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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. 

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. 

Abstract Subspace clustering is the unsupervised grouping of points lying near a union of low-dimensional linear subspaces. Algorithms based directly on geometric properties of such data tend to either provide poor empirical performance, lack theoretical guarantees or depend heavily on their initialization. We present a novel geometric approach to the subspace clustering problem that leverages ensembles of the $K$-subspace (KSS) algorithm via the evidence accumulation clustering framework. Our algorithm, referred to as ensemble $K$-subspaces (EKSSs), forms a co-association matrix whose $(i,j)$th entry is the number of times points $i$ and $j$ are clustered together by several runs of KSS with random initializations. We prove general recovery guarantees for any algorithm that forms an affinity matrix with entries close to a monotonic transformation of pairwise absolute inner products. We then show that a specific instance of EKSS results in an affinity matrix with entries of this form, and hence our proposed algorithm can provably recover subspaces under similar conditions to state-of-the-art algorithms. The finding is, to the best of our knowledge, the first recovery guarantee for evidence accumulation clustering and for KSS variants. We show on synthetic data that our method performs well in the traditionally challenging settings of subspaces with large intersection, subspaces with small principal angles and noisy data. Finally, we evaluate our algorithm on six common benchmark datasets and show that unlike existing methods, EKSS achieves excellent empirical performance when there are both a small and large number of points per subspace. 

We consider the problem of active learning in the context of spatial sampling for boundary estimation, where the goal is to estimate an unknown boundary as accurately and quickly as possible. We present a finite-horizon search procedure to optimally minimize both the final estimation error and the distance traveled for a fixed number of samples, where a tuning parameter is used to trade off between the estimation accuracy and distance traveled. We show that the resulting optimization problem can be solved in closed form and that the resulting policy generalizes existing approaches to this problem. 

Water quality parameters such as dissolved oxygen and turbidity play a key role in policy decisions regarding the maintenance and use of the nation's major bodies of water. In particular, the United States Geological Survey (USGS) maintains a massive suite of sensors throughout the nation's waterways that are used to inform such decisions, with all data made available to the public. However, the corresponding measurements are regularly corrupted due to sensor faults, fouling, and decalibration, and hence USGS scientists are forced to spend costly time and resources manually examining data to look for anomalies. We present a method of automatically detecting such events using supervised machine learning. We first present an extensive study of which water quality parameters can be reliably predicted, using support vector machines and gradient boosting algorithms for regression. We then show that the trained predictors can be used to automatically detect sensor decalibration, providing a system that could be easily deployed by the USGS to reduce the resources needed to maintain data fidelity.