Markov locality, which will use the language of Markov blankets. Markov blanket but not all blankets are boundaries. A Markov boundary can be thought of as the set of variables that'locally' communicate with the parameter Importantly, for Markov-locality to be of use, we would like the Markov boundaries of random variables in the model of interest to be unique. Assume all quantities are as in A.1, that the conditional independence relationships This proof relies on Lemma A.1, proved below. We wish to prove Eq. 2 Eq.

Over the last several decades, computational neuroscience researchers have proposed a variety of "biologically plausible" models of synaptic plasticity that seek to provide normative accounts of a variety of learning processes in the brain--these models aim to explain how modifications of

We analyze the complexity of learning directed acyclic graphical models from observational data in general settings without specific distributional assumptions. Our approach is information-theoretic and uses a local Markov boundary search procedure in order to recursively construct ancestral sets in the underlying graphical model. Perhaps surprisingly, we show that for certain graph ensembles, a simple forward greedy search algorithm (i.e.

"why," is crucial for attribution and explanation,

Lasso performance, with the added benefit of providing multiple solutions.

Understanding causality in event sequences with thousands of sparse event types is critical in domains such as healthcare, cybersecurity, or vehicle diagnostics, yet current methods fail to scale. We present OSCAR, a one-shot causal autoregressive method that infers per-sequence Markov Boundaries using two pretrained Transformers as density estimators. This enables efficient, parallel causal discovery without costly global CI testing. On a real-world automotive dataset with 29,100 events and 474 labels, OSCAR recovers interpretable causal structures in minutes, while classical methods fail to scale, enabling practical scientific diagnostics at production scale.