{"id":899,"date":"2024-12-31T07:03:47","date_gmt":"2024-12-31T07:03:47","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2024\/12\/31\/2412-20355\/"},"modified":"2024-12-31T07:03:47","modified_gmt":"2024-12-31T07:03:47","slug":"2412-20355","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2024\/12\/31\/2412-20355\/","title":{"rendered":"Confidence Interval Construction and Conditional Variance Estimation with Dense ReLU Networks"},"content":{"rendered":"

Confidence Interval Construction and Conditional Variance Estimation with Dense ReLU Networks
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arXiv:2412.20355v1 Announce Type: new
\nAbstract: This paper addresses the problems of conditional variance estimation and confidence interval construction in nonparametric regression using dense networks with the Rectified Linear Unit (ReLU) activation function. We present a residual-based framework for conditional variance estimation, deriving nonasymptotic bounds for variance estimation under both heteroscedastic and homoscedastic settings. We relax the sub-Gaussian noise assumption, allowing the proposed bounds to accommodate sub-Exponential noise and beyond. Building on this, for a ReLU neural network estimator, we derive non-asymptotic bounds for both its conditional mean and variance estimation, representing the first result for variance estimation using ReLU networks. Furthermore, we develop a ReLU network based robust bootstrap procedure (Efron, 1992) for constructing confidence intervals for the true mean that comes with a theoretical guarantee on the coverage, providing a significant advancement in uncertainty quantification and the construction of reliable confidence intervals in deep learning settings.<\/div>\n

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\n Carlos Misael Madrid Padilla, Oscar Hernan Madrid Padilla, Yik Lun Kei, Zhi Zhang, Yanzhen Chen
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Confidence Interval Construction and Conditional Variance Estimation with Dense ReLU Networks arXiv:2412.20355v1 Announce Type: new Abstract: This paper addresses the problems of conditional variance estimation and confidence interval construction in nonparametric regression using dense networks with the Rectified Linear Unit (ReLU) activation function. We present a residual-based framework for conditional variance estimation, deriving nonasymptotic bounds […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,112],"tags":[374,1046,659],"class_list":["post-899","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-estimation","tag-relu","tag-variance"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/899"}],"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=899"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/899\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=899"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=899"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=899"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}