{"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/on-the-pitfalls-of-heteroscedastic-1","title":"On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networks","arxiv_id":"2203.09168","date":"2022-03-17","proceeding":"ICLR 2022 4","authors":["Maximilian Seitzer","Arash Tavakoli","Dimitrije Antic","Georg Martius"],"abstract":"Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by maximizing the logarithm of the likelihood function under the observed data. In this work, we examine this approach and identify potential hazards associated with the use of log-likelihood in conjunction with gradient-based optimizers. First, we present a synthetic example illustrating how this approach can lead to very poor but stable parameter estimates. Second, we identify the culprit to be the log-likelihood loss, along with certain conditions that exacerbate the issue. Third, we present an alternative formulation, termed $\\beta$-NLL, in which each data point's contribution to the loss is weighted by the $\\beta$-exponentiated variance estimate. We show that using an appropriate $\\beta$ largely mitigates the issue in our illustrative example. Fourth, we evaluate this approach on a range of domains and tasks and show that it achieves considerable improvements and performs more robustly concerning hyperparameters, both in predictive RMSE and log-likelihood criteria.","url_abs":"https://arxiv.org/abs/2203.09168v2","url_pdf":"https://arxiv.org/pdf/2203.09168v2.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":"on-the-pitfalls-of-heteroscedastic-1","repo_url":"https://github.com/martius-lab/beta-nll","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"on-the-pitfalls-of-heteroscedastic-1","repo_url":"https://github.com/ensta-u2is/torch-uncertainty","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2203.09168","atlas_url":"https://app.syntology.ai/?focus=2203.09168","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2203.09168"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/martius-lab/beta-nll","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/ensta-u2is/torch-uncertainty","reach":null}],"summary":{"ran":2},"by_repo_kind":{"official":{"samples":1,"ran":1,"repositories":1},"listed":{"samples":1,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"0f6ef5bf12d93077","entry":"BetaNLL","repo":"ensta-u2is/torch-uncertainty","repo_kind":"listed","path":"src/torch_uncertainty/losses/regression.py","file_url":"https://github.com/ensta-u2is/torch-uncertainty/blob/HEAD/src/torch_uncertainty/losses/regression.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"0f6ef5bf12d93077"}},{"code_sha256_prefix":"470eed4195a8ae0d","entry":"GaussianLogLikelihoodLoss","repo":"martius-lab/beta-nll","repo_kind":"official","path":"depth_estimation/loss.py","file_url":"https://github.com/martius-lab/beta-nll/blob/HEAD/depth_estimation/loss.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"470eed4195a8ae0d"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}