C-Docs: New structure

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Signed-off-by: Tibor Frank <tifrank@cisco.com>

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-title: "Trending Analysis"
-weight: 2
----
-
-# Trend Analysis
-
-All measured performance trend data is treated as time-series data
-that is modeled as a concatenation of groups,
-within each group the samples come (independently) from
-the same normal distribution (with some center and standard deviation).
-
-Center of the normal distribution for the group (equal to population average)
-is called a trend for the group.
-All the analysis is based on finding the right partition into groups
-and comparing their trends.
-
-## Anomalies in graphs
-
-In graphs, the start of the following group is marked as a regression (red
-circle) or progression (green circle), if the new trend is lower (or higher
-respectively) then the previous group's.
-
-## Implementation details
-
-### Partitioning into groups
-
-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 current presentation takes average of
-all trials within the run as the sample. Effectively, this acts as a single
-trial with aggregate duration.
-
-Performance graphs show the run average as a dot (not all individual trial
-results).
-
-The group boundaries are selected based on `Minimum Description Length`[^1].
-
-### Minimum Description Length
-
-`Minimum Description Length`[^1] (MDL) is a particular formalization
-of `Occam's razor`[^2] 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 discourages 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 hard-coded.
-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`[^3]) the groups tend to focus on less relevant factors
-(such as "outlier" density).
-
-## Common Patterns
-
-When an anomaly is detected, it frequently falls into few known patterns,
-each having its typical behavior over time.
-
-We are going to describe the behaviors,
-as they motivate our choice of trend compliance metrics.
-
-### Sample time and analysis time
-
-But first we need to distinguish two roles time plays in analysis,
-so it is more clear which role we are referring to.
-
-Sample time is the more obvious one.
-It is the time the sample is generated.
-It is the start time or the end time of the Jenkins job run,
-does not really matter which (parallel runs are disabled,
-and length of gap between samples does not affect metrics).
-
-Analysis time is the time the current analysis is computed.
-Again, the exact time does not usually matter,
-what matters is how many later (and how fewer earlier) samples
-were considered in the computation.
-
-For some patterns, it is usual for a previously reported
-anomaly to "vanish", or previously unseen anomaly to "appear late",
-as later samples change which partition into groups is more probable.
-
-Dashboard and graphs are always showing the latest analysis time,
-the compliance metrics are using earlier sample time
-with the same latest analysis time.
-
-Alerting e-mails use the latest analysis time at the time of sending,
-so the values reported there are likely to be different
-from the later analysis time results shown in dashboard and graphs.
-
-### Ordinary regression
-
-The real performance changes from previously stable value
-into a new stable value.
-
-For medium to high magnitude of the change, one run
-is enough for anomaly detection to mark this regression.
-
-Ordinary progressions are detected in the same way.
-
-### Small regression
-
-The real performance changes from previously stable value
-into a new stable value, but the difference is small.
-
-For the anomaly detection algorithm, this change is harder to detect,
-depending on the standard deviation of the previous group.
-
-If the new performance value stays stable, eventually
-the detection algorithm is able to detect this anomaly
-when there are enough samples around the new value.
-
-If the difference is too small, it may remain undetected
-(as new performance change happens, or full history of samples
-is still not enough for the detection).
-
-Small progressions have the same behavior.
-
-### Reverted regression
-
-This pattern can have two different causes.
-We would like to distinguish them, but that is usually
-not possible to do just by looking at the measured values (and not telemetry).
-
-In one cause, the real DUT performance has changed,
-but got restored immediately.
-In the other cause, no real performance change happened,
-just some temporary infrastructure issue
-has caused a wrong low value to be measured.
-
-For small measured changes, this pattern may remain undetected.
-For medium and big measured changes, this is detected when the regression
-happens on just the last sample.
-
-For big changes, the revert is also immediately detected
-as a subsequent progression. The trend is usually different
-from the previously stable trend (as the two population averages
-are not likely to be exactly equal), but the difference
-between the two trends is relatively small.
-
-For medium changes, the detection algorithm may need several new samples
-to detect a progression (as it dislikes single sample groups),
-in the meantime reporting regressions (difference decreasing
-with analysis time), until it stabilizes the same way as for big changes
-(regression followed by progression, small difference
-between the old stable trend and last trend).
-
-As it is very hard for a fault code or an infrastructure issue
-to increase performance, the opposite (temporary progression)
-almost never happens.
-
-### Summary
-
-There is a trade-off between detecting small regressions
-and not reporting the same old regressions for a long time.
-
-For people reading e-mails, a sudden regression with a big number of samples
-in the last group means this regression was hard for the algorithm to detect.
-
-If there is a big regression with just one run in the last group,
-we are not sure if it is real, or just a temporary issue.
-It is useful to wait some time before starting an investigation.
-
-With decreasing (absolute value of) difference, the number of expected runs
-increases. If there is not enough runs, we still cannot distinguish
-real regression from temporary regression just from the current metrics
-(although humans frequently can tell by looking at the graph).
-
-When there is a regression or progression with just a small difference,
-it is probably an artifact of a temporary regression.
-Not worth examining, unless temporary regressions happen somewhat frequently.
-
-It is not easy for the metrics to locate the previous stable value,
-especially if multiple anomalies happened in the last few weeks.
-It is good to compare last trend with long term trend maximum,
-as it highlights the difference between "now" and "what could be".
-It is good to exclude last week from the trend maximum,
-as including the last week would hide all real progressions.
-
-[^1]: [Minimum Description Length](https://en.wikipedia.org/wiki/Minimum_description_length)
-[^2]: [Occam's razor](https://en.wikipedia.org/wiki/Occam%27s_razor)
-[^3]: [bimodal distribution](https://en.wikipedia.org/wiki/Bimodal_distribution)