Errata

I submitted a "numerical overflow" issue, and said I fixed it by unitizing the gradient average. Well...never mind. Much later I found that I had a typo in vector_mean. Fix that. All good. Sorry.

When running the code at the bottom of the page, trying to find the slope and intercept of the line, the code does as asked for [-14, 14] input range, but I get numeric overflow for [-15, 15] (and larger).

I can fix that by unitizing grad in the linear gradient function (top of page), so that I have a direction, but not a magnitude. I'm not sure that's quite kosher.

While the code for the return statement is accurate, it is slightly difficult to follow because it is structured differently from the equation given above it. It could be made easier to comprehend by utilizing parentheses like
math.exp((-(x-mu)**2/2)/sigma**2)/(SQRT_TWO_PI/sigma)
or
math.exp(-(x-mu)**2/(2*sigma**2))/(SQRT_TWO_PI/sigma)

This would make it easier to understand the order of operations.

"Imagine instead that our null hypothesis was that the coin is not biased
toward heads, or that p ≤ 0. 5. In that case we want a one-sided test that
rejects the null hypothesis when X is much larger than 500 but not when X
is smaller than 500. So, a 5% significance test involves using
normal_probability_below to find the cutoff below which 95% of the
probability lies: ...."

In the first line should not "our null hypothesis" be replaced with "our alternative hypothesis"? Because the null hypothesis is always the default one and the alternative hypothesis is the scenario we may change and test to evaluate its compliance with the real world.

For the first example of the A/B testing code ["tastes great" 200 clicks, "less bias" 180 clicks] the books says: "The probability of seeing such a large difference if the means were actually equal..."
Isn't "large" a misleading quantifier in this case, as the difference is not significant?

When using a line chart to show the normal approximation, you create the heights by taking the difference of two CDF calls. In the first CDF call, you add 0.5 and in the second CDF call you subtract 0.5. I suspect this is because you assume the integer value of x covers the range from x + 0.5 to x - 0.5 and you map this full probability to x. It would be ideal if you clarified the reason behind this. Thank you.

Personal opinion about optimizing part of the Data Science from Scratch 2nd edition book

Hello
Thank you very much and the author of Data Science from Scratch 2nd edition book for its very useful content.
I have an opinion on optimizing a part of the Randomness section in Chapter 2 ( A Crash Course in Python ):

For the Randomness section, you can use the Numpy library, because this library is used in Data Science, and in addition, it can make the subject of the image sent from the book (topic is choice 1 or more elements and with replacement or without replacement) easier and more understandable because its no need to use random.sample rather, we play with numpy.random.choice so I optimized the method. My code is:

#importing module
from numpy import random

#for choosing 1 element
my_best_friend = random.choice(["Alice", "Bob", "Charlie"])
#for choosing 3 element with replecement
my_best_friend = random.choice(["Alice", "Bob", "Charlie"], size=2)
#for choosing 3 element without replecement
my_best_friend = random.choice(["Alice", "Bob", "Charlie"], size=2, replace=False)

I’m working through the examples in the statistics chapter in “Data Science from Scratch, 2nd edition”,by Joel Grus, and I am getting the following error:

ModuleNotFoundError: No module named 'scratch'

Where do I get the module “scratch”? I’ve tried updating Anaconda and that didn’t help.

In the comments below is it the o-th neuron or the o-th layer of neurons?


# self.w[o] is the weights for the o-th neuron
self.w = random_tensor(output_dim, input_dim, init=init)

# self.b[o] is the bias term for the o-th neuron
self.b = random_tensor(output_dim, init=init)

The text says: "Whitespace is ignored inside parentheses and brackets...", which is true, but it is meant that line breaks are ignored inside parentheses.

Instead of using the specific sum_of_squares_gradient we could have used the generic estimate_gradient method as

grad = estimate_gradient(sum_of_squares, v, 0.0001 )

The beginning of this paragraph talks about testing the null hypothesis "beta_i = 0". However, the subsequent formula and example code all uses "beta_j" / "beta_hat_j". Is this difference in subscript letter deliberate? Do beta_i and beta_j actually mean slightly different things, or is this just a typo? Thanks very much!

On looking more closely at the github code, there is another similarly named variable.
There is no problem with the text.

xor_net = Sequential([
Linear(input_dim=2, output_dim=2),
Sigmoid(),
Linear(input_dim=2, output_dim=1),
Sigmoid()
])

In the github code, the assignment to "net" is the same except the last call to Sigmoid() is omitted. Which is the correct representation of a neural network for xor?

Paragraph states that East coast data scientists skew more towards PhD types, but it makes nos sense with the exp[lanation and the table above shows the oposite.

The news.cnet.com site is not available.
Is there an alternative site?

This could be due to the SpamAssassin files on the site changing.
When I run the program (as copied from github), I get different numbers
for the "confusion_matrix" counter:

text: "This gives 84 true positives ..., 25 false positives ..., 703 true negatives ...
and 44 false negatives"
My run results in 86 true positives, 40 false positives, 670 true negatives, and 29 false negatives

"...if you want to know the probability that (say) a fair coin
turns up more than 60 heads in 100 flips, you can estimate
it as that the probability that a Normal(50, 5) ..."

How it is known that the coin flipping follows (at least approximately)
the normal distribution?

"The mean of a Bernoulli variable is p, and its standard deviation
sqrt(p(1 - p)). The central limit theorem says that as n gets large,
a Binomial(n,p) variable is approximately a normal random variable
with mean mu = np and standard deviation sigma = sqrt(np(1 - p))."

However at bottom of pg 92, with n presumbably 1000, the # of flips:

"... the central limit theorem tells us that the average of those
Bernoulli variables should be approximately normal, with mean p
and standard deviation math.sqrt(p * (1 - p) / 1000)"

pg 92, 93 assignments:
"sigma = math.sqrt(p_hat * (1 - p_hat) / 1000)"

------------------------------------------------------------
I can't reconcile the text's initial description of using the
central limit theorem to determine the mean & standard deviation
with the later wording and assignment statements