Be perfect, do better. The definition problem.

Be perfect, do better. Is it a good thing?

It seems to be the motto for lots of people. But do they really believe in it? Do I really believe in it? Can anyone achive this?

What is perfect? What is better? There’s always an issue of definition. Be positive? Be hardworking? Be mindful? Be … ?

Maths are simple. You can define an order to define what is better, and where it leads to. You can define many things strictly. But this is almost impossible in life? Or it makes life “less” fun? Has anyone ever  been truly consistent with any definitions in life? Is it even possible?

Ok. Let’s say it’s possible. And people understand perfectly what is to be better and what is to be perfect. Where does it take us then?

There are things in life that you care, things you don’t care, things when you start to care about them they start to annoy you, things when you care about them and they reward you back.  Then maybe do better = get more rewards. Good we have a direction now!

Rewards could be ambigious as well. In my mind, a case by case analysis could help, but it is unlikely to be unavoidable since it comes from the complexity of the society and each individual and situation. History repeats but never exactly!

As off-topic as usual, but let’s come back to “aiming upwards”. Thinking in terms of all sorts of competitions. People make strategies for different stages: from the start, in the middle, and at the final stage. Strategies and rewards change as time gone by, but something could stays the same: the goal of “winning”.  But to win, to make changing startegies for chaning rewards, you need to be “flexible”. Then the question comes: how about the goal then? Is it “flexible” too? Maybe we don’t have to “win” but it’s already “winning” and maybe we don’t have to be better nor perfect but it’s already there. (This is probably also why starts new things later in life is “hard”. )

I might disagree with myself later on this. But. Be free. Also.

Photo taken close to where I live:

IMG_1180

Advertisements

The symmetry between recall and precision

Arguably the most common metrics: recall and precision, are very easy to understand once you see the symmetry.

What makes everything clear is the reference: what is the reference frame for this number (the denominator). For recall, the reference frame is the ground truth data; for precision, the reference frame is the data we found using our algorithm. The numerator is the same thing, so that’s simple.

It’s basically different normalisation methods. Recall normalise with the number of things we are trying to approach (ground truth), so the recall tells you how much we approached the “truth”; precision normalise with the number of things we calculated, so the precision tell us how likely that our calculation is correct.

The ideal case would be a bijection: for every ground truth we have one calculated value corresponds to, and vice versa. But this is not always the case! If it’s possible to have repeated value in the ground truth or the calculated value, be careful to not double count!

The problem is clearer when we allow a certain degree of fuzziness:

IMG_2197.png

For example, the problem in the figure above, we want to see: given the ground truth (in red), how close are the calculated values (in orange). So we need a threshold to define how close is close!

It’s easy so far because in the case above I plotted a bijection. How about the cases below:

What should we do now? The precision and recall better not to be > 1, right?

One way is to “find” a one-to-one(injective) mapping (not necessarily onto or surjective) by not counting the value even if they are close to the ground truth/calculated value.

Also, depending on which reference frame you are in (whether you are calculating recall or precision), you need to discard different values. The mapping can be different! And the way to create the two mappings is symmetric to each other! You can even find a injective/surjective symmetry there. Fun fun!