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1500 questions
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5 answers

Time series 'clustering' in R

I have a set of time series data. Each series covers the same period, although the actual dates in each time series may not all 'line up' exactly. That is to say, if the Time series were to be read into a 2D matrix, it would look something like…
morpheous
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44
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4 answers

Variance of $K$-fold cross-validation estimates as $f(K)$: what is the role of "stability"?

TL,DR: It appears that, contrary to oft-repeated advice, leave-one-out cross validation (LOO-CV) -- that is, $K$-fold CV with $K$ (the number of folds) equal to $N$ (the number of training observations) -- yields estimates of the generalization…
Jake Westfall
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44
votes
4 answers

Good accuracy despite high loss value

During the training of a simple neural network binary classifier I get an high loss value, using cross-entropy. Despite this, accuracy's value on validation set holds quite good. Does it have some meaning? There is not a strict correlation between…
user146655
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44
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3 answers

Were generative adversarial networks introduced by Jürgen Schmidhuber?

I read on https://en.wikipedia.org/wiki/Generative_adversarial_networks : [Generative adversarial networks] were introduced by Ian Goodfellow et al in 2014. but Jurgen Schmidhuber claims to have performed similar work earlier in that direction…
Franck Dernoncourt
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44
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4 answers

Intuition for Conditional Expectation of $\sigma$-algebra

Let $(\Omega,\mathscr{F},\mu)$ be a probability space, given a random variable $\xi:\Omega \to \mathbb{R}$ and a $\sigma$-algebra $\mathscr{G}\subseteq \mathscr{F}$ we can construct a new random variable $E[\xi|\mathscr{G}]$, which is the…
Nicolas Bourbaki
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44
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3 answers

Computing p-value using bootstrap with R

I use "boot" package to compute an approximated 2-sided bootstrapped p-value but the result is too far away from p-value of using t.test. I can't figure out what I did wrong in my R code. Can someone please give me a hint for this time =…
Tu.2
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44
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1 answer

Training loss goes down and up again. What is happening?

My training loss goes down and then up again. It is very weird. The cross-validation loss tracks the training loss. What is going on? I have two stacked LSTMS as follows (on Keras): model = Sequential() model.add(LSTM(512, return_sequences=True,…
patapouf_ai
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44
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3 answers

How to decide which glm family to use?

I have fish density data that I am trying to compare between several different collection techniques, the data has lots of zeros, and the histogram looks vaugley appropriate for a poisson distribution except that, as densities, it is not integer…
C. Denney
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4 answers

Do null and alternative hypotheses have to be exhaustive or not?

I saw a lot of times claims that they have to be exhaustive (the examples in such books were always set in such way, that they were indeed), on the other hand I also saw a lot of times books stating they should be exclusive (for example…
greenoldman
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44
votes
2 answers

What is elastic net regularization, and how does it solve the drawbacks of Ridge ($L^2$) and Lasso ($L^1$)?

Is elastic net regularization always preferred to Lasso & Ridge since it seems to solve the drawbacks of these methods? What is the intuition and what is the math behind elastic net?
GeorgeOfTheRF
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44
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3 answers

Relation between confidence interval and testing statistical hypothesis for t-test

It is well known that confidence intervals and testing statistical hypothesis are strongly related. My questions is focused on comparison of means for two groups based on a numerical variable. Let's assume that such hypothesis is tested using…
Lan
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44
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1 answer

When is nested cross-validation really needed and can make a practical difference?

When using cross-validation to do model selection (such as e.g. hyperparameter tuning) and to assess the performance of the best model, one should use nested cross-validation. The outer loop is to assess the performance of the model, and the inner…
amoeba
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44
votes
5 answers

Why is the CDF of a sample uniformly distributed

I read here that given a sample $ X_1,X_2,...,X_n $ from a continuous distribution with cdf $ F_X $, the sample corresponding to $ U_i = F_X(X_i) $ follows a standard uniform distribution. I have verified this using qualitative simulations in…
Maxime Tremblay
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44
votes
3 answers

10-fold Cross-validation vs leave-one-out cross-validation

I'm doing nested cross-validation. I have read that leave-one-out cross-validation can be biased (don't remember why). Is it better to use 10-fold cross-validation or leave-one-out cross-validation apart from the longer runtime for leave-one-out…
machinery
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44
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1 answer

What is the intuitive reason behind doing rotations in Factor Analysis/PCA & how to select appropriate rotation?

My Questions What is the intuitive reason behind doing rotations of factors in factor analysis (or components in PCA)? My understanding is, if variables are almost equally loaded in the top components (or factors) then obviously it is difficult to…
GeorgeOfTheRF
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