{"paper":{"title":"Convergence of Contrastive Divergence with Annealed Learning Rate in Exponential Family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Bai Jiang, Tung-yu Wu, Wing H. Wong","submitted_at":"2016-05-20T06:26:38Z","abstract_excerpt":"In our recent paper, we showed that in exponential family, contrastive divergence (CD) with fixed learning rate will give asymptotically consistent estimates \\cite{wu2016convergence}. In this paper, we establish consistency and convergence rate of CD with annealed learning rate $\\eta_t$. Specifically, suppose CD-$m$ generates the sequence of parameters $\\{\\theta_t\\}_{t \\ge 0}$ using an i.i.d. data sample $\\mathbf{X}_1^n \\sim p_{\\theta^*}$ of size $n$, then $\\delta_n(\\mathbf{X}_1^n) = \\limsup_{t \\to \\infty} \\Vert \\sum_{s=t_0}^t \\eta_s \\theta_s / \\sum_{s=t_0}^t \\eta_s - \\theta^* \\Vert$ converges"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06220","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"}