Logistic Regression Through the Veil of Imprecise Data
Abstract: Logistic regression is a popular supervised learning algorithm used to assess the probability of a variable having a binary label based on some predictive features. Standard methods can only deal with precisely known data; however, many datasets have uncertainties that traditional methods either reduce to a single point or completely disregard. This paper shows that it is possible to include these uncertainties by considering an imprecise logistic regression model using the set of possible models obtained from values within the intervals. This method can express the epistemic uncertainty neglected by traditional methods.
Submission Length: Long submission (more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=gyCX6UxRI8&referrer=%5Bthe%20profile%20of%20Nicholas%20Gray%5D(%2Fprofile%3Fid%3D~Nicholas_Gray1)
Changes Since Last Submission: I have added a new subsection and two appendices to discuss the algorithms used within the paper, explaining the logic behind the algorithms and exploring how good at estimating the set they are. Further comparisons between the suggested algorithms have also been included.
To address the thoughtful comments raised by Sxmf about the nature of the uncertainty about the logistic regression model, I have added a fuller discussion of these comments within the conclusion section of the paper. Additionally, their point that “formally, every x without a label can be considered as an unlabelled example, one can thus arbitrarily increase uncertainty by adding new unlabelled examples, which does not seem right to me.” has now been addressed within Section 4 by stating that datapoints that are in u should only contain x values that have been observed but for which the label is unidentified for some reason.
I have reviewed the literature suggested by L5Uz and added references within the manuscript where appropriate.
I have fixed the grammatical errors highlighted by the reviewers.
To address Sxmf’s concern about the reproducibility of the experiments within the paper, I intend to publish the code I have used. I was told I needed to remove the link from the manuscript to meet the journal’s double-blind peer-review standards.
Assigned Action Editor: ~Benjamin_Guedj1
Submission Number: 397
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