论文标题
观察性非可识别性，普遍的可能性和自由能
Observational nonidentifiability, generalized likelihood and free energy
论文作者
论文摘要
我们研究了具有观察性非识别性的混合模型中的参数估计问题：完整的模型（也包含隐藏变量）是可识别的，但是边际（观察到的）模型却没有。因此，边际可能性的全球最大值是（无限）退化，边际可能性的预测并非唯一。我们通过引入有效的温度来展示如何概括边际可能性，并与自由能类似。这种概括解决了观察性的非识别性，因为它的最大化会导致独特的结果，比随机选择一个边缘可能性的一个变性最大值或在许多此类最大值上的平均值。广义的可能性从通常的可能性中继承了许多特征，例如它持有条件性原则，可以通过适当修改的期望最大化方法来搜索其局部最大值。广义可能性的最大化与熵优化有关。
We study the parameter estimation problem in mixture models with observational nonidentifiability: the full model (also containing hidden variables) is identifiable, but the marginal (observed) model is not. Hence global maxima of the marginal likelihood are (infinitely) degenerate and predictions of the marginal likelihood are not unique. We show how to generalize the marginal likelihood by introducing an effective temperature, and making it similar to the free energy. This generalization resolves the observational nonidentifiability, since its maximization leads to unique results that are better than a random selection of one degenerate maximum of the marginal likelihood or the averaging over many such maxima. The generalized likelihood inherits many features from the usual likelihood, e.g. it holds the conditionality principle, and its local maximum can be searched for via suitably modified expectation-maximization method. The maximization of the generalized likelihood relates to entropy optimization.
