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1. Constants Matter: The Performance Gains of Active Learning

   Mussmann, S.; Dasgupta, S. (January 2022, Proceedings of the 39th International Conference on Machine Learning)

   Within machine learning, active learning studies the gains in performance made possible by adaptively selecting data points to label. In this work, we show through upper and lower bounds, that for a simple benign setting of well-specified logistic regression on a uniform distribution over a sphere, the expected excess error of both active learning and random sampling have the same inverse proportional dependence on the number of samples. Importantly, due to the nature of lower bounds, any more general setting does not allow a better dependence on the number of samples. Additionally, we show a variant of uncertainty sampling can achieve a faster rate of convergence than random sampling by a factor of the Bayes error, a recent empirical observation made by other work. Qualitatively, this work is pessimistic with respect to the asymptotic dependence on the number of samples, but optimistic with respect to finding performance gains in the constants. 

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2. Efficient Active Learning with Abstention

   Zhu, Yinglun; Nowak, Robert D (November 2022, Advances in Neural Information Processing Systems)

   The goal of active learning is to achieve the same accuracy achievable by passive learning, while using much fewer labels. Exponential savings in terms of label complexity have been proved in very special cases, but fundamental lower bounds show that such improvements are impossible in general. This suggests a need to explore alternative goals for active learning. Learning with abstention is one such alternative. In this setting, the active learning algorithm may abstain from prediction and incur an error that is marginally smaller than random guessing. We develop the first computationally efficient active learning algorithm with abstention. Our algorithm provably achieves p o l y l o g ( 1 ε ) label complexity, without any low noise conditions. Such performance guarantee reduces the label complexity by an exponential factor, relative to passive learning and active learning that is not allowed to abstain. Furthermore, our algorithm is guaranteed to only abstain on hard examples (where the true label distribution is close to a fair coin), a novel property we term \emph{proper abstention} that also leads to a host of other desirable characteristics (e.g., recovering minimax guarantees in the standard setting, and avoiding the undesirable noise-seeking'' behavior often seen in active learning). We also provide novel extensions of our algorithm that achieve \emph{constant} label complexity and deal with model misspecification. 

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3. Predicting Geothermal Favorability in the Western United States by Using Machine Learning: Addressing Challenges and Developing Solutions

   Mordensky, Stanley P.; Lipor, John J.; DeAngelo, J.; Burns, Erick R.; Lindsey, Cary R. (February 2022, Forty Seventh Workshop on Geothermal Reservoir Engineering)

   Previous moderate- and high-temperature geothermal resource assessments of the western United States utilized weight-of-evidence and logistic regression methodstoestimateresourcefavorability,buttheseanalyses relied uponsomeexpert decisions.Whileexpert decisions can add confidence to aspects of the modeling process by ensuring only reasonable models are employed, expert decisions also introduce human bias into assessments. This bias presents a source of error that may affect the performance of the models and resulting resource estimates. Our study aims to reduce expert input through robust data-driven analyses and better-suited data science techniques, with the goals of saving time, reducing bias, and improving predictive ability. We present six favorability maps for geothermal resources in the western United States created using two strategies applied to three modern machine learning algorithms (logistic regression, support- vector machines, and XGBoost). To provide a direct comparison to previous assessments, we use the same input data as the 2008 U.S. Geological Survey (USGS) conventional moderate- to high-temperature geothermal resource assessment. The six new favorability maps required far less expert decision-making, but broadly agree with the previous assessment. Despite the fact that the 2008 assessment results employed linear methods, the non-linear machine learning algorithms (i.e., support-vector machines and XGBoost) produced greater agreement with the previous assessment than the linear machine learning algorithm (i.e., logistic regression). It is not surprising that geothermal systems depend on non-linear combinations of features, and we postulate that the expert decisions during the 2008 assessment accounted for system non-linearities. Substantial challenges to applying machine learning algorithms to predict geothermal resource favorability include severe class imbalance (i.e., there are very few known geothermal systems compared to the large area considered), and while there are known geothermal systems (i.e., positive labels), all other sites have an unknown status (i.e., they are unlabeled), instead of receiving a negative label (i.e., the known/proven absence of a geothermal resource). We address both challenges through a custom undersampling strategy that can be used with any algorithm and then evaluated using F1 scores. 

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4. Predicting Geothermal Favorability in the Western United States by Using Machine Learning: Addressing Challenges and Developing Solutions

   Mordensky, Stanley P.; Lipor, John J.; DeAngelo, J.; Burns, Erick R.; Lindsey, Cary R. (February 2022, Proceedings: Forty Seventh Workshop on Geothermal Reservoir Engineering)

   Previous moderate- and high-temperature geothermal resource assessments of the western United States utilized weight-of-evidence and logistic regression methodstoestimateresourcefavorability,buttheseanalyses relied uponsomeexpert decisions.Whileexpert decisions can add confidence to aspects of the modeling process by ensuring only reasonable models are employed, expert decisions also introduce human bias into assessments. This bias presents a source of error that may affect the performance of the models and resulting resource estimates. Our study aims to reduce expert input through robust data-driven analyses and better-suited data science techniques, with the goals of saving time, reducing bias, and improving predictive ability. We present six favorability maps for geothermal resources in the western United States created using two strategies applied to three modern machine learning algorithms (logistic regression, support- vector machines, and XGBoost). To provide a direct comparison to previous assessments, we use the same input data as the 2008 U.S. Geological Survey (USGS) conventional moderate- to high-temperature geothermal resource assessment. The six new favorability maps required far less expert decision-making, but broadly agree with the previous assessment. Despite the fact that the 2008 assessment results employed linear methods, the non-linear machine learning algorithms (i.e., support-vector machines and XGBoost) produced greater agreement with the previous assessment than the linear machine learning algorithm (i.e., logistic regression). It is not surprising that geothermal systems depend on non-linear combinations of features, and we postulate that the expert decisions during the 2008 assessment accounted for system non-linearities. Substantial challenges to applying machine learning algorithms to predict geothermal resource favorability include severe class imbalance (i.e., there are very few known geothermal systems compared to the large area considered), and while there are known geothermal systems (i.e., positive labels), all other sites have an unknown status (i.e., they are unlabeled), instead of receiving a negative label (i.e., the known/proven absence of a geothermal resource). We address both challenges through a custom undersampling strategy that can be used with any algorithm and then evaluated using F1 scores. 

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5. Coresets for Classification - Simplified and Strengthened

   Mai, Tung; Musco, Cameron; Rao, Anup (December 2021, Advances in neural information processing systems)

   We give relative error coresets for training linear classifiers with a broad class of loss functions, including the logistic loss and hinge loss. Our construction achieves $$(1\pm \epsilon)$$ relative error with $$\tilde O(d \cdot \mu_y(X)^2/\epsilon^2)$$ points, where $$\mu_y(X)$$ is a natural complexity measure of the data matrix $$X \in \mathbb{R}^{n \times d}$$ and label vector $$y \in \{-1,1\}^n$$, introduced in Munteanu et al. 2018. Our result is based on subsampling data points with probabilities proportional to their \textit{$$\ell_1$$ Lewis weights}. It significantly improves on existing theoretical bounds and performs well in practice, outperforming uniform subsampling along with other importance sampling methods. Our sampling distribution does not depend on the labels, so can be used for active learning. It also does not depend on the specific loss function, so a single coreset can be used in multiple training scenarios. 

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