Name
Abstract | ||
|---|---|---|
We propose a new approach for learning a sparse graphical model approximation to a specified multivariate probability distri- bution (such as the empirical distribution of sample data). The selection of sparse graph structure arises naturally in our ap- proach through solution of a convex opti- mization problem, which differentiates our method from standard combinatorial ap- proaches. We seek the maximum entropy re- laxation (MER) within an exponential fam- ily, which maximizes entropy subject to con- straints that marginal distributions on small subsets of variables are close to the prescribed marginals in relative entropy. To solve MER, we present a modified primal-dual interior point method that exploits sparsity of the Fisher information matrix in models defined on chordal graphs. This leads to a tractable, scalable approach provided the level of relax- ation in MER is sufficient to obtain a thin graph. The merits of our approach are inves- tigated by recovering the structure of some simple graphical models from sample data. |
Year | Venue | Keywords |
|---|---|---|
2007 | AISTATS | chordal graph,maximum entropy,graphical model,fisher information matrix,relative entropy,empirical distribution |
Field | DocType | Citations |
Entropy rate,Mathematical optimization,Maximum-entropy Markov model,Maximum entropy thermodynamics,Joint entropy,Artificial intelligence,Graphical model,Principle of maximum entropy,Machine learning,Kullback–Leibler divergence,Mathematics,Maximum entropy probability distribution | Journal | 5 |
PageRank | References | Authors |
0.63 | 10 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jason K. Johnson | 1 | 201 | 14.07 |
| Venkat Chandrasekaran | 2 | 716 | 37.92 |
| Alan S. Willsky | 3 | 7466 | 847.01 |