{"id":5812,"date":"2025-08-04T07:02:54","date_gmt":"2025-08-04T07:02:54","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/08\/04\/2507-22786\/"},"modified":"2025-08-04T07:02:54","modified_gmt":"2025-08-04T07:02:54","slug":"2507-22786","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/08\/04\/2507-22786\/","title":{"rendered":"DO-EM: Density Operator Expectation Maximization"},"content":{"rendered":"

DO-EM: Density Operator Expectation Maximization
\n \t

\n
<\/BR>
\n
\n \t

\n
<\/BR><\/p>\n

arXiv:2507.22786v1 Announce Type: cross
\nAbstract: Density operators, quantum generalizations of probability distributions, are gaining prominence in machine learning due to their foundational role in quantum computing. Generative modeling based on density operator models (textbf{DOMs}) is an emerging field, but existing training algorithms — such as those for the Quantum Boltzmann Machine — do not scale to real-world data, such as the MNIST dataset. The Expectation-Maximization algorithm has played a fundamental role in enabling scalable training of probabilistic latent variable models on real-world datasets. textit{In this paper, we develop an Expectation-Maximization framework to learn latent variable models defined through textbf{DOMs} on classical hardware, with resources comparable to those used for probabilistic models, while scaling to real-world data.} However, designing such an algorithm is nontrivial due to the absence of a well-defined quantum analogue to conditional probability, which complicates the Expectation step. To overcome this, we reformulate the Expectation step as a quantum information projection (QIP) problem and show that the Petz Recovery Map provides a solution under sufficient conditions. Using this formulation, we introduce the Density Operator Expectation Maximization (DO-EM) algorithm — an iterative Minorant-Maximization procedure that optimizes a quantum evidence lower bound. We show that the textbf{DO-EM} algorithm ensures non-decreasing log-likelihood across iterations for a broad class of models. Finally, we present Quantum Interleaved Deep Boltzmann Machines (textbf{QiDBMs}), a textbf{DOM} that can be trained with the same resources as a DBM. When trained with textbf{DO-EM} under Contrastive Divergence, a textbf{QiDBM} outperforms larger classical DBMs in image generation on the MNIST dataset, achieving a 40–60% reduction in the Fr’echet Inception Distance.<\/div>\n

\t

\n
<\/BR>
\n Adit Vishnu, Abhay Shastry, Dhruva Kashyap, Chiranjib Bhattacharyya
\n \t

\n
<\/BR>
\nGo to original source<\/a>
\n \t

\n
<\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"

DO-EM: Density Operator Expectation Maximization arXiv:2507.22786v1 Announce Type: cross Abstract: Density operators, quantum generalizations of probability distributions, are gaining prominence in machine learning due to their foundational role in quantum computing. Generative modeling based on density operator models (textbf{DOMs}) is an emerging field, but existing training algorithms — such as those for the Quantum Boltzmann […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,877,112],"tags":[3250,1146,2911],"class_list":["post-5812","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-quant-ph","category-stat-ml","tag-expectation","tag-quantum","tag-textbf"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5812"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=5812"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5812\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=5812"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=5812"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=5812"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}