We study the problem of hyperparameter tuning in sparse matrix factorization under Bayesian framework. In the prior work, an analytical solution of sparse matrix factorization with Laplace prior was obtained by variational Bayes method under several approximations. Based on this solution, we propose a novel numerical method of hyperparameter tuning by evaluating the zero point of normalization factor in sparse matrix prior. We also verify that our method shows excellent performance for ground-truth sparse matrix reconstruction by comparing it with the widely-used algorithm of sparse principal component analysis.

翻译：我们研究了贝叶斯框架下稀疏矩阵分解中的超参数调优问题。在先前工作中，通过变分贝叶斯方法在若干近似条件下获得了具有拉普拉斯先验的稀疏矩阵分解的解析解。基于该解，我们提出了一种新的超参数调优数值方法，通过评估稀疏矩阵先验中归一化因子的零点。同时，通过与广泛使用的稀疏主成分分析算法进行比较，我们验证了该方法在真实稀疏矩阵重构中展现出优越性能。