id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
cord-197127-o30tiqel	Breugel, Floris van	Numerical differentiation of noisy data: A unifying multi-objective optimization framework	2020-09-03		.txt	text/plain	5981	330	48	In this work, we take a principled approach and propose a multi-objective optimization framework for choosing parameters that minimize a loss function to balance the faithfulness and smoothness of the derivative estimate. To understand the qualities of the derivative estimates resulting from parameters selected by our loss function, we begin by analyzing the derivative estimates of noisy sinusoidal curves using the Savitzky-Golay filter and return to our original metrics, RMSE and error correlation to evaluate the results. To characterize this relationship, we evaluated the performance of derivative estimates achieved by a Savitzky-Golay filter by sweeping through different values of γ for a suite of sinusoidal data with various frequencies (f ), noise levels (additive white (zero-mean) Gaussian noise with variance σ 2 ), temporal resolutions (∆t), and dataset lengths (in time steps, L) ( Fig. 2A-B) .	./cache/cord-197127-o30tiqel.txt	./txt/cord-197127-o30tiqel.txt