Simplex-valued data appear throughout statistics and machine learning, for example in the context of transfer learning and compression of deep networks. Existing models for this class of data rely on the Dirichlet distribution or other related loss functions; here we show these standard choices suffer systematically from a number of limitations, including bias and numerical issues that frustrate the use of flexible network models upstream of these distributions. We resolve these limitations by introducing a novel exponential family of distributions for modeling simplex-valued data - the continuous categorical, which arises as a nontrivial multivariate generalization of the recently discovered continuous Bernoulli. Unlike the Dirichlet and other typical choices, the continuous categorical results in a well-behaved probabilistic loss function that produces unbiased estimators, while preserving the mathematical simplicity of the Dirichlet. As well as exploring its theoretical properties, we introduce sampling methods for this distribution that are amenable to the reparameterization trick, and evaluate their performance. Lastly, we demonstrate that the continuous categorical outperforms standard choices empirically, across a simulation study, an applied example on multi-party elections, and a neural network compression task.

介绍了一个新的连续分类型分布-continuous categorical，用于建模单纯值数据。与Dirichlet和其他典型选择不同，continuous categorical产生一个行为良好的概率损失函数，产生无偏估计器，同时保留了Dirichlet的数学简单性，并在多方选举和神经网络压缩任务中超越其他标准选择。

连续分类：一种新颖的简单值指数族