Precision vs Recall made clear without any formulas

#datascience #machinelearning

Have you too been struggling to understand what precision and recall ACTUALLY mean? Not in terms of formulae, but, actually how to interpret it? Well, I struggled with this too.

So, let me try and explain you, without using any formulae, but just intuition and a real, practical example, what they actually mean.

For this, we'll take 2 different binary classification scenarios:

Scenario 1. Classifying whether a person have committed murder(=1) or not(=0).
Scenario 2. Classifying whether a person has diabetes(=1) or not(=0).

Now, what if I were to ask you, which of these have more dire consequences:

Falsely marking 0 as 1, or
Falsely marking 1 as 0?

Let's take the first case: the murder one:

Falsely marking 0 as 1: You falsely classify an innocent person of murder.

Consequence: That person dies.
Falsely marking 1 as 0: You falsely classify the murderer as innocent.

Consequence: The murderer goes free

Which of these 2 cases is the one having more dire consequences?

Don't answer yet.

Let's do the same for second case now: the diabetes one:

Falsely marking 0 as 1: You falsely classify a person as having diabetes, even though that person doesn't have it.

Consequence: Starts to take medicines, a few side effects, maybe, maybe, death because of those medicines
Falsely marking 1 as 0: You falsely classify a person as NOT having diabetes, even though that person actually has.

Consequence: A definite death

Now let's answer that question about which of these scenarios is more dire:

Wrongly convicting an innocent person of murder, and subsequently letting that person die of death punishment is far, far more dire than letting a murderer go free.
Wrongly diagnosing a diabetic person as NOT having diabetes, and letting that person go without any medication, which ultimately will lead to the person's death is far, far more dire than wrongly diagnosing a non-diabetic person as diabetic.

That means:

For case 1, the consequence of Falsely marking 0 as 1(False Positive) if greater than Falsely marking 1 as 0(False Negative)
For case 2, the consequence of Falsely marking 1 as 0(False Negative) if greater than Falsely marking 0 as 1(False Positive)

And this is where our precision and recall comes into play.

Wherever the consequences of False Positive is greater than that of False Negative (case 1 here), go with higher precision.
Wherever the consequences of False Negative is greater than that of False Positive (case 2 here), go with higher recall.

Let me expand on this with another example, but, this time a little less intuitive, but, more close to numbers:

Consider a certain binary classification problem in which true 1 cases are 8, but, your model gave 10. In this case, those 2 extra 1's are false positives. This is what precision can mathematically tell you. This here has a precision of: 8/(8+2) => 0.8 => 80%.
Now consider that true no. of 1 outcomes are actually 10, but, your model gave only 8 (rest 2 were classified as 0). In this case, those 2 less 1's, which were classified as 0's are false negatives. This is what recall can mathematically tell you. This here has a recall of: 10/(10+2) => 0.8333 => 83.33%.