# Mistake in this Anomaly Detection paper?

While reading the paper Anomaly Detection over Noisy Data using Learned Probability Distributions, I think I have discovered a mistake. On page 3, right column. They say (italic text between brackets is mine):

We measure how likely each element $x_i$ is an outlier (an anomaly) by comparing the difference change in the log likelihood of the distribution if ...

Followed by ($LL$ denotes log-likelihood):

If this difference $(LL_t - LL_{t-1})$ is greater than some value $c$, we declare the element an anomaly and permanently move the element from the majority set to the anomaly set.

Then they provide insight in this principle by saying:

The parameter $c$ affects the number of anomalies that are detected by the system. With very low values of $c$ only the most extreme anomalies are detected while with higher values of $c$ more elements are declared anomalies.

I believe that the last part should be just the opposite: the higher the value of $c$, the harder it becomes for the difference in log-likelihood to reach the threshold, the fewer elements are classified as anomalies. Note that the difference in log-likelihood is defined as the increase of log-likelihood.

I couldn't find anything online stating that the paper indeed has this mistake. Am I missing something, or is it indeed wrong?

• e-mail the authors ..?
– Tim
Commented Jul 17, 2017 at 9:34
• Email sent ;) (After trying to figure out what this guy's up-to-date email address was.) Commented Jul 17, 2017 at 9:48

• I don't get it: log-likelihood is monotonically increasing with respect to the likelihood: $log(x) > log(y) \iff x > y$. The fact that they these numbers are negative doesn't change my argument I believe. The difference in log likelihood will still be positive if the change made the result more probable. Commented Jul 24, 2017 at 12:23