Sketching is a stochastic dimension reduction method that preserves geometric structures of data and has applications in high-dimensional regression, low rank approximation and graph sparsification. In this work, we show that sketching can be used to compress simulation data and still accurately estimate time autocorrelation and power spectral density. For a given compression ratio, the accuracy is much higher than using previously known methods. In addition to providing theoretical guarantees, we apply sketching to a molecular dynamics simulation of methanol and find that the estimate of spectral density is 90% accurate using only 10% of the data.

中文翻译：

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通过草图模拟的光谱估计

草图是一种随机降维方法，它保留了数据的几何结构，在高维回归、低秩逼近和图稀疏化方面有应用。在这项工作中，我们表明草图可用于压缩模拟数据，并且仍然可以准确估计时间自相关和功率谱密度。对于给定的压缩比，精度比使用以前已知的方法要高得多。除了提供理论保证外，我们还将草图应用到甲醇的分子动力学模拟中，发现仅使用 10% 的数据，光谱密度的估计准确度为 90%。