Anomaly detection in monitored systems (part 2)

Learning how Gaussian distributions and the properties they have can help us perform anomaly detection on monitored data. In the first article of this series, we’ve discussed the properties of the Gaussian function and how they can be used to detect anomalies in monitored data. In this part, we will be putting that knowledge to practice and build our very own anomaly detection program.

Gaussian function and how they can be used to detect anomalies in monitored data. In this part, we will be putting that knowledge to practice and build our very own anomaly detection program.

To recap, we finished the previous article with the Gaussian function in the graph above, on which two points mark different values a given data sample x might take. We then stated that the farther away x is from the mean, the higher the probability it represents an anomaly.

Two points p(x1) and p(x2) plotted on a Gaussian function g(x) (image by author)

The only problem in that statement is that the probability of getting any single value is precisely zero. Why is that? It turns out that the Gaussian function is a member of a group of functions calls “Probability Density Functions”, or PDF’s for short. Without diving too deep into the mathematics behind PDFs, it suffices to understand that they give us the probability of a “continuous random variable” yielding a value within a given “range”.

Now let’s explain that: a range is simply a length between two numbers and is expressed by subtracting them. The common notation for the range between two points a and b is (a, b). A number x is considered “within” a range i

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