论文标题
非负二进制矩阵分解的大型最小化算法
A majorization-minimization algorithm for nonnegative binary matrix factorization
论文作者
论文摘要
本文使用矩阵分解解决了分解二进制数据的问题。我们考虑了均值份量的Bernoulli模型的家族，这是一类生成模型，非常适合对二进制数据进行建模并可以解释因素。我们将Bernoulli参数分解，并考虑其中一个因素之一，以进一步提高模型的表现力。尽管文献中已经提出了类似的模型，但它们仅利用Beta先验作为代理，以确保在贝叶斯环境中有效的Bernoulli参数。在实践中，它会减少到统一或不信息的先验。此外，这些模型中的估计集中在昂贵的贝叶斯推论上。在本文中，我们提出了一种简单但非常有效的多数化最小化算法，以最大程度地估计。我们的方法利用了Beta先验，可以调整其参数以提高矩阵完成任务中的性能。在三个公共二进制数据集上进行的实验表明，我们的方法在预测性能，计算复杂性和可解释性之间提供了出色的权衡。
This paper tackles the problem of decomposing binary data using matrix factorization. We consider the family of mean-parametrized Bernoulli models, a class of generative models that are well suited for modeling binary data and enables interpretability of the factors. We factorize the Bernoulli parameter and consider an additional Beta prior on one of the factors to further improve the model's expressive power. While similar models have been proposed in the literature, they only exploit the Beta prior as a proxy to ensure a valid Bernoulli parameter in a Bayesian setting; in practice it reduces to a uniform or uninformative prior. Besides, estimation in these models has focused on costly Bayesian inference. In this paper, we propose a simple yet very efficient majorization-minimization algorithm for maximum a posteriori estimation. Our approach leverages the Beta prior whose parameters can be tuned to improve performance in matrix completion tasks. Experiments conducted on three public binary datasets show that our approach offers an excellent trade-off between prediction performance, computational complexity, and interpretability.
