This is my presentation at Monitorama PDX in Portland on May 5, 2014 Simple math to get some signal out of your noisy sea of data You’ve instrumented your system and application to the hilt. You can now “measure all the things”. Your team has set up thousands of metrics collecting millions of data points a day. Now what? Most IT ops teams only keep an eye on a small fraction of the metrics they collect because analyzing this mountain of data and extracting signal from the noise is not easy. The choice of what analytic method to use ranges from simple statistical analysis to sophisticated machine learning techniques. And one algorithm doesn’t fit all data.

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2. Some Simple Math for
Anomaly Detection
#Monitorama PDX
2014.05.05
Toufic Boubez, Ph.D.
Co-Founder, CTO
Metafor Software
toufic@metaforsoftware.com
@tboubez

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Preamble
• I lied!
– There are no “simple” tricks
– If it’s too good to be true, it probably is
• I usually beat up on parametric, Gaussian, supervised techniques
– This talk is to show some alternatives
– Only enough time to cover a couple of relatively simple but very useful
techniques
– Oh, and I will still beat up on the usual suspects
• Adrian and James are right! Listen to them! 
– What’s the point of collecting all that data if you can’t get useful information
out of it!?
• Note: real data
• Note: no y-axis labels on charts – on purpose!!
• Note to self: remember to SLOW DOWN!
• Note to self: mention the cats!! Everybody loves cats!!

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• Co-Founder/CTO Metafor Software
• Co-Founder/CTO Layer 7 Technologies
– Acquired by Computer Associates in 2013
– I escaped 
• Co-Founder/CTO Saffron Technology
• IBM Chief Architect for SOA
• Co-Author, Co-Editor: WS-Trust, WS-
SecureConversation, WS-Federation, WS-Policy
• Building large scale software systems for >20
years (I’m older than I look, I know!)
Toufic intro – who I am

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Wall of Charts™

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The WoC side-effects: alert fatigue
“Alert fatigue is the single
biggest problem we have
right now … We need to be
more intelligent about our
alerts or we’ll all go insane.”
- John Vincent (@lusis)
(#monitoringsucks)

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Watching screens cannot scale + it’s useless

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Gotta turn things over to the machines

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TO THE RESCUE: Anomaly Detection!!
• Anomaly detection (also known as outlier
detection) is the search for items or events
which do not conform to an expected pattern.
[Chandola, V.; Banerjee, A.; Kumar, V. (2009). "Anomaly detection: A
survey". ACM Computing Surveys 41 (3): 1]
• For devops: Need to know when one or more
of our metrics is going wonky

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Attempt #1: thresholds …
• Roots in manufacturing process QC

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… are based on Gaussian distributions
• Make assumptions about probability
distributions and process behaviour
– Data is normally distributed with a useful and
usable mean and standard deviation
– Data is probabilistically “stationary”

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Three-Sigma Rule
• Three-sigma rule
– ~68% of the values lie within 1 std deviation of the mean
– ~95% of the values lie within 2 std deviations
– 99.73% of the values lie within 3 std deviations: anything
else is an outlier

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Aaahhhh
• The mysterious red lines explained

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Stationary Gaussian distributions are powerful
• Because far far in the future, in a galaxy far far
away:
– I can make the same predictions because the
statistical properties of the data haven’t changed
– I can easily compare different metrics since they
have similar statistical properties
• Let’s do this!!
• BUT…
• Cue in DRAMATIC MUSIC

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Then THIS happens

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3-sigma rule alerts

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Or worse, THIS happens!

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3-sigma rule alerts

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WTF!? So what gives!?
• Remember this?

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Histogram – probability distribution

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Histogram – probability distribution

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Attempts #2, #3, etc: mo’ better thresholds
• Static thresholds ineffective on dynamic data
– Thresholds use the mean as predictor and alert if
data falls more than 3 sigma outside the mean
• Need “moving” or “adaptive” thresholds:
– Value of mean changes with time to
accommodate new data values/trends

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Moving Averages “big idea”
• At any point in time in a well-behaved time
series, your next value should not significantly
deviate from the general trend of your data
• Mean as a predictor is too static, relies on too
much past data (ALL of the data!)
• Instead of overall mean use a finite window of
past values, predict most likely next value
• Alert if actual value “significantly” (3 sigmas?)
deviates from predicted value

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Moving Averages typical method
• Generate a “smoothed” version of the time series
– Average over a sliding (moving) window
• Compute the squared error between raw series
and its smoothed version
• Compute a new effective standard deviation by
smoothing the squared error
• Generate a moving threshold:
– Outliers are 3-sigma outside the new, smoothed data!
• Ta-da!

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Simple and Weighted Moving Averages
• Simple Moving Average
– Average of last N values in your time series
• S[t] <- sum(X[t-(N-1):t])/N
– Each value in the window contributes equally to
prediction
– …INCLUDING spikes and outliers
• Weigthed Moving Average
– Similar to SMA but assigns linearly (arithmetically)
decreasing weights to every value in the window
– Older values contribute less to the prediction

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Exponential Smoothing techniques
• Exponential Smoothing
– Similar to weighted average, but with weights decay
exponentially over the whole set of historic samples
• S[t]=αX[t-1] + (1-α)S[t-1]
– Does not deal with trends in data
• DES
– In addition to data smoothing factor (α), introduces a trend
smoothing factor (β)
– Better at dealing with trending
– Does not deal with seasonality in data
• TES, Holt-Winters
– Introduces additional seasonality factor
– … and so on

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Let’s look at an example

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Holt-Winters predictions

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A harder example

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Exponential smoothing predictions

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Hmmmm, so are we doomed?
• No!
• ALL smoothing predictive methods work best
with normally distributed data!
• But there are lots of other non-Gaussian
based techniques
– We can only scratch the surface in this talk

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Trick #1: Histogram!

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THIS is normal

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This isn’t

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Neither is this

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Trick #2: Kolmogorov-Smirnov test
• Non-parametric test
– Compare two probability
distributions
– Makes no assumptions (e.g.
Gaussian) about the
distributions of the samples
– Measures maximum
distance between
cumulative distributions
– Can be used to compare
periodic/seasonal metric
periods (e.g. day-to-day or
week-to-week)
http://en.wikipedia.org/wiki/Kolmogorov%E2%
80%93Smirnov_test

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KS with windowing

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KS Test on difficult data

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Trick #3: Diffing/Derivatives
• Often, even when the data itself is not
stationary, its derivatives tends to be!
• Most frequently, first difference is sufficient:
dS(t) <- S(t+1) – S(t)
• Can then perform some analytics on first
difference

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CPU time series

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Its first difference – possible random walk?

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We’re not doomed, but: Know your data!!
• You need to understand the statistical properties
of your data, and where it comes from, in order
to determine what kind of analytics to use.
– Your data is very important!
– You spend time collecting it so spend time analyzing
it!
• A large amount of data center data is non-
Gaussian
– Guassian statistics won’t work
– Use appropriate techniques

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More?
• Only scratched the surface
• I want to talk more about algorithms, analytics,
current issues, etc, in more depth, but time’s up!!
– Come talk to me or email me if interested.
• Thank you!
toufic@metaforsoftware.com
@tboubez

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Oh yeah, and we’re hiring!
In Vancouver, BC