We provide new algorithms for two tasks relating to heterogeneous tabular datasets: clustering, and synthetic data generation. Tabular datasets typically consist of heterogeneous data types (numerical, ordinal, categorical) in columns, but may also have hidden cluster structure in their rows: for example, they may be drawn from heterogeneous (geographical, socioeconomic, methodological) sources, such that the outcome variable they describe (such as the presence of a disease) may depend not only on the other variables but on the cluster context. Moreover, sharing of biomedical data is often hindered by patient confidentiality laws, and there is current interest in algorithms to generate synthetic tabular data from real data, for example via deep learning. We demonstrate a novel EM-based clustering algorithm, MMM (``Madras Mixture Model''), that outperforms standard algorithms in determining clusters in synthetic heterogeneous data, and recovers structure in real data. Based on this, we demonstrate a synthetic tabular data generation algorithm, MMMsynth, that pre-clusters the input data, and generates cluster-wise synthetic data assuming cluster-specific data distributions for the input columns. We benchmark this algorithm by testing the performance of standard ML algorithms when they are trained on synthetic data and tested on real published datasets. Our synthetic data generation algorithm outperforms other literature tabular-data generators, and approaches the performance of training purely with real data.

翻译：我们针对异构表格数据集的两个任务——聚类与合成数据生成——提出了新算法。表格数据集通常由异构数据类型（数值型、有序型、分类型）的列构成，但其行中可能隐藏着聚类结构：例如，这些数据可能来自异构（地理、社会经济、方法论）来源，使得其所描述的结果变量（如疾病的存在）不仅依赖于其他变量，还可能受聚类背景影响。此外，生物医学数据的共享常因患者隐私法受阻，目前业界对通过深度学习等算法从真实数据生成合成表格数据的方法存在浓厚兴趣。我们提出了一种基于期望最大化（EM）的新型聚类算法MMM（"Madras Mixture Model"），该算法在合成异构数据的聚类效果上优于标准算法，并能恢复真实数据中的结构。基于此，我们提出了一种合成表格数据生成算法MMMSynth，该算法对输入数据进行预聚类，并假设输入列存在聚类特定的数据分布，从而生成分聚类合成数据。我们通过测试标准机器学习算法在合成数据上训练，并在真实公开数据集上进行验证的表现，对该算法进行了基准评估。我们的合成数据生成算法优于文献中其他表格数据生成器，其性能接近纯真实数据训练的效果。