighted Mixtures enable straightforward density evaluation, explicit sampling, and enhanced expressivity in variational estimation problems, without increasing the number of components nor the complexity of the mixture components.

This paper provides a formalism for an important class of causal inference problems inspired by user-advertiser interaction in online advertiser. Then this formalism is specialized to an extension of temporal marked point processes and the neural point processes are suggested as practical solutions to some interesting special cases.

The emergence of machine learning (ML) has been phenomenal, with ML-based models outperforming human intelligence, as in the case of AlphaGo [1] and, more recently, large language models (LLMs). With these advances, ML became state-of-the-art for scientific discovery in various fields of study [2]. However, ML algorithms fail to answer the crucial question "what" brings about an effect and "what if" questions i.e., ML cannot identify causal relationships in data and counterfactual questions. Hence, the need for causality and causal inference a field that focuses on unravelling causal interactions in data. Characterising these interactions in complex dynamical systems is a fundamental question in science [3]. Causal structure learning (CSL)--a computational causal discovery field, taking advantage of statistics and machine learning (ML) to unravel causal relations in data--is particularly appealing because it enables us to answer counterfactual questions [4, 5, 6, 7]. We adopt Pearl's causality framework.

Inferring sky surface brightness distributions from noisy interferometric data in a principled statistical framework has been a key challenge in radio astronomy. In this work, we introduce Imaging for Radio Interferometry with Score-based models (IRIS). We use score-based models trained on optical images of galaxies as an expressive prior in combination with a Gaussian likelihood in the uv-space to infer images of protoplanetary disks from visibility data of the DSHARP survey conducted by ALMA. We demonstrate the advantages of this framework compared with traditional radio interferometry imaging algorithms, showing that it produces plausible posterior samples despite the use of a misspecified galaxy prior. Through coverage testing on simulations, we empirically evaluate the accuracy of this approach to generate calibrated posterior samples.

Uncertainty quantification (UQ) is a critical aspect of artificial intelligence (AI) systems, particularly in high-risk domains such as healthcare, autonomous systems, and financial technology, where decision-making processes must account for uncertainty. This review explores the evolution of uncertainty quantification techniques in AI, distinguishing between aleatoric and epistemic uncertainties, and discusses the mathematical foundations and methods used to quantify these uncertainties. We provide an overview of advanced techniques, including probabilistic methods, ensemble learning, sampling-based approaches, and generative models, while also highlighting hybrid approaches that integrate domain-specific knowledge. Furthermore, we examine the diverse applications of UQ across various fields, emphasizing its impact on decision-making, predictive accuracy, and system robustness. The review also addresses key challenges such as scalability, efficiency, and integration with explainable AI, and outlines future directions for research in this rapidly developing area. Through this comprehensive survey, we aim to provide a deeper understanding of UQ's role in enhancing the reliability, safety, and trustworthiness of AI systems.

Transformers (Vaswani et al. 2017) have achieved tremendous success across various fields. These models are known to be particularly strong in terms of sequence generation, and have revolutionized the way we approach problems related to text generation, translation, and scientific discoveries such as protein generation. Despite these achievements, there remains limited understanding of the theoretical capabilities of transformers as sequence generators. To theoretically understand how transformers efficiently generate sequences, several recent works have studied the the power of transformers in learning specific probability models for sequential data (Ildiz et al. 2024, Rajaraman et al. 2024, Makkuva et al. 2024, Nichani et al. 2024). Specifically, Ildiz et al. (2024) studied the problem of learning Markov chains with a one-layer self-attention model, and developed identifiability and convergence guarantees under certain conditions. Rajaraman et al. (2024) studied the behavior of transformers on data drawn from k-order Markov processes, where the conditional distribution of the next variable in a sequence depends on the previous k variables, and showed that such processes can be learned well by transformers of a constant-order depth. Makkuva et al. (2024) further studied the loss function landscape of one-layer transformers in learning Markov chains. Nichani et al. (2024) studied a setting where the tokens consist of multiple sequences of samples generated from a causal network, and demonstrated that transformers can be trained to learn the causal network structure so that, when seeing a new context-query pair, it can generate prediction according to the learned causal structure and the context. However, similar to the studies of Markov chains, Nichani et al. (2024) mostly focused on the setting where each variable has at most one parent.

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.