The BigML Support Team takes security and privacy very seriously. The only way to access BigML is through HTTPS. The BigML services are backed by Amazon Web Services and take advantage of the excellent security, fault tolerance, and availability that this platform offers. For more details, please see here the BigML privacy policy, which precludes the BigML Support Team from having access to any data in the BigML system. Therefore, the BigML Team would need the explicit consent from the user to do so.
Nevertheless, the BigML Support Team strongly advise not to upload any data that is personal. Leaving those items out or obfuscating them is the simplest and most effective form of privacy protection. Bear in mind that personally identifiable information is rarely needed for most analysis tasks.