This paper presents a statistical approach to active learning, where the goal is to select the most informative data points for training to minimize the learner's variance. The authors review how optimal data selection techniques have been applied to feedforward neural networks and show that similar principles can be used for mixtures of Gaussians and locally weighted regression. While neural networks require computationally expensive and approximate methods, mixtures of Gaussians and locally weighted regression offer efficient and accurate data selection. Empirically, the optimal data selection significantly reduces the number of training examples needed to achieve good performance. Active learning involves the learner selecting data to add to its training set, rather than passively receiving data. The paper discusses various heuristics for selecting data, including choosing places with no data, where the model performs poorly, where confidence is low, where the model is expected to change, and where previous data led to learning. The authors focus on statistically optimal data selection, which aims to minimize the learner's variance. For neural networks, the variance is estimated using a second-order Taylor series expansion, and the selection of new data points is based on minimizing the expected variance. However, this approach is computationally expensive. In contrast, mixtures of Gaussians and locally weighted regression allow for efficient and accurate data selection. The paper demonstrates that these models can be used to compute the expected variance of the learner, and the optimal data points are selected to minimize this variance. The authors also discuss the application of these techniques to the "Arm2D" problem, where the goal is to learn the kinematics of a 2-degree-of-freedom robot arm. The results show that the variance-minimizing criterion significantly improves performance compared to random data selection. The experiments with mixtures of Gaussians and LOESS regression demonstrate that these models can achieve better performance with fewer training examples. The paper concludes that mixtures of Gaussians and locally weighted regression offer efficient and statistically correct methods for active learning. These models can be used to minimize the learner's variance and improve performance with fewer training examples. The authors also note that future work should focus on minimizing both bias and variance to produce a criterion that truly minimizes the learner's expected error.This paper presents a statistical approach to active learning, where the goal is to select the most informative data points for training to minimize the learner's variance. The authors review how optimal data selection techniques have been applied to feedforward neural networks and show that similar principles can be used for mixtures of Gaussians and locally weighted regression. While neural networks require computationally expensive and approximate methods, mixtures of Gaussians and locally weighted regression offer efficient and accurate data selection. Empirically, the optimal data selection significantly reduces the number of training examples needed to achieve good performance. Active learning involves the learner selecting data to add to its training set, rather than passively receiving data. The paper discusses various heuristics for selecting data, including choosing places with no data, where the model performs poorly, where confidence is low, where the model is expected to change, and where previous data led to learning. The authors focus on statistically optimal data selection, which aims to minimize the learner's variance. For neural networks, the variance is estimated using a second-order Taylor series expansion, and the selection of new data points is based on minimizing the expected variance. However, this approach is computationally expensive. In contrast, mixtures of Gaussians and locally weighted regression allow for efficient and accurate data selection. The paper demonstrates that these models can be used to compute the expected variance of the learner, and the optimal data points are selected to minimize this variance. The authors also discuss the application of these techniques to the "Arm2D" problem, where the goal is to learn the kinematics of a 2-degree-of-freedom robot arm. The results show that the variance-minimizing criterion significantly improves performance compared to random data selection. The experiments with mixtures of Gaussians and LOESS regression demonstrate that these models can achieve better performance with fewer training examples. The paper concludes that mixtures of Gaussians and locally weighted regression offer efficient and statistically correct methods for active learning. These models can be used to minimize the learner's variance and improve performance with fewer training examples. The authors also note that future work should focus on minimizing both bias and variance to produce a criterion that truly minimizes the learner's expected error.