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Logistic Regression is a widely used generalized linear model applied in classification settings to assign probabilities to class labels. It is also well known that logistic regression is a maximum entropy procedure subject to what are sometimes called the balance conditions. The dominant view in existing explanations are all discriminative, i.e., modeling labels given the data. This paper adds to the maximum entropy interpretation, establishing a generative, maximum entropy explanation for the commonly used logistic regression training and optimization procedures. We show that logistic regression models the conditional distribution on the instance space given class labels with a maximum entropy model subject to a first moment constraint on the training data, and that the commonly used fitting procedure would be a Monte-Carlo fit for the generative view.more » « lessFree, publicly-accessible full text available June 27, 2026
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Host-Madsen, Anders; Zaeri_Amirani, Mohammad; Santhanam, Narayana P (, International Symposium on Information Theory and its Applications (ISITA))This paper develops bounds for learning lossless source coding under the PAC (probably approximately correct) framework. The paper considers iid sources with online learning: first the coder learns the data structure from training sequences. When presented with a test sequence for compression, it continues to learn from/adapt to the test sequence. The results show, not unsurprisingly, that there is little gain from online learning when the training sequence length is much longer than the test sequence length. But if the test sequence length is longer than the training sequence, there is a significant gain. Coders for online learning has a somewhat surprising structure: the training sequence is used to estimate a confidence interval for the distribution, and the coding distribution is found through a prior distribution over this interval.more » « lessFree, publicly-accessible full text available November 10, 2025
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Abolfazli, Mojtaba; Zaeri_Amirani, Mohammad; Host-Madsen, Anders; Zhang, June; Bratincsak, Andras (, International Symposium on Information Theory and its Applications (ISITA))Free, publicly-accessible full text available November 10, 2025
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