Tractable Bayesian learning of tree belief networks
Tractable Bayesian learning of tree belief networks
复制标题
DOI：
10.1007/s11222-006-5535-3
复制
发表时间：
2006-03-01
影响因子：
2.2
通讯作者：
Jaakkola, T
中科院分区：
文献类型：
--
作者：
Meila, M;Jaakkola, T
在本文中，我们提出了可分解先验，这是树信念网的结构和参数上的一组先验，对于这些先验，具有完全观测的贝叶斯学习是可处理的，因为后验也是可分解的，并且可以在多项式时间内完全解析地确定。我们的结果是第一个可以在多项式时间内计算归一化常数并对超指数数量的图结构进行平均的结果。这源于两个主要结果：首先，我们证明了图中生成树上的因子分布可以以封闭形式集成。其次，我们检查了树参数的先验，并表明一组类似于Heckerman， Geiger和Chickering（1995）的假设将树参数先验约束为Dirichlet分布的紧参数化积。除了允许精确的贝叶斯学习之外，这些结果使我们能够制定一类新的可处理的潜在变量模型，其中数据点的可能性是通过树结构上的集合平均来计算的。
In this paper we present decomposable priors, a family of priors over structure and parameters of tree belief nets for which Bayesian learning with complete observations is tractable, in the sense that the posterior is also decomposable and can be completely determined analytically in polynomial time. Our result is the first where computing the normalization constant and averaging over a super-exponential number of graph structures can be performed in polynomial time. This follows from two main results: First, we show that factored distributions over spanning trees in a graph can be integrated in closed form. Second, we examine priors over tree parameters and show that a set of assumptions similar to Heckerman, Geiger and Chickering (1995) constrain the tree parameter priors to be a compactly parametrized product of Dirichlet distributions. Besides allowing for exact Bayesian learning, these results permit us to formulate a new class of tractable latent variable models in which the likelihood of a data point is computed through an ensemble average over tree structures.