The existence of water markets establishes water prices, promoting trading of water from low- to high-valued uses. However, market participants can face uncertainty when asking and offering prices because water rights are heterogeneous, resulting in inefficiency of the market. This paper proposes three random forest regression models (RFR) to predict water price in the western United States: a full variable set model and two reduced ones with optimal numbers of variables using a backward variable elimination (BVE) approach. Transactions of 12 semiarid states, from 1987 to 2009, and a dataset containing various predictors, were assembled. Multiple replications of k-fold cross-validation were applied to assess the model performance and their generalizability was tested on unused data. The importance of price influencing factors was then analyzed based on two plausible variable importance rankings. Results show that the RFR models have good predictive power for water price. They outperform a baseline model without leading to overfitting. Also, the higher degree of accuracy of the reduced models is insignificant, reflecting the robustness of RFR to including lower informative variables. This study suggests that, due to its ability to automatically learn from and make predictions on data, RFR-based models can aid water market participants in making more efficient decisions.

The increasing needs of clustering massive datasets and the high cost of running clustering algorithms poses difficult problems for users. In this context it is important to determine if a data set is clusterable, that is, it may be partitioned efficiently into well-differentiated groups containing similar objects. We approach data clusterability from an ultrametricbased perspective. A novel approach to determine the ultrametricity of a dataset is proposed via a special type of matrix product, which allows us to evaluate the clusterability of the dataset. Furthermore, we show that by applying our technique to a dissimilarity space will generate the sub-dominant ultrametric of the dissimilarity. *

This paper proposes a deep-learning-based optimal battery management scheme for frequency regulation (FR) by integrating model predictive control (MPC), supervised learning (SL), reinforcement learning (RL), and high-fidelity battery models. By taking advantage of deep neural networks (DNNs), the derived DNN-approximated policy is computationally efficient in online implementation. The design procedure of the proposed scheme consists of two sequential processes: (1) the SL process, in which we first run a simulation with an MPC embedding a lowfidelity battery model to generate a training data set, and then, based on the generated data set, we optimize a DNN-approximated policy using SL algorithms; (2) the RL process, in which we utilize RL algorithms to improve the performance of the DNN-approximated policy by balancing short-term economic incentives and longterm battery degradation. The SL process speeds up the subsequent RL process by providing a good initialization. By utilizing RL algorithms, one prominent property of the proposed scheme is that it can learn from the data generated by simulating the FR policy on the high-fidelity battery simulator to adjust the DNN-approximated policy, which is originally initialized using a low-fidelity battery model. A case study using real-world data of FR signals and prices is performed. Simulation results show that, compared to conventional MPC schemes, the proposed deep-learning-based scheme can effectively achieve higher economic benefits of FR participation while maintaining lower online computational cost.

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