Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that is routinely generated. In applications that are constrained by memory and computational intensity, excessively large datasets may hinder scientific discovery, making data reduction a critical component of data-driven methods. Datasets are growing in two directions: the number of data points and their dimensionality. Whereas dimension reduction typically aims at describing each data sample on lower-dimensional space, the focus here is on reducing the number of data points. A strategy is proposed to select data points such that they uniformly span the phase-space of the data. The algorithm proposed relies on estimating the probability map of the data and using it to construct an acceptance probability. An iterative method is used to accurately estimate the probability of the rare data points when only a small subset of the dataset is used to construct the probability map. Instead of binning the phase-space to estimate the probability map, its functional form is approximated with a normalizing flow. Therefore, the method naturally extends to high-dimensional datasets. The proposed framework is demonstrated as a viable pathway to enable data-efficient machine learning when abundant data is available. An implementation of the method is available in a companion repository (https://github.com/NREL/Phase-space-sampling).
翻译:计算和实验能力的改进正在迅速增加常规产生的科学数据的数量。在受内存和计算强度限制的应用中,过大数据集可能阻碍科学发现,使数据减少成为数据驱动方法的一个关键组成部分。数据集正在朝着两个方向增长:数据点的数量及其维度。虽然尺寸减少通常旨在描述低维空间的每个数据样本,但这里的重点是减少数据点的数量。提议了一个战略,选择数据点,以便它们能够统一跨越数据的相位空间。提议的算法依靠估算数据的概率图,并利用它构建一个接受概率。在只使用少量数据集来构建概率图时,使用迭代法来准确估计稀有数据点的概率。在将相位空间用于估计概率图时,其功能形式与正常流相近。因此,该方法自然延伸到高维的数据集。拟议的框架被证明为一种可行的途径,以便在数据充足数据可用时能够进行数据高效的机器学习。使用迭代方法在可访问中可以使用。</s>