Flexible models for probability distributions are an essential ingredient in many machine learning tasks. We develop and investigate a new class of probability distributions, which we call a Squared Neural Family (SNEFY), formed by squaring the 2-norm of a neural network and normalising it with respect to a base measure. Following the reasoning similar to the well established connections between infinitely wide neural networks and Gaussian processes, we show that SNEFYs admit a closed form normalising constants in many cases of interest, thereby resulting in flexible yet fully tractable density models. SNEFYs strictly generalise classical exponential families, are closed under conditioning, and have tractable marginal distributions. Their utility is illustrated on a variety of density estimation and conditional density estimation tasks. Software available at https://github.com/RussellTsuchida/snefy.

翻译：概率分布的灵活模型是许多机器学习任务中的关键要素。我们开发并研究了一类新的概率分布，称为平方神经族（SNEFY），它通过平方神经网络的二范数并相对于基测度进行归一化而形成。遵循类似于无穷宽神经网络与高斯过程之间已知联系的方法，我们证明在许多感兴趣的情况下，SNEFY具有封闭形式的归一化常数，从而产生灵活且完全可处理的密度模型。SNEFY严格推广了经典指数族，在条件化下封闭，并且具有可处理的边际分布。其效用通过多种密度估计和条件密度估计任务得到了说明。软件可在https://github.com/RussellTsuchida/snefy获取。