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Shared Features in Log-Linear Models

This document discusses the efficiency of representation in probabilistic graphical models, particularly focusing on log-linear models and Ising models, which employ shared features and weights. It highlights how the same feature and weight can be utilized across various scopes in Markov Random Fields (MRFs) for tasks in natural language processing and image segmentation. The text emphasizes the importance of defining scopes for each feature and illustrates reusability of parameters and structures within and across multiple models, thereby enhancing model efficiency.

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Shared Features in Log-Linear Models

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  1. Representation Probabilistic Graphical Models Template Models Shared Features in Log-Linear Models

  2. Ising Models • In most MRFs, same feature and weight are used over many scopes Ising Model same weight for every adjacent pair

  3. Natural Language Processing • In most MRFs, same feature and weight are used over many scopes Yi Xi Same energy terms wkfk(Xi,Yi) repeat for all positions i in the sequence Same energy terms wmfm(Yi,Yi+1) a;sp repeat for all positions i

  4. Image Segmentation • In most MRFs, same feature and weight are used over many scopes Same features and weights for all superpixels in the image

  5. Repeated Features • Need to specify for each feature fk a set of scopes Scopes[fk] • For each DkScopes[fk] we have a term wkfk(Dk) in the energy function

  6. Summary • Same feature & weight can be used for multiple subsets of variables • Pairs of adjacent pixels/atoms/words • Occurrences of same word in document • Can provide a single template for multiple MNs • Different images • Different sentences • Parameters and structure are reused within an MN and across different MNs • Need to specify set of scopes for each feature

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