We study analytically the performance of a recently proposed algorithm for
learning the couplings of a random asymmetric kinetic Ising model from finite
length trajectories of the spin dynamics. Our analysis shows the importance of
the nontrivial equal time correlations between spins induced by the dynamics
for the speed of learning. These correlations become more important as the
spin's stochasticity is decreased. We also analyse the deviation of the
estimation error from asymptotic optimality.

研究了最近提出的一种从动力学相互作用的异构性动力学 Ising 模型有限长度轨迹的学习耦合的算法的性能，分析了学习速度与动力学引起的自旋之间的非平凡等时互相关性之间的重要性，尤其是当自旋的随机性降低时。同时，还分析了估计误差与渐近最优性的偏差。

重新访问随机不对称动力学伊辛模型的耦合学习：随机相关矩阵和学习曲线

Learning of couplings for random asymmetric kinetic Ising models  revisited: random correlation matrices and learning curves

Based on dynamical cavity method, we propose an approach to the inference of
kinetic Ising model, which asks to reconstruct couplings and external fields
from given time-dependent output of original system. Our approach gives an
exact result on tree graphs and a good approximation on sparse graphs, it can
be seen as an extension of Belief Propagation inference of static Ising model
to kinetic Ising model. While existing mean field methods to the kinetic Ising
inference e.g., na\" ive mean-field, TAP equation and simply mean-field, use
approximations which calculate magnetizations and correlations at time $t$ from
statistics of data at time $t-1$, dynamical cavity method can use statistics of
data at times earlier than $t-1$ to capture more correlations at different time
steps. Extensive numerical experiments show that our inference method is
superior to existing mean-field approaches on diluted networks.

文章提出了一种基于动态空腔方法的方法来推断动力学 Ising 模型中的耦合和外部场，相较于现有的平均场方法，此方法能够更好地获取不同时间步长下的相关性。

稀疏图上动力学 Ising 模型的推断

Inference of kinetic Ising model on sparse graphs

Neurons subject to a common non-stationary input may exhibit a correlated
firing behavior. Correlations in the statistics of neural spike trains also
arise as the effect of interaction between neurons. Here we show that these two
situations can be distinguished, with machine learning techniques, provided the
data are rich enough. In order to do this, we study the problem of inferring a
kinetic Ising model, stationary or nonstationary, from the available data. We
apply the inference procedure to two data sets: one from salamander retinal
ganglion cells and the other from a realistic computational cortical network
model. We show that many aspects of the concerted activity of the salamander
retinal neurons can be traced simply to the external input. A model of
non-interacting neurons subject to a non-stationary external field outperforms
a model with stationary input with couplings between neurons, even accounting
for the differences in the number of model parameters. When couplings are added
to the non-stationary model, for the retinal data, little is gained: the
inferred couplings are generally not significant. Likewise, the distribution of
the sizes of sets of neurons that spike simultaneously and the frequency of
spike patterns as function of their rank (Zipf plots) are well-explained by an
independent-neuron model with time-dependent external input, and adding
connections to such a model does not offer significant improvement. For the
cortical model data, robust couplings, well correlated with the real
connections, can be inferred using the non-stationary model. Adding connections
to this model slightly improves the agreement with the data for the probability
of synchronous spikes but hardly affects the Zipf plot.

应用机器学习技术，研究从剪辑数据中推断的动力学 Ising 模型，发现一个非互作神经元的非平稳输入模型优于一个带有神经元耦合的静态输入模型，后者即使增加了连接，对于突触间的耦合也只有轻微的影响。