Microcanonical gradient descent is a sampling procedure for energy-based models allowing for efficient sampling of distributions in high dimension. It works by transporting samples from a high-entropy distribution, such as Gaussian white noise, to a low-energy region using gradient descent. We put this model in the framework of normalizing flows, showing how it can often overfit by losing an unnecessary amount of entropy in the descent. As a remedy, we propose a mean-field microcanonical gradient descent that samples several weakly coupled data points simultaneously, allowing for better control of the entropy loss while paying little in terms of likelihood fit. We study these models in the context of financial time series, illustrating the improvements on both synthetic and real data.

翻译：微正则梯度下降是一种基于能量的模型采样过程，能够高效地对高维分布进行采样。该方法通过梯度下降将样本从高熵分布（如高斯白噪声）传输至低能区域。我们将此模型置于归一化流的框架下，揭示了其在降维过程中因熵的不必要损失而常导致过拟合的现象。作为解决方案，我们提出平均场微正则梯度下降，该方法同时采样多个弱耦合的数据点，在几乎不牺牲似然拟合度的前提下，能更好地控制熵损失。我们以金融时间序列为背景研究这些模型，并通过合成数据与真实数据验证了改进效果。