{"paper":{"title":"Informational and Causal Architecture of Continuous-time Renewal and Hidden Semi-Markov Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.ST","nlin.CD","stat.TH"],"primary_cat":"cond-mat.stat-mech","authors_text":"James P. Crutchfield, Sarah E. Marzen","submitted_at":"2016-11-03T17:24:11Z","abstract_excerpt":"We introduce the minimal maximally predictive models ({\\epsilon}-machines) of processes generated by certain hidden semi-Markov models. Their causal states are either hybrid discrete-continuous or continuous random variables and causal-state transitions are described by partial differential equations. Closed-form expressions are given for statistical complexities, excess entropies, and differential information anatomy rates. We present a complete analysis of the {\\epsilon}-machines of continuous-time renewal processes and, then, extend this to processes generated by unifilar hidden semi-Markov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01099","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}