Building Machine Learning Systems with Python - Richert, Coelho

Getting Started with Python Machine Learning
Answering our initial question
Finally, we have arrived at a model that we think represents the underlying process
best; it is now a simple task of finding out when our infrastructure will reach 100,000
requests per hour. We have to calculate when our model function reaches the value
100,000.
Having a polynomial of degree 2, we could simply compute the inverse of the
function and calculate its value at 100,000. Of course, we would like to have an
approach that is applicable to any model function easily.
This can be done by subtracting 100,000 from the polynomial, which results in
another polynomial, and finding the root of it. SciPy's optimize module has the
fsolve function to achieve this when providing an initial starting position. Let
fbt2 be the winning polynomial of degree 2:
>>> print(fbt2)
2
0.08844 x - 97.31 x + 2.853e+04
>>> print(fbt2-100000)
2
0.08844 x - 97.31 x - 7.147e+04
>>> from scipy.optimize import fsolve
>>> reached_max = fsolve(fbt2-100000, 800)/(7*24)
>>> print("100,000 hits/hour expected at week %f" % reached_max[0])
100,000 hits/hour expected at week 9.827613
Our model tells us that given the current user behavior and traction of our startup,
it will take another month until we have reached our threshold capacity.
Of course, there is a certain uncertainty involved with our prediction. To get the real
picture, you can draw in more sophisticated statistics to find out about the variance
that we have to expect when looking farther and further into the future.
And then there are the user and underlying user behavior dynamics that we cannot
model accurately. However, at this point we are fine with the current predictions.
After all, we can prepare all the time-consuming actions now. If we then monitor
our web traffic closely, we will see in time when we have to allocate new resources.
[ 30 ]