Papers › Sparse Logistic Regression Learns All Discrete Pairwise Graphical Models
Sparse Logistic Regression Learns All Discrete Pairwise Graphical Models
Shanshan Wu, Sujay Sanghavi, Alexandros G. Dimakis
We characterize the effectiveness of a classical algorithm for recovering the Markov graph of a general discrete pairwise graphical model from i.i.d. samples. The algorithm is (appropriately regularized) maximum conditional log-likelihood, which involves solving a convex program for each node; for Ising models this is ℓ₁-constrained logistic regression, while for more general alphabets an ℓ_(2,1) group-norm constraint needs to be used. We show that this algorithm can recover any arbitrary discrete pairwise graphical model, and also characterize its sample complexity as a function of model width, alphabet size, edge parameter accuracy, and the number of variables. We show that along every one of these axes, it matches or improves on all existing results and algorithms for this problem. Our analysis applies a sharp generalization error bound for logistic regression when the weight vector has an ℓ₁ constraint (or ℓ_(2,1) constraint) and the sample vector has an ℓ_∞ constraint (or ℓ_(2, ∞) constraint). We also show that the proposed convex programs can be efficiently solved in Õ(n²) running time (where n is the number of variables) under the same statistical guarantees. We provide experimental results to support our analysis.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Tasks
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Methods
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections