We here focus on the task of learning Granger causality matrices for multivariate point processes. In order to accomplish this task, our work is the first to explore the use of Wold processes. By doing so, we are able to develop asymptotically fast MCMC learning algorithms. With $N$ being the total number of events and $K$ the number of processes, our learning algorithm has a $O(N(\,\log(N)\,+\,\log(K)))$ cost per iteration. This is much faster than the $O(N^3\,K^2)$ or $O(K^3)$ for the state of the art. Our approach, called GrangerBusca, is validated on nine datasets. This is an advance in relation to most prior efforts which focus mostly on subsets of the Memetracker data. Regarding accuracy, GrangerBusca is three times more accurate (in Precision@10) than the state of the art for the commonly explored subsets Memetracker. Due to GrangerBusca's much lower training complexity, our approach is the only one able to train models for larger, full, sets of data.

The description of the dynamics of complex systems, in particular the capture of the interaction structure and causal relationships between elements of the system, is one of the central questions of interdisciplinary research. While the characterization of pairwise causal interactions is a relatively ripe field with established theoretical concepts and the current focus is on technical issues of their efficient estimation, it turns out that the standard concepts such as Granger causality or transfer entropy may not faithfully reflect possible synergies or interactions of higher orders, phenomena highly relevant for many real-world complex systems. In this paper, we propose a generalization and refinement of the information-theoretic approach to causal inference, enabling the description of truly multivariate, rather than multiple pairwise, causal interactions, and moving thus from causal networks to causal hypernetworks. In particular, while keeping the ability to control for mediating variables or common causes, in case of purely synergetic interactions such as the exclusive disjunction, it ascribes the causal role to the multivariate causal set but \emph{not} to individual inputs, distinguishing it thus from the case of e.g. two additive univariate causes. We demonstrate this concept by application to illustrative theoretical examples as well as a biophysically realistic simulation of biological neuronal dynamics recently reported to employ synergetic computations.

Most approaches for assessing causality in complex dynamical systems fail when the interactions between variables are inherently non-linear and non-stationary. Here we introduce Temporal Autoencoders for Causal Inference (TACI), a methodology that combines a new surrogate data metric for assessing causal interactions with a novel two-headed machine learning architecture to identify and measure the direction and strength of time-varying causal interactions. Through tests on both synthetic and real-world datasets, we demonstrate TACI's ability to accurately quantify dynamic causal interactions across a variety of systems. Our findings display the method's effectiveness compared to existing approaches and also highlight our approach's potential to build a deeper understanding of the mechanisms that underlie time-varying interactions in physical and biological systems.

Identifying causal relationships among distinct brain areas, known as effective connectivity, holds key insights into the brain's information processing and cognitive functions. Electroencephalogram (EEG) signals exhibit intricate dynamics and inter-areal interactions within the brain. However, methods for characterizing nonlinear causal interactions among multiple brain regions remain relatively underdeveloped. In this study, we proposed a data-driven framework to infer effective connectivity by perturbing the trained neural networks. Specifically, we trained neural networks (i.e., CNN, vanilla RNN, GRU, LSTM, and Transformer) to predict future EEG signals according to historical data and perturbed the networks' input to obtain effective connectivity (EC) between the perturbed EEG channel and the rest of the channels. The EC reflects the causal impact of perturbing one node on others. The performance was tested on the synthetic EEG generated by a biological-plausible Jansen-Rit model. CNN and Transformer obtained the best performance on both 3-channel and 90-channel synthetic EEG data, outperforming the classical Granger causality method. Our work demonstrated the potential of perturbing an artificial neural network, learned to predict future system dynamics, to uncover the underlying causal structure.

Determining causal effects of temporal multi-intervention assists decision-making. Restricted by time-varying bias, selection bias, and interactions of multiple interventions, the disentanglement and estimation of multiple treatment effects from individual temporal data is still rare. To tackle these challenges, we propose a comprehensive framework of temporal counterfactual forecasting from an individual multiple treatment perspective (TCFimt). TCFimt constructs adversarial tasks in a seq2seq framework to alleviate selection and time-varying bias and designs a contrastive learning-based block to decouple a mixed treatment effect into separated main treatment effects and causal interactions which further improves estimation accuracy. Through implementing experiments on two real-world datasets from distinct fields, the proposed method shows satisfactory performance in predicting future outcomes with specific treatments and in choosing optimal treatment type and timing than state-of-the-art methods.

We present a novel task that measures how people generalize objects' causal powers based on observing a single (Experiment 1) or a few (Experiment 2) causal interactions between object pairs. We propose a computational modeling framework that can synthesize human-like generalization patterns in our task setting, and sheds light on how people may navigate the compositional space of possible causal functions and categories efficiently. Our modeling framework combines a causal function generator that makes use of agent and recipient objects' features and relations, and a Bayesian non-parametric inference process to govern the degree of similarity-based generalization. Our model has a natural "resource-rational" variant that outperforms a naive Bayesian account in describing participants, in particular reproducing a generalization-order effect and causal asymmetry observed in our behavioral experiments. We argue that this modeling framework provides a computationally plausible mechanism for real world causal generalization.

Causal discovery, i.e., inferring underlying cause-effect relationships from observations of a scene or system, is an inherent mechanism in human cognition, but has been shown to be highly challenging to automate. The majority of approaches in the literature aiming for this task consider constrained scenarios with fully observed variables or data from stationary time-series. In this work we aim for causal discovery in a more general class of scenarios, scenes with non-stationary behavior over time. For our purposes we here regard a scene as a composition objects interacting with each other over time. Non-stationarity is modeled as stationarity conditioned on an underlying variable, a state, which can be of varying dimension, more or less hidden given observations of the scene, and also depend more or less directly on these observations. We propose a probabilistic deep learning approach called State-Dependent Causal Inference (SDCI) for causal discovery in such conditionally stationary time-series data. Results in two different synthetic scenarios show that this method is able to recover the underlying causal dependencies with high accuracy even in cases with hidden states.

Thanks to technological advances leading to near-continuous time observations, emerging multivariate point process data offer new opportunities for causal discovery. However, a key obstacle in achieving this goal is that many relevant processes may not be observed in practice. Naive estimation approaches that ignore these hidden variables can generate misleading results because of the unadjusted confounding. To plug this gap, we propose a deconfounding procedure to estimate high-dimensional point process networks with only a subset of the nodes being observed. Our method allows flexible connections between the observed and unobserved processes. It also allows the number of unobserved processes to be unknown and potentially larger than the number of observed nodes. Theoretical analyses and numerical studies highlight the advantages of the proposed method in identifying causal interactions among the observed processes.

They say in chaos theory that a butterfly flapping its wings in Brazil could unwittingly set up a tornado in Texas. But that tornado should at least need some time to form, given the 5,000-mile distance between the two regions. This time delay between cause and effects in climate patterns is well apparent in the less-dramatized example of El Niño events (as explained in this video). These events occur roughly every two to seven years. But when they do, they build up over several months and their effects can take several months more to spread around the world.

Causal inference from observation data is a core problem in many scientific fields. Here we present a general supervised deep learning framework that infers causal interactions by transforming the input vectors to an image-like representation for every pair of inputs. Given a training dataset we first construct a normalized empirical probability density distribution (NEPDF) matrix. We then train a convolutional neural network (CNN) on NEPDFs for causality predictions. We tested the method on several different simulated and real world data and compared it to prior methods for causal inference. As we show, the method is general, can efficiently handle very large datasets and improves upon prior methods.