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Monitoring the development of infectious diseases is of great importance for the prevention of major outbreaks. Syndromic surveillance aims at developing algorithms which can detect outbreaks as early as possible by monitoring data sources which allow to capture the occurrences of a certain disease. Recent research mainly concentrates on the surveillance of specific, known diseases, putting the focus on the definition of the disease pattern under surveillance. Until now, only little effort has been devoted to what we call non-specific syndromic surveillance, i.e., the use of all available data for detecting any kind of infectious disease outbreaks. In this work, we give an overview of non-specific syndromic surveillance from the perspective of machine learning and propose a unified framework based on global and local modeling techniques. We also present a set of statistical modeling techniques which have not been used in a local modeling context before and can serve as benchmarks for the more elaborate machine learning approaches. In an experimental comparison of different approaches to non-specific syndromic surveillance we found that these simple statistical techniques already achieve competitive results and sometimes even outperform more elaborate approaches. In particular, applying common syndromic surveillance methods in a non-specific setting seems to be promising.