C3w5 video2 - Is blue curve monotonic?

In video Intrinsically Interpretable Models, from 2min40sec, lecturer says:

“In this graph, the blue and green curves are monotonic, while the red curve is not because it does not consistently increase or decrease or remain the same.”
Screenshot 2021-07-20 at 17.45.14

To my eyes, the blue curve does not consistently increase, decrease or remain the same. It increases, but then it stays the same and then increases again, hence like the red curve, it is not consistent and therefore should not be labelled monotonic by the definition given. Am I wrong ?

hi @shahin , according to the definition of monotonic function, it is called is called monotonic if and only if it is either entirely non-increasing, or entirely non-decreasing., so the blue curve is monotonic. The red curve is not because it is increasing and decreasing in different periods.

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How did you conclude this please?

Lecturer’s definition of monotonic: “consistently increase or decrease or remain the same” def1

Your definition of monotonic: “entirely non-increasing or entirely non-decreasing” def2

To help myself understand, I’m making a truth table:

def1 has 3 parts:

  1. consistently increase
  2. consistently decrease
  3. consistently remain the same
       1.      2.     3.         1. or 2. or 3.   
green: 0       1      0                1
blue:  0       0      0                0
red:   0       0      0                0

def2 has 2 parts:
4. entirely non-increasing
5. entirely non-decreasing

       4.      5.        4. or 5.   
green: 1       0            1
blue:  0       0            0
red:   0       0            0

Blue still seems to be non-monotonic to me, whether I use your quoted definition or the lecturer’s one.


Moving slightly away from these definitions, am I correct in saying that the point of this is simply that it is easier to interpret an input-to-output relationship if their correlation with one another does not change direction from negatively-correlated to positively-correlated (or vice versa).

In my interpretation, the blue curve is entirely non-decreasing, which means it is increasing or stay the same.

This course is about MLOps so I don’t expect all the math definitions to be strictly defined and stated in the video lectures. I think you can check some math textbooks for the definition of monotonic if you are still in doubt. Maybe it will have a better explanation.

Happy learning :slight_smile:

I think your interpretation here matches with mine. The model is easier to interpret if the relation between input and output is monotonic.