Department of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA.
Philos Trans A Math Phys Eng Sci. 2012 Dec 31;371(1984):20110543. doi: 10.1098/rsta.2011.0543. Print 2013 Feb 13.
We present an unsupervised learning algorithm (GenESeSS) to infer the causal structure of quantized stochastic processes, defined as stochastic dynamical systems evolving over discrete time, and producing quantized observations. Assuming ergodicity and stationarity, GenESeSS infers probabilistic finite state automata models from a sufficiently long observed trace. Our approach is abductive; attempting to infer a simple hypothesis, consistent with observations and modelling framework that essentially fixes the hypothesis class. The probabilistic automata we infer have no initial and terminal states, have no structural restrictions and are shown to be probably approximately correct-learnable. Additionally, we establish rigorous performance guarantees and data requirements, and show that GenESeSS correctly infers long-range dependencies. Modelling and prediction examples on simulated and real data establish relevance to automated inference of causal stochastic structures underlying complex physical phenomena.
我们提出了一种无监督学习算法（GenESeSS），用于推断量化随机过程的因果结构，这些过程被定义为在离散时间上演变并产生量化观测值的随机动力系统。假设遍历性和稳定性，GenESeSS 可以从足够长的观测轨迹中推断出概率有限状态自动机模型。我们的方法是溯因的；试图推断一个简单的假设，该假设与观测和建模框架一致，该框架本质上固定了假设类。我们推断的概率自动机没有初始和终端状态，没有结构限制，并且被证明是可能近似正确可学习的。此外，我们建立了严格的性能保证和数据要求，并表明 GenESeSS 可以正确推断出长程相关性。对模拟和真实数据的建模和预测示例表明，该方法与复杂物理现象背后因果随机结构的自动推断相关。
