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.

微正则梯度下降是一种用于高维分布高效采样的能量模型采样过程，通过使用梯度下降从高熵分布（如高斯白噪声）将样本传输到低能量区域。我们将这个模型放置在归一化流框架中，展示它常常通过在下降过程中损失了不必要的熵而过拟合。为了解决这个问题，我们提出了一种多场微正则梯度下降法，同时采样多个弱耦合数据点，以更好地控制熵损失，并在可能度拟合方面几乎不付出代价。我们在金融时间序列的背景下研究了这些模型，展示了在合成和真实数据上的改进。