Temporal Biased Streaming Submodular Optimization

Abstract

Submodular optimization lies at the core of many data mining and machine learning applications such as data summarization and subset selection. For data streams where elements arrive one at a time, streaming submodular optimization (SSO) algorithms are desired. Existing SSO solutions are mainly designed for insertion-only streams where elements in the stream all participate in the analysis, or sliding-window streams where only the most recent data participates in the analysis. SSO for insertion-only streams does not sufficiently emphasize recent data. SSO for sliding-window streams abruptly forgets all past data. In this work, we propose a new SSO problem, i.e., temporal biased streaming submodular optimization (TBSSO), which embraces the special settings of all previous studies. TBSSO leverages a temporal bias function to force each element in the stream to participate in the analysis with a probability decreasing over time and hence elements in the stream are forgotten gradually. We design novel streaming algorithms to solve the TBSSO problem with provable approximation guarantees. Experiments show that our algorithm can find high quality solutions and improve the efficiency to about one order of magnitude faster than the baseline method.