Mixed and Covariate-Dependent Graphical Models
Talkat Workshop on Succinct Data Representations and Applications (Simons Institute Big Data 2013) · 2013-09-16..09-19·
summary
Proposes a covariate-dependent Ising with linear parameters estimated by nodewise penalized logistic regressions (neighborhood selection) and L1 penalties, uses stability selection, and applies it to a breast cancer copy‑number dataset with 620 binary loci and 143 patients and 3 covariates, recovering cross‑chromosome edges that match known biology. Extends to mixed data by a truncated conditional Gaussian with weighted L1 (overlapping group structure approximated by weighted L1), fits nodewise linear or logistic regressions, and demonstrates it on 52 songs with 120 labels plus continuous audio features.
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chapters (21)
- 0:00Intro
- 2:08Example: Senate votes
- 4:07Gaussian Graphical Models
- 6:23Binary Markov networks (aka Ising models)
- 7:28Fitting Ising models
- 8:11Covariate dependent graphical models
- 12:32Optimization Criterion
- 12:49Fitting the model
- 14:15Data Description
- 17:37Asymptotic behavior
- 19:19Assumptions
- 19:30Theorem
- 19:43Simulation: Effect of Sparsity
- 19:56Simulation results: Effect of Sparsity
- 21:49Mixed graphical models
- 24:07Markovian conditional Gaussian distributions
- 26:40Model parameters and conditional independence
- 28:54Model fitting
- 32:12Example: music annotation dataset
- 33:18Fitted edges for music data
- 34:22Summary
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