Web servers on the Internet need to maintain high reliability, but the cause of intermittent failures of web transactions is non-obvious. We use approximate Bayesian inference to diagnose problems with web services. This diagnosis problem is far larger than any previously attempted: it requires inference of 104 possible faults from 105 observations. Further, such inference must be performed in less than a second. Inference can be done at
this speed by combining a mean-field variational approximation and the use of stochastic gradient descent to optimize a variational cost function. We use this fast inference to diagnose a time series of anomalous HTTP requests taken from a real web service. The inference is fast enough to analyze network logs with billions of entries in a matter of hours.