{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/learning-hierarchical-interactions-at-scale-a","title":"Learning Hierarchical Interactions at Scale: A Convex Optimization Approach","arxiv_id":"1902.01542","date":"2019-02-05","proceeding":null,"authors":["Hussein Hazimeh","Rahul Mazumder"],"abstract":"In many learning settings, it is beneficial to augment the main features with pairwise interactions. Such interaction models can be often enhanced by performing variable selection under the so-called strong hierarchy constraint: an interaction is non-zero only if its associated main features are non-zero. Existing convex optimization based algorithms face difficulties in handling problems where the number of main features $p \\sim 10^3$ (with total number of features $\\sim p^2$). In this paper, we study a convex relaxation which enforces strong hierarchy and develop a highly scalable algorithm based on proximal gradient descent. We introduce novel screening rules that allow for solving the complicated proximal problem in parallel. In addition, we introduce a specialized active-set strategy with gradient screening for avoiding costly gradient computations. The framework can handle problems having dense design matrices, with $p = 50,000$ ($\\sim 10^9$ interactions)---instances that are much larger than current state of the art. Experiments on real and synthetic data suggest that our toolkit hierScale outperforms the state of the art in terms of prediction and variable selection and can achieve over a 4900x speed-up.","url_abs":"https://arxiv.org/abs/1902.01542v5","url_pdf":"https://arxiv.org/pdf/1902.01542v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"learning-hierarchical-interactions-at-scale-a","repo_url":"https://github.com/hazimehh/hierScale","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"structured-prediction","task_name":"Structured Prediction"},{"task_slug":"variable-selection","task_name":"Variable Selection"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1902.01542","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1902.01542"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/hazimehh/hierScale","reach":null}],"summary":{"unverified":1},"by_repo_kind":{"listed":{"samples":1,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"5d1d139b4a1079c7","entry":"hier_fit","repo":"hazimehh/hierScale","repo_kind":"listed","path":"hierScale/FitPath.py","file_url":"https://github.com/hazimehh/hierScale/blob/HEAD/hierScale/FitPath.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"5d1d139b4a1079c7"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}