quester
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Interpretations of negative confidence interval
4 votes

what you did - you created confidence intervals under assumption that chicken weights are drawn from normal disrtibution (with value range $(-\infty, \infty)$) - in fact these can be drawn from other ...

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Why is $\sum{(x_i-\overline{x})^2}$ = $\sum{(x_i-\overline{x})x_i}$ true?
Accepted answer
3 votes

$$\sum{(x_i-\overline{x})^2} = \sum{(x_i-\overline{x})x_i} - \sum{(x_i-\overline{x})\overline{x}} = \sum{(x_i-\overline{x})x_i} - \overline{x}\sum{x_i} + n\overline{x}^2 = \sum{(x_i-\overline{x})x_i} -...

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How is $P(|X| > t) \le E(\phi(X))/ \phi(t)$?
3 votes

$[X>0 => P(X>t) = P(\phi(X) > \phi(t))] \\ \land [X<0 => P(X<t) = P(-X>-t) = P(\phi(-X) > \phi(-t)) = P(\phi(-X) > \phi(t)) = P(\phi(X) > \phi(t))] \\ => P(|X| > ...

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How does one sample all images uniformly when the data set is organized in hierarchies?
2 votes

just create list of all files, then sample this list and voila!, as for calculations: probability sampling image from class $A$ sampling from whole set is $P(class\_A)=size(A)/size(whole\_set)$ but in ...

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How $E(X/X+Y)=E(Y/X+Y)$ when $X,Y$ are i.i.d's
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2 votes

since $X, Y$ are iid then for joint distribution we have: $$\forall_{(x,y) \in \Omega} f_{XY}(x, y) = f_{XY}(y,x)$$ then: $$E[\frac{Y}{X+Y}] = \iint_{\Omega} \frac{y}{x+y}f_{XY}(x,y)dxdy=\iint_{\...

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Are Python classes in Spark notebooks beneficial or common in the data scientist community?
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2 votes

In general you are writing pipelines and you relay on fact that "you run n+1 cell only if previous n completed with success" and you don't have to rely on super structurized code. On the other hand ...

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Confusion with softmax
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2 votes

why we are using softmax in first place - when we have on output [.5, -1] we would want to have positive values that sums to 1 so softmax was invented but you can develop your own function for this ...

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Gaps in histogram for geometric distribution
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2 votes

in python hist sometimes bins tend to "cluster" and then for one value you will have observations from many values example: import numpy as np import matplotlib.pyplot as plt q = np.random.choice([...

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Probability of drawing two differently colored balls in a partition of equally sized partitions
1 votes

let's presume that you have 10000 boxes, and you place blue balls in these boxes at random, and then you are placing red balls at random, let's count probability of success: $$p_b(i) = p(\text{10 blue ...

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Is there a test that uses $|{\mu_A}-{\mu_B}|\le \delta $ as the null hypothesis?
1 votes

one of ideas is to add $\delta$ to one population (raising mean) and in second test substracting $\delta$ and then computing statistic and figure out in two "one-sided tests" p-values, after ...

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Interesting question on confidence intervals
1 votes

https://besjournals.onlinelibrary.wiley.com/doi/10.1111/1365-2656.12382 please read this article, here you will see differences in different calculation methods for confidence interval, of course ...

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How can I tell whether this is a negative binomial distribution or binomial distribution?
1 votes

you can do it like this: $$P(Y \ge 8| succ == 3) = P(Y == 7| succ == 0) + P(Y == 7| succ == 1) + P(Y == 7| succ == 2) = \binom{7}{0}(\frac{5}{6})^7 + \binom{7}{1}\frac{1}{6}(\frac{5}{6})^6 + \binom{7}...

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Show that the distribution of $\frac{1}{\sqrt{n}}\sum_{i=1}^n(X_i^2-3)$ is normal
1 votes

according to Lindeberg-Levy CLT https://en.wikipedia.org/wiki/Central_limit_theorem let $ S_n = \frac{\sum_{k=1}^n X_k}{n}$ Suppose {X1, X2, …} is a sequence of i.i.d. random variables with E[Xi] ...

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Is a loss function computed after each step of gradient descent or after a whole epoch?
1 votes

it can be done either way but more important is gradient and it also can be done either way, but one thing to clarify you should: start epoch, compute loss, then gradient(sgd step), then next epoch ...

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Poisson Process Conditional Probability computation
0 votes

$$P(N(t_2)>N_2|N(t_1)<N_1)=P(N(t_1)<N_1 \land N(t_2)>N_2)/P(N(t_1)<N_1)=\sum_{k=0}^{N_1-1} [P(N(t_1)=k)P(N(t_2) >N_2)]/P(N(t_1)<N_1)= \frac{\sum_{k=0}^{N_1-1} [P(N(t_1)=k)(1-P(N(...

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Gamma Distribution satisfying property
0 votes

from markov inequality: $$P(X \ge a) \le E(X^q)/a^q$$ $$P(X \ge a) = 1 - P(X \lt a) \le E(X^q)/a^q => P(X < a) \ge 1 - E(X^q)/a^q$$ from https://en.wikipedia.org/wiki/...

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Does a neural network require non-linear activations?
0 votes

In general polynomial regression yields better results than neural networks, but they suffer from combinatorial explosion, so in order to tackle this we use neural networks with non-linear activations ...

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which is the meaning of scatterplot between a pair of 2 consecutive pseudo random numbers with respect to the independence of the sequence?
0 votes

correlation will get you nowhere since correlation 0 can be yield for 2 variables that will form V-shape in scatter plot, so it's bad idea to say $corr==0 <=> 2$ variables are independent all ...

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How to compare two joint probability distributions? How to measure the distance between them?
0 votes

best indicator of change would be avg vertical distance between these two lines after all you want to know what is the improvement for given traffic value, so avg vertical distance would be avg ...

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Reconstructing face from randomised embedding
0 votes

if you will permute input you would have to also permute coeficients in first layer of network and if these permutations "will agree" then yes, otherwise you will just generate face on random input ...

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Similar loss, different results
0 votes

since machine learning consists of stochastic methods unless you will set specific random seed on beginning, your model will be initialized with different values and this will lead to different values ...

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Gibb's sampling where target prob distribution is itself a conditional joint distribution - p(x,y|t)
0 votes

I assume you sample vertors (p1, p2, q, x), gibbs sampling says "keep n-1 coordinates from last result and sample next coordinate" here I would add "keep x=1"

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Density estimation for big feature space
0 votes

one of the idea is to have a lot of clusters let's say 10000, run KNN on all training observations and this will provide "tree search" in your samples then when you will have new observation take ...

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step size in the first epochs of adam are too large
0 votes

you can experiment with https://keras.io/callbacks/#learningratescheduler to find propper setting, general idea is that at beginning you are probably in area that cause your NN to perform badly and ...

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Is there an S-shaped (like sigmoid function) probability distribution?
0 votes

technically if we would treat sigmoid $S(x)$ as CDF then $\frac{d\,S(x)}{dx} = \frac{e^{-x}}{(1+e^{-x})^2}$ is PMF of Logistic distribution en.wikipedia.org/wiki/Logistic_distribution // name was ...

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How to find nearest neighbors using cosine similarity for all items from a large embeddings matrix?
0 votes

one weak point is sorting, and second is creating new collection so you could just make another collection (list) and then keep topK items until some point this way instead of sorting everytnig and ...

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Probability of a random variable being between two random variables
Accepted answer
0 votes

$\mathbb P (X \in [Y, Z)) = \int_{-\infty}^{\infty} \mathbb P (x \in [Y, Z)) f_X(x) dx = \int_{-\infty}^{\infty} (\underset{(x, \infty) \times (-\infty, x)}{\iint} f_{YZ}(y, z) dydz) f_X(x) dx$ ...

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Is a kernel density estimate meaningful if > 25% of my data are duplicates?
0 votes

if these duplicates are drawn from same random variable then yes (experiment can yield same observation sometimes and it is normal) - although it would be better to give answer in terms of probability ...

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Does $\hat \theta_n=\theta+O_p\bigg(\dfrac{1}{\sqrt{n}}\bigg)$ imply that $p_{\hat \theta_n X}(x)=p_{\theta X}(x)+O_p\bigg(\dfrac{1}{\sqrt{n}}\bigg)$?
-1 votes

I would say that $p_{\hat{\theta}_nX}(x)=p_{\theta X}(x(1+o_p(\frac{1}{n})/\theta))$ because you are affecting characteristics of distribution by shifting mean(and scaling variance), $$p_{\hat{\theta}...

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Group By and Scale Data vs Scaling Data Without Grouping
-1 votes

better solution is to scale the data 'normally' and add column that will contain values scaled with group by, for neural any algorithm it will be next feature and you will not lose any information... ...

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