--- /dev/null
+Trend Analysis
+--------------
+
+All measured performance trend data is treated as time-series data that
+can be modelled as concatenation of groups, each group modelled
+using normal distribution. While sometimes the samples within a group
+are far from being distributed normally, currently we do not have a
+better tractable model.
+
+Here, "sample" should be the result of single trial measurement,
+with group boundaries set only at test run granularity.
+But in order to avoid detecting causes unrelated to VPP performance,
+the default presentation (without /new/ in URL)
+takes average of all trials within the run as the sample.
+Effectively, this acts as a single trial with aggregate duration.
+
+Performance graphs always show the run average (not all trial results).
+
+The group boundaries are selected based on `Minimum Description Length`_.
+
+Minimum Description Length
+``````````````````````````
+
+`Minimum Description Length`_ (MDL) is a particular formalization
+of `Occam's razor`_ principle.
+
+The general formulation mandates to evaluate a large set of models,
+but for anomaly detection purposes, it is useful to consider
+a smaller set of models, so that scoring and comparing them is easier.
+
+For each candidate model, the data should be compressed losslessly,
+which includes model definitions, encoded model parameters,
+and the raw data encoded based on probabilities computed by the model.
+The model resulting in shortest compressed message is the "the" correct model.
+
+For our model set (groups of normally distributed samples),
+we need to encode group length (which penalizes too many groups),
+group average (more on that later), group stdev and then all the samples.
+
+Luckily, the "all the samples" part turns out to be quite easy to compute.
+If sample values are considered as coordinates in (multi-dimensional)
+Euclidean space, fixing stdev means the point with allowed coordinates
+lays on a sphere. Fixing average intersects the sphere with a (hyper)-plane,
+and Gaussian probability density on the resulting sphere is constant.
+So the only contribution is the "area" of the sphere, which only depends
+on the number of samples and stdev.
+
+A somehow ambiguous part is in choosing which encoding
+is used for group size, average and stdev.
+Different encodings cause different biases to large or small values.
+In our implementation we have chosen probability density
+corresponding to uniform distribution (from zero to maximal sample value)
+for stdev and average of the first group,
+but for averages of subsequent groups we have chosen a distribution
+which disourages delimiting groups with averages close together.
+
+Our implementation assumes that measurement precision is 1.0 pps.
+Thus it is slightly wrong for trial durations other than 1.0 seconds.
+Also, all the calculations assume 1.0 pps is totally negligible,
+compared to stdev value.
+
+The group selection algorithm currently has no parameters,
+all the aforementioned encodings and handling of precision is hardcoded.
+In principle, every group selection is examined, and the one encodable
+with least amount of bits is selected.
+As the bit amount for a selection is just sum of bits for every group,
+finding the best selection takes number of comparisons
+quadratically increasing with the size of data,
+the overall time complexity being probably cubic.
+
+The resulting group distribution looks good
+if samples are distributed normally enough within a group.
+But for obviously different distributions (for example `bimodal distribution`_)
+the groups tend to focus on less relevant factors (such as "outlier" density).
+
+Anomaly Detection
+`````````````````
+
+Once the trend data is divided into groups, each group has its population average.
+The start of the following group is marked as a regression (or progression)
+if the new group's average is lower (higher) then the previous group's.
+
+In the text below, "average at time <t>", shorthand "AVG[t]"
+means "the group average of the group the sample at time <t> belongs to".
+
+Trend Compliance
+````````````````
+
+Trend compliance metrics are targeted to provide an indication of trend
+changes over a short-term (i.e. weekly) and a long-term (i.e.
+quarterly), comparing the last group average AVG[last], to the one from week
+ago, AVG[last - 1week] and to the maximum of trend values over last
+quarter except last week, max(AVG[last - 3mths]..ANV[last - 1week]),
+respectively. This results in following trend compliance calculations:
+
++-------------------------+---------------------------------+-----------+-------------------------------------------+
+| Trend Compliance Metric | Trend Change Formula | Value | Reference |
++=========================+=================================+===========+===========================================+
+| Short-Term Change | (Value - Reference) / Reference | AVG[last] | AVG[last - 1week] |
++-------------------------+---------------------------------+-----------+-------------------------------------------+
+| Long-Term Change | (Value - Reference) / Reference | AVG[last] | max(AVG[last - 3mths]..AVG[last - 1week]) |
++-------------------------+---------------------------------+-----------+-------------------------------------------+
+
+.. _Minimum Description Length: https://en.wikipedia.org/wiki/Minimum_description_length
+.. _Occam's razor: https://en.wikipedia.org/wiki/Occam%27s_razor
+.. _bimodal distribution: https://en.wikipedia.org/wiki/Bimodal_distribution
Code Review / csit.git / blobdiff