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In causal graphical models based on directed acyclic graphs (DAGs), directed paths represent causal pathways between the corresponding variables. The variable at the beginning of such a path is referred to as an ancestor of the variable at the end of the path. Ancestral relations between variables play an important role in causal modeling. In existing literature on structure learning, these relations are usually deduced from learned structures and used for orienting edges or formulating constraints of the space of possible DAGs. However, they are usually not posed as immediate target of inference. In this work we investigate the graphical characterization of ancestral relations via CPDAGs and d-separation relations. We propose a framework that can learn definite non-ancestral relations without first learning the skeleton. This frame-work yields structural information that can be used in both score- and constraint-based algorithms to learn causal DAGs more efficiently.
We present the Cholesky-factored symmetric positive definite neural network (SPD-NN) for modeling constitutive relations in dynamical equations. Instead of directly predicting the stress, the SPD-NN trains a neural network to predict the Cholesky fac
Constraint-based causal discovery from limited data is a notoriously difficult challenge due to the many borderline independence test decisions. Several approaches to improve the reliability of the predictions by exploiting redundancy in the independ
Representations in the form of Symmetric Positive Definite (SPD) matrices have been popularized in a variety of visual learning applications due to their demonstrated ability to capture rich second-order statistics of visual data. There exist several
In settings ranging from weather forecasts to political prognostications to financial projections, probability estimates of future binary outcomes often evolve over time. For example, the estimated likelihood of rain on a specific day changes by the
Crucial for building trust in deep learning models for critical real-world applications is efficient and theoretically sound uncertainty quantification, a task that continues to be challenging. Useful uncertainty information is expected to have two k