We study the identification of causal effects in the presence of different types of constraints (e.g., logical constraints) in addition to the causal graph. These constraints impose restrictions on the models (parameterizations) induced by the causal graph, reducing the set of models considered by the identifiability problem. We formalize the notion of constrained identifiability, which takes a set of constraints as another input to the classical definition of identifiability. We then introduce a framework for testing constrained identifiability by employing tractable Arithmetic Circuits (ACs), which enables us to accommodate constraints systematically. We show that this AC-based approach is at least as complete as existing algorithms (e.g., do-calculus) for testing classical identifiability, which only assumes the constraint of strict positivity. We use examples to demonstrate the effectiveness of this AC-based approach by showing that unidentifiable causal effects may become identifiable under different types of constraints.

We introduce a causal modeling framework that captures the input-output behavior of predictive models (e.g., machine learning models) by representing it using causal graphs. The framework enables us to define and identify features that directly cause the predictions, which has broad implications for data collection and model evaluation. We show two assumptions under which the direct causes can be discovered from data, one of which further simplifies the discovery process. In addition to providing sound and complete algorithms, we propose an optimization technique based on an independence rule that can be integrated with the algorithms to speed up the discovery process both theoretically and empirically.

Although deep learning techniques show promising results for many neuroimaging tasks in research settings, they have not yet found widespread use in clinical scenarios. One of the reasons for this problem is that many machine learning models only identify correlations between the input images and the outputs of interest, which can lead to many practical problems, such as encoding of uninformative biases and reduced explainability. Thus, recent research is exploring if integrating a priori causal knowledge into deep learning models is a potential avenue to identify these problems. This work introduces a new causal generative architecture named Masked Causal Flow (MACAW) for neuroimaging applications. Within this context, three main contributions are described. First, a novel approach that integrates complex causal structures into normalizing flows is proposed. Second, counterfactual prediction is performed to identify the changes in effect variables associated with a cause variable. Finally, an explicit Bayesian inference for classification is derived and implemented, providing an inherent uncertainty estimation. The feasibility of the proposed method was first evaluated using synthetic data and then using MRI brain data from more than 23000 participants of the UK biobank study. The evaluation results show that the proposed method can (1) accurately encode causal reasoning and generate counterfactuals highlighting the structural changes in the brain known to be associated with aging, (2) accurately predict a subject's age from a single 2D MRI slice, and (3) generate new samples assuming other values for subject-specific indicators such as age, sex, and body mass index. The code for a toy dataset is available at the following link: https://github.com/vibujithan/macaw-2D.git.

The rapid advancements in machine learning have made its application to anomalous diffusion analysis both essential and inevitable. This review systematically introduces the integration of machine learning techniques for enhanced analysis of anomalous diffusion, focusing on two pivotal aspects: single trajectory characterization via machine learning and representation learning of anomalous diffusion. We extensively compare various machine learning methods, including both classical machine learning and deep learning, used for the inference of diffusion parameters and trajectory segmentation. Additionally, platforms such as the Anomalous Diffusion Challenge that serve as benchmarks for evaluating these methods are highlighted. On the other hand, we outline three primary strategies for representing anomalous diffusion: the combination of predefined features, the feature vector from the penultimate layer of neural network, and the latent representation from the autoencoder, analyzing their applicability across various scenarios. This investigation paves the way for future research, offering valuable perspectives that can further enrich the study of anomalous diffusion and advance the application of artificial intelligence in statistical physics and biophysics.

The AI safety literature is full of examples of powerful AI agents that, in blindly pursuing a specific and usually narrow objective, ends up with unacceptable and even catastrophic collateral damage to others. In this paper, we consider the problem of social harms that can result from actions taken by learning and utility-maximising agents in a multi-agent environment. The problem of measuring social harms or impacts in such multi-agent settings, especially when the agents are artificial generally intelligent (AGI) agents, was listed as an open problem in Everitt et al, 2018. We attempt a partial answer to that open problem in the form of market-based mechanisms to quantify and control the cost of such social harms. The proposed setup captures many well-studied special cases and is more general than existing formulations of multi-agent reinforcement learning with mechanism design in two ways: (i) the underlying environment is a history-based general reinforcement learning environment like in AIXI; (ii) the reinforcement-learning agents participating in the environment can have different learning strategies and planning horizons. To demonstrate the practicality of the proposed setup, we survey some key classes of learning algorithms and present a few applications, including a discussion of the Paperclips problem and pollution control with a cap-and-trade system.

We introduce a novel algorithm for controlling linear time invariant systems in a tracking problem. The controller is based on a Gaussian Process (GP) whose realizations satisfy a system of linear ordinary differential equations with constant coefficients. Control inputs for tracking are determined by conditioning the prior GP on the setpoints, i.e. control as inference. The resulting Model Predictive Control scheme incorporates pointwise soft constraints by introducing virtual setpoints to the posterior Gaussian process. We show theoretically that our controller satisfies asymptotical stability for the optimal control problem by leveraging general results from Bayesian inference and demonstrate this result in a numerical example.

A hallmark of intelligence is the ability to flesh out underspecified situations using "common sense." We propose to extract that common sense from large language models (LLMs), in a form that can feed into probabilistic inference. We focus our investigation on $\textit{guesstimation}$ questions such as "How much are Airbnb listings in Newark, NJ?" Formulating a sensible answer without access to data requires drawing on, and integrating, bits of common knowledge about how $\texttt{Price}$ and $\texttt{Location}$ may relate to other variables, such as $\texttt{Property Type}$. Our framework answers such a question by synthesizing an $\textit{ad hoc}$ probabilistic model. First we prompt an LLM to propose a set of random variables relevant to the question, followed by moment constraints on their joint distribution. We then optimize the joint distribution $p$ within a log-linear family to maximize the overall constraint satisfaction. Our experiments show that LLMs can successfully be prompted to propose reasonable variables, and while the proposed numerical constraints can be noisy, jointly optimizing for their satisfaction reconciles them. When evaluated on probabilistic questions derived from three real-world tabular datasets, we find that our framework performs comparably to a direct prompting baseline in terms of total variation distance from the dataset distribution, and is similarly robust to noise.

Causal discovery aims to automatically uncover causal relationships from data, a capability with significant potential across many scientific disciplines. However, its real-world applications remain limited. Current methods often rely on unrealistic assumptions and are evaluated only on simple synthetic toy datasets, often with inadequate evaluation metrics. In this paper, we substantiate these claims by performing a systematic review of the recent causal discovery literature. We present applications in biology, neuroscience, and Earth sciences - fields where causal discovery holds promise for addressing key challenges. We highlight available simulated and real-world datasets from these domains and discuss common assumption violations that have spurred the development of new methods. Our goal is to encourage the community to adopt better evaluation practices by utilizing realistic datasets and more adequate metrics.

Hypergraphs extend traditional graphs by allowing edges to connect multiple nodes, while superhypergraphs further generalize this concept to represent even more complex relationships. Neural networks, inspired by biological systems, are widely used for tasks such as pattern recognition, data classification, and prediction. Graph Neural Networks (GNNs), a well-established framework, have recently been extended to Hypergraph Neural Networks (HGNNs), with their properties and applications being actively studied. The Plithogenic Graph framework enhances graph representations by integrating multi-valued attributes, as well as membership and contradiction functions, enabling the detailed modeling of complex relationships. In the context of handling uncertainty, concepts such as Fuzzy Graphs and Neutrosophic Graphs have gained prominence. It is well established that Plithogenic Graphs serve as a generalization of both Fuzzy Graphs and Neutrosophic Graphs. Furthermore, the Fuzzy Graph Neural Network has been proposed and is an active area of research. This paper establishes the theoretical foundation for the development of SuperHyperGraph Neural Networks (SHGNNs) and Plithogenic Graph Neural Networks, expanding the applicability of neural networks to these advanced graph structures. While mathematical generalizations and proofs are presented, future computational experiments are anticipated.

Natural language syntax can serve as a major test for how to integrate two infamously distinct frameworks: symbolic representations and connectionist neural networks. Building on a recent neurocomputational architecture for syntax (ROSE), I discuss the prospects of reconciling the neural code for hierarchical 'vertical' syntax with linear and predictive 'horizontal' processes via a hybrid neurosymbolic model. I argue that the former can be accounted for via the higher levels of ROSE in terms of vertical phrase structure representations, while the latter can explain horizontal forms of linguistic information via the tuning of the lower levels to statistical and perceptual inferences. One prediction of this is that artificial language models will contribute to the cognitive neuroscience of horizontal morphosyntax, but much less so to hierarchically compositional structures. I claim that this perspective helps resolve many current tensions in the literature. Options for integrating these two neural codes are discussed, with particular emphasis on how predictive coding mechanisms can serve as interfaces between symbolic oscillatory phase codes and population codes for the statistics of linearized aspects of syntax. Lastly, I provide a neurosymbolic mathematical model for how to inject symbolic representations into a neural regime encoding lexico-semantic statistical features.