Related papers: Multi-trek separation in Linear Structural Equatio…
We prove a tangle-tree theorem and a tangle duality theorem for abstract separation systems $\vec S$ that are submodular in the structural sense that, for every pair of oriented separations, $\vec S$ contains either their meet or their join…
Causality plays an important role in understanding intelligent behavior, and there is a wealth of literature on mathematical models for causality, most of which is focused on causal graphs. Causal graphs are a powerful tool for a wide range…
We propose a new method of discovering causal structures, based on the detection of local, spontaneous changes in the underlying data-generating model. We analyze the classes of structures that are equivalent relative to a stream of…
Unobserved confounding is one of the greatest challenges for causal discovery. The case in which unobserved variables have a widespread effect on many of the observed ones is particularly difficult because most pairs of variables are…
Causal discovery algorithms aim at untangling complex causal relationships from data. Here, we study causal discovery and inference methods based on staged tree models, which can represent complex and asymmetric causal relationships between…
Structural equation models (SEMs) have been widely adopted for inference of causal interactions in complex networks. Recent examples include unveiling topologies of hidden causal networks over which processes such as spreading diseases, or…
Massive data collection holds the promise of a better understanding of complex phenomena and, ultimately, better decisions. Representation learning has become a key driver of deep learning applications, as it allows learning latent spaces…
Causal discovery, the task of automatically constructing a causal model from data, is of major significance across the sciences. Evaluating the performance of causal discovery algorithms should ideally involve comparing the inferred models…
We consider the problem of causal discovery (a.k.a., causal structure learning) in a multi-domain setting. We assume that the causal functions are invariant across the domains, while the distribution of the exogenous noise may vary. Under…
In the mixture models problem it is assumed that there are $K$ distributions $\theta_{1},\ldots,\theta_{K}$ and one gets to observe a sample from a mixture of these distributions with unknown coefficients. The goal is to associate instances…
Gaussian graphical models are parametric statistical models for jointly normal random variables whose dependence structure is determined by a graph. In previous work, we introduced trek separation, which gives a necessary and sufficient…
Discovering causal relationships from observational data, particularly in the presence of latent variables, poses a challenging problem. While current local structure learning methods have proven effective and efficient when the focus lies…
Structural analysis methods (e.g., probing and feature attribution) are increasingly important tools for neural network analysis. We propose a new structural analysis method grounded in a formal theory of causal abstraction that provides…
Overparameterized neural networks often contain many removable neurons, yet what makes a neuron redundant remains poorly understood. Existing pruning criteria commonly rely on local quantities such as weight magnitude, activation strength,…
We introduce the problem of reconstructing a sequence of multidimensional real vectors where some of the data are missing. This problem contains regression and mapping inversion as particular cases where the pattern of missing data is…
The broad concept of emergence is instrumental in various of the most challenging open scientific questions -- yet, few quantitative theories of what constitutes emergent phenomena have been proposed. This article introduces a formal theory…
Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater…
We consider the problem of predicting several response variables using the same set of explanatory variables. This setting naturally induces a group structure over the coefficient matrix, in which every explanatory variable corresponds to a…
In this paper, the relationship between probabilistic graphical models, in particular Bayesian networks, and causal diagrams, also called structural causal models, is studied. Structural causal models are deterministic models, based on…
We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…