Bias aware probabilistic Boolean matrix factorization
Bias aware probabilistic Boolean matrix factorization
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发表时间：
2022-08
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通讯作者：
Changlin Wan;Pengtao Dang;Tong Zhao;Y. Zang;Chi Zhang-;Sha Cao
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作者：
Changlin Wan;Pengtao Dang;Tong Zhao;Y. Zang;Chi Zhang-;Sha Cao
布尔矩阵分解（BMF）是一个组合问题，广泛应用于推荐系统、协同过滤、降维等领域。目前，现有BMF方法的噪声模型通常被假设为同方差;然而，在真实的世界数据场景中，由于随机噪声，观测数据与其真实值的偏差几乎肯定是不同的，使得每个数据点并不同样适合拟合模型。在这种情况下，将所有数据点视为均匀分布并不理想。出于这样的观察，我们引入了一个概率BMF模型，识别对象和功能明智的偏见分布分别，称为偏见感知BMF（BABF）。据我们所知，BABF是第一种考虑二进制数据中特征和对象偏差的布尔分解方法。我们在具有不同背景噪声水平、偏差水平和信号模式大小的数据集上进行了实验，以测试我们的方法在各种情况下的有效性。我们证明了我们的模型在恢复原始数据集的准确性和效率方面优于最先进的因子分解方法，并且推断的偏差水平与模拟和真实的世界数据集中的真实存在的偏差高度显著相关。
Boolean matrix factorization (BMF) is a combinatorial problem arising from a wide range of applications including recommendation system, collaborative filtering, and dimensionality reduction. Currently, the noise model of existing BMF methods is often assumed to be homoscedastic; however, in real world data scenarios, the deviations of observed data from their true values are almost surely diverse due to stochastic noises, making each data point not equally suitable for fitting a model. In this case, it is not ideal to treat all data points as equally distributed. Motivated by such observations, we introduce a probabilistic BMF model that recognizes the object- and feature-wise bias distribution respectively, called bias aware BMF (BABF). To the best of our knowledge, BABF is the first approach for Boolean decomposition with consideration of the feature-wise and object-wise bias in binary data. We conducted experiments on datasets with different levels of background noise, bias level, and sizes of the signal patterns, to test the effectiveness of our method in various scenarios. We demonstrated that our model outperforms the state-of-the-art factorization methods in both accuracy and efficiency in recovering the original datasets, and the inferred bias level is highly significantly correlated with true existing bias in both simulated and real world datasets.