{"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/bayesian-allocation-model-inference-by","title":"Bayesian Allocation Model: Inference by Sequential Monte Carlo for Nonnegative Tensor Factorizations and Topic Models using Polya Urns","arxiv_id":"1903.04478","date":"2019-03-11","proceeding":null,"authors":["Ali Taylan Cemgil","Mehmet Burak Kurutmaz","Sinan Yildirim","Melih Barsbey","Umut Simsekli"],"abstract":"We introduce a dynamic generative model, Bayesian allocation model (BAM),\nwhich establishes explicit connections between nonnegative tensor factorization\n(NTF), graphical models of discrete probability distributions and their\nBayesian extensions, and the topic models such as the latent Dirichlet\nallocation. BAM is based on a Poisson process, whose events are marked by using\na Bayesian network, where the conditional probability tables of this network\nare then integrated out analytically. We show that the resulting marginal\nprocess turns out to be a Polya urn, an integer valued self-reinforcing\nprocess. This urn processes, which we name a Polya-Bayes process, obey certain\nconditional independence properties that provide further insight about the\nnature of NTF. These insights also let us develop space efficient simulation\nalgorithms that respect the potential sparsity of data: we propose a class of\nsequential importance sampling algorithms for computing NTF and approximating\ntheir marginal likelihood, which would be useful for model selection. The\nresulting methods can also be viewed as a model scoring method for topic models\nand discrete Bayesian networks with hidden variables. The new algorithms have\nfavourable properties in the sparse data regime when contrasted with\nvariational algorithms that become more accurate when the total sum of the\nelements of the observed tensor goes to infinity. We illustrate the performance\non several examples and numerically study the behaviour of the algorithms for\nvarious data regimes.","url_abs":"http://arxiv.org/abs/1903.04478v1","url_pdf":"http://arxiv.org/pdf/1903.04478v1.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":"bayesian-allocation-model-inference-by","repo_url":"https://github.com/atcemgil/bam","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"model-selection","task_name":"Model Selection"},{"task_slug":"topic-models","task_name":"Topic Models"}],"methods":[{"method_slug":"bam","method_name":"BAM"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}