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1500 questions
36
votes
11 answers
Why is generating 8 random bits uniform on (0, 255)?
I am generating 8 random bits (either a 0 or a 1) and concatenating them together to form an 8-bit number. A simple Python simulation yields a uniform distribution on the discrete set [0, 255]. I am trying to justify why this makes sense in my head.…
glassy
- 491
36
votes
7 answers
Convolutional Layers: To pad or not to pad?
AlexNet architecture uses zero-paddings as shown in the pic. However, there is no explanation in the paper why this padding is introduced. Standford CS 231n course teaches we use padding to preserve the spatial size: I am curious if that is the only…
Jumabek Alihanov
- 413
36
votes
3 answers
How to measure smoothness of a time series in R?
Is there a good way to measure smoothness of a time series in R? For example, -1, -0.8, -0.6, -0.4, -0.2, 0, 0.2, 0.4, 0.6, 0.8, 1.0 is much smoother than -1, 0.8, -0.6, 0.4, -0.2, 0, 0.2, -0.4, 0.6, -0.8, 1.0 although they have same mean and…
agmao
- 461
36
votes
6 answers
Does mean=mode imply a symmetric distribution?
I know this question has been asked with the case mean=median, but I did not find anything related to mean=mode. If the mode equals the mean, can I always conclude this is a symmetric distribution? Will I be forced to know also the median for this…
tzipy
- 559
36
votes
3 answers
How to build the final model and tune probability threshold after nested cross-validation?
Firstly, apologies for posting a question that has already been discussed at length here , here , here , here , here , and for reheating an old topic. I know @DikranMarsupial has written about this topic at length in posts and journal papers, but…
Dr. Andi Lowe
- 461
36
votes
2 answers
When should we discretize/bin continuous independent variables/features and when should not?
When should we discretize/bin independent variables/features and when should not? My attempts to answer the question: In general, we should not bin, because binning will lose information. Binning is actually increasing the degree of freedom of the…
HXD
- 38,018
36
votes
6 answers
Why do some people use -999 or -9999 to replace missing values?
I have a dataset. There are lots of missing values. For some columns, the missing value was replaced with -999, but other columns, the missing value was marked as 'NA'. Why would we use -999 to replace the missing value?
qqqwww
- 503
36
votes
1 answer
Cross-validation misuse (reporting performance for the best hyperparameter value)
Recently I have come across a paper that proposes using a k-NN classifier on an specific dataset. The authors used all the data samples available to perform k-fold cross validation for different k values and report cross validation results of the…
Daniel López
- 5,726
36
votes
5 answers
Wikipedia entry on likelihood seems ambiguous
I have a simple question regarding "conditional probability" and "Likelihood". (I have already surveyed this question here but to no avail.) It starts from the Wikipedia page on likelihood . They say this: The likelihood of a set of parameter…
Creatron
- 1,705
36
votes
7 answers
Why are symmetric positive definite (SPD) matrices so important?
I know the definition of symmetric positive definite (SPD) matrix, but want to understand more. Why are they so important, intuitively? Here is what I know. What else? For a given data, Co-variance matrix is SPD. Co-variance matrix is a important…
HXD
- 38,018
36
votes
3 answers
What's in a name: Precision (inverse of variance)
Intuitively, the mean is just the average of observations. The variance is how much these observations vary from the mean. I would like to know why the inverse of the variance is known as the precision. What intuition can we make from this? And why…
cgo
- 9,587
36
votes
4 answers
ANOVA vs multiple linear regression? Why is ANOVA so commonly used in experimental studies?
ANOVA vs multiple linear regression? I understand that both of these methods seem to use the same statistical model. However under what circumstances should I use which method? What are the advantages and disadvantages of these methods when…
florian
- 611
36
votes
3 answers
Building an autoencoder in Tensorflow to surpass PCA
Hinton and Salakhutdinov in Reducing the Dimensionality of Data with Neural Networks, Science 2006 proposed a non-linear PCA through the use of a deep autoencoder. I have tried to build and train a PCA autoencoder with Tensorflow several times but I…
Donbeo
- 3,237
36
votes
3 answers
Why is variable selection necessary?
Common data-based variable selection procedures (for example, forward, backward, stepwise, all subsets) tend to yield models with undesirable properties, including: Coefficients biased away from zero. Standard errors that are too small and…
user7322
36
votes
2 answers
Why is Lasso penalty equivalent to the double exponential (Laplace) prior?
I have read in a number of references that the Lasso estimate for the regression parameter vector $B$ is equivalent to the posterior mode of $B$ in which the prior distribution for each $B_i$ is a double exponential distribution (also known as…
Wintermute
- 1,347