Human opinion is entertaining, data is trustworthy. — Bryan Johnson
Without data you’re just another person with an opinion. — William Edwards Deming
https://www.youtube.com/playlist?list=PLSQl0a2vh4HC9lvrBhVt4UUkhzpp3N5_x
https://taylor.town/compress-code
https://seeing-theory.brown.edu/
Not all scientific studies are created equal
$$ P(A \mid B)= \frac{P(A \cap B)}{P(B)} $$
$$ P(A \cap B) = P(B \mid A)P(A) = \frac{P(A \cap B)}{\cancel{P(A)}}\cancel{P(A)} $$
Machine Learning, Neural Networks, Deep Learning
say we want to classify into $Ys$ given $Xs$
maybe $Y = 1 = \text{cat}$ and $Y=0 = \text{not cat}$
$$ P(A, B) = P(A \cap B) = P(A)P(B \mid A) = P(B)P(A \mid B) $$
$$ P(Y| X) = \frac{P(Y)P(X|Y)}{P(X)} $$
for classification,
$$ \argmax_\theta(\theta \mid X) = \argmax_\theta \frac{P(X \mid \theta)P(\theta)}{\cancel{P(X)}} = \argmax_\theta P(X\mid\theta)P(\theta) $$
we can just cut $P(X)$ out because it’s not dependent on $\theta$, it’s just a constant that stretches the data.
$P(\text{probability of the \color{red}{data}\color{default}{, given params)}}$
$L(\text{likelihood of the \color{green}{params}\color{default}{, given data)}}$
https://www.youtube.com/playlist?list=PLblh5JKOoLUK0FLuzwntyYI10UQFUhsY9
https://www.youtube.com/playlist?list=PLUl4u3cNGP60hI9ATjSFgLZpbNJ7myAg6
https://youtube.com/watch?v=XJnIdRXUi7A
https://www.youtube.com/playlist?list=PLZHQObOWTQDOjmo3Y6ADm0ScWAlEXf-fp
https://www.youtube.com/watch?v=zeJD6dqJ5lo&t=66s
https://www.youtube.com/watch?v=cy8r7WSuT1I