论文标题
学习具有神经网络的离散图形模型
Learning of Discrete Graphical Models with Neural Networks
论文作者
论文摘要
图形模型在科学中广泛使用，以表示具有潜在条件依赖性结构的联合概率分布。从其联合分布中进行i.I.D样品的离散图形模型的逆问题可以使用近乎最佳的样品复杂性使用凸优化方法来解决，称为广义正则化相互作用筛选估计器（GRISE）。但是，当真实图形模型的能量函数具有较高的术语时，磨砂的计算成本变得过于望而却步。我们介绍了一种用于图形模型学习的神经网络算法，以应对这种磨碎的局限性。我们在交互筛选目标函数中使用神经网作为函数近似值。然后，该目标的优化产生了图形模型条件的神经网络表示。当真实模型的能量功能具有高度对称性时，神经算法被认为是磨碎的更好替代方法。在这些情况下，神经化能够找到适当的有条件的简约表示，而无需为真实模型提供任何先前的信息。神经外观也可以用来学习真实模型的基础结构，并对其训练程序进行一些简单的修改。此外，我们还展示了一种神经化的变体，可用于学习真实模型的完整能量函数的神经净表示。
Graphical models are widely used in science to represent joint probability distributions with an underlying conditional dependence structure. The inverse problem of learning a discrete graphical model given i.i.d samples from its joint distribution can be solved with near-optimal sample complexity using a convex optimization method known as Generalized Regularized Interaction Screening Estimator (GRISE). But the computational cost of GRISE becomes prohibitive when the energy function of the true graphical model has higher-order terms. We introduce NeurISE, a neural net based algorithm for graphical model learning, to tackle this limitation of GRISE. We use neural nets as function approximators in an Interaction Screening objective function. The optimization of this objective then produces a neural-net representation for the conditionals of the graphical model. NeurISE algorithm is seen to be a better alternative to GRISE when the energy function of the true model has a high order with a high degree of symmetry. In these cases NeurISE is able to find the correct parsimonious representation for the conditionals without being fed any prior information about the true model. NeurISE can also be used to learn the underlying structure of the true model with some simple modifications to its training procedure. In addition, we also show a variant of NeurISE that can be used to learn a neural net representation for the full energy function of the true model.
