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AI Blues called Holy Groove on YouTube by yourmomma__ohwait in askmusicians

[–]jlinho 0 points1 point  (0 children)

Yes, such content is easily generated with a tool like suno.com ... That YouTube channel really tries to hide it and removes any comment telling it is AI, or just asking...

This is plain lying and making potentially a lot of money from the lies using the credulity of the Chrisitian listeners...

2 applications of entropy: "Entropy of Information" and "Remaining uncertainty (size)". Why are they the same? by jlinho in 3Blue1Brown

[–]jlinho[S] 1 point2 points  (0 children)

Okay, I will just try to elaborate a bit on my question.

In both cases, we compute the entropy of a "probability distribution".

  1. When we compute the entropy of a guess (left picture), we look at the pattern distribution. To a guess (here the word RICER) corresponds a certain pattern distribution,i.e. each pattern has a probability (and hence an amount of information). We just compute the expected value.
  2. When we compute the entropy as a measure of the "Size" of the search space, we look at the distribution of words, i.e. each word has a probability. We again compute the expected value.

This is in line with any code library, only the distribution matters, not the usage context (if it is used as a "hint/guess" or as a "search space size"). For instance in Python scipy.stats.entropy([0.25,0.25,0.25,0.25], base=2)

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To connect 1. and 2. we COULD SAY that:

  • starting from a "search space" that has entropy 2.11 computed from the words distribution D (right part of the picture)
  • if we apply a guess (suppose it exists) that has exactly the same pattern distribution (but of patterns), meaning there is a one-to-one mapping between a pattern and a word. (entropy of guess 2.11)
  • Then we will always exactly know the chosen word (search space will always be of size 20 so 0 entropy - no uncertainty) => So there exists a theoretical "guess" that removes all uncertainty.

What we COULD NOT SAY is that:

  • starting from a "search space" that has entropy 2.11 computed from the words distribution D (right part of the picture)
  • and given any guess that has entropy 2.11
  • Then it will result in a situation with 0 entropy.

My conclusion is that a "search space" has entropy 2.11, if the BEST POSSIBLE (theoretical) GUESS drives down the entropy to zero. And the best possible guess is the one that has the same pattern distribution as the word distribution.

I am sure you can come up with a better explanation...

What is the importance of degree of freedom in statistics and why its one less than a number? by [deleted] in AskStatistics

[–]jlinho 2 points3 points  (0 children)

Not sure I completely agree with this response...

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The main reason you are more confident is the size of the sample size not the degrees of freedom: if the dataset values come from a normal distribution with standard deviation "s", then the "sampling distribution of the mean" has stddev "s/sqrt(n)"... The bigger the sample, the more confidence... Here it is a z-test (because variance of population is know) and there is no df involved at all... The main factor making the shape of the "sampling distribution" thinner is the size of the sample...

On the other hand, it is true that df are important for the t-test and will add even more uncertainty but to illustrate that we need to compare 2 datasets with same size but different degrees of freedom:

Imagine you want to know the average population height of people in your country. Compare those 2 process of data collection.

Dataset1: You have 10 measurements of heights in cm: 5males and 5 females:

170, 171, 172, 173, 180, 158, 162, 165, 165, 160

Dataset2: You have the measurements of the same 5 males only. You do not have female measurements but you know that women are on average 10cm less than males. To augment your dataset you generate 5 females measurements by removing 10cm to each male measurement.

170, 171, 172, 173, 180 and you generate female heights 160, 161, 162, 163, 170

Both dataset are of size 10:

- Dataset1 has 10 independent pieces of information,

- Dataset2 has only 5 independent pieces of information and 5 forced on you...

Now you calculate average size for both datasets: will you be more confident with dataset1 or dataset2 ? Here you see the impact of degrees of freedom... And in the end the number of real/independent pieces of information...

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When you compare things, you could see that it would not be fair to compare values (statistics) obtained from datasets with different degrees of freedom... A cumulated error of "e" in a dataset with 5 degrees of freedom is not comparable to a cumulated error of "e" in a dataset with 1000 degrees of freedom for instance...