{"id":2834,"date":"2025-04-03T07:02:29","date_gmt":"2025-04-03T07:02:29","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/04\/03\/2504-01570\/"},"modified":"2025-04-03T07:02:29","modified_gmt":"2025-04-03T07:02:29","slug":"2504-01570","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/04\/03\/2504-01570\/","title":{"rendered":"Density estimation via mixture discrepancy and moments"},"content":{"rendered":"

Density estimation via mixture discrepancy and moments
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arXiv:2504.01570v1 Announce Type: new
\nAbstract: With the aim of generalizing histogram statistics to higher dimensional cases, density estimation via discrepancy based sequential partition (DSP) has been proposed [D. Li, K. Yang, W. Wong, Advances in Neural Information Processing Systems (2016) 1099-1107] to learn an adaptive piecewise constant approximation defined on a binary sequential partition of the underlying domain, where the star discrepancy is adopted to measure the uniformity of particle distribution. However, the calculation of the star discrepancy is NP-hard and it does not satisfy the reflection invariance and rotation invariance either. To this end, we use the mixture discrepancy and the comparison of moments as a replacement of the star discrepancy, leading to the density estimation via mixture discrepancy based sequential partition (DSP-mix) and density estimation via moments based sequential partition (MSP), respectively. Both DSP-mix and MSP are computationally tractable and exhibit the reflection and rotation invariance. Numerical experiments in reconstructing the $d$-D mixture of Gaussians and Betas with $d=2, 3, dots, 6$ demonstrate that DSP-mix and MSP both run approximately ten times faster than DSP while maintaining the same accuracy.<\/div>\n

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\n Zhengyang Lei, Sihong Shao
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Density estimation via mixture discrepancy and moments arXiv:2504.01570v1 Announce Type: new Abstract: With the aim of generalizing histogram statistics to higher dimensional cases, density estimation via discrepancy based sequential partition (DSP) has been proposed [D. Li, K. Yang, W. Wong, Advances in Neural Information Processing Systems (2016) 1099-1107] to learn an adaptive piecewise constant approximation […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,377,183,112],"tags":[1502,560,374],"class_list":["post-2834","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-physics-comp-ph","category-stat-me","category-stat-ml","tag-density","tag-discrepancy","tag-estimation"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2834"}],"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=2834"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2834\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=2834"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=2834"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=2834"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}