Dissimilar Batch Decompositions of Random Datasets

Noname manuscript No. (will be inserted by the editor) Ghurumuruhan Ganesan IISER Bhopal Abstract For better learning, large datasets are often split into small batch es and fed sequentially to the predictive model. In this paper, we study suc h batch decompositions from a probabilistic perspective. We assume that data poin ts (possibly corrupted) are drawn independently from a given space and define a co ncept of similarity between two data points. We then consider decompositions that restrict the amount of similarity within each batch and obtain high probability bounds for the minimum size. We demonstrate an inherent tradeoff between relaxing the similarity constraint and the overall size and also use martingale methods to obtain bounds fo r the maximum size of data subsets with a given similarity.