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Graphical Models: A Combinatorial and Geometric Perspective
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Caroline Uhler, MIT
Winter School on Geometric Constraint Systems
Abstract: Graphical models are used throughout the natural sciences, social sciences, and economics to model statistical relationships between variables of interest. When studying graphical models, combinatorial and geometric constraints naturally arise and their understanding is required to advance the statistical methodology. The first lecture introduces graphical models, providing the foundations to connect networks with probability distributions. The second lecture discusses undirected graphical models and additional structure such as total positivity and its impact on structure learning. The last lecture discusses causality and the inherent combinatorial and geometric constraints underlying causal structure discovery.
Winter School on Geometric Constraint Systems
Abstract: Graphical models are used throughout the natural sciences, social sciences, and economics to model statistical relationships between variables of interest. When studying graphical models, combinatorial and geometric constraints naturally arise and their understanding is required to advance the statistical methodology. The first lecture introduces graphical models, providing the foundations to connect networks with probability distributions. The second lecture discusses undirected graphical models and additional structure such as total positivity and its impact on structure learning. The last lecture discusses causality and the inherent combinatorial and geometric constraints underlying causal structure discovery.
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