There are two datasets on UCI for activity recognition. 

http://archive.ics.uci.edu/ml/datasets/Activity+Recognition+from+Single+Chest-Mounted+Accelerometer

https://archive.ics.uci.edu/ml/datasets/PAMAP2+Physical+Activity+Monitoring

Regarding the anomalies you can inject some anomalies in the background data (e.g. see http://dx.doi.org/10.1016/j.neucom.2016.04.006)

We have a publicly available dataset called WUIL (The Windows-Users and -Intruder simulations Logs Dataset) that can be useful, but it will depend on your needs. Let us know.

Please see our articles:

Benito Camiña, Raúl Monroy, Luis A. Trejo, Miguel Ángel Medina-Pérez

Temporal and Spatial Locality: an Abstraction for Masquerade Detection. IEEE Transactions on Information Forensics & Security (T-IFS). Accepted for publication (May 2016). ISSN: 1556-6013

J. Benito Camiña, C. Hernández-Gracidas, R. Monroy and L. Trejo. The Windows-Users and -Intruder simulations Logs Dataset (WUIL): An Experimental Framework for Masquerade Detection Mechanisms. Expert Systems with Applications. Methods and Applications of Artificial and Computational Intelligence. Volume 41, Issue 3, 15 February 2014, Pages 919–930. Elsevier

doi:10.1016/j.eswa.2013.08.022. ISSN: 0957-4174

https://docs.oracle.com/cd/B28359_01/server.111/b28337/tdpsg_auditing.htm#TDPSG50000