All Questions
210,244
questions
1321
votes
27
answers
908k
views
Making sense of principal component analysis, eigenvectors & eigenvalues
In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues.
I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like ...
- 13.5k
800
votes
11
answers
1.1m
views
How to choose the number of hidden layers and nodes in a feedforward neural network?
Is there a standard and accepted method for selecting the number of layers, and the number of nodes in each layer, in a feed-forward neural network? I'm interested in automated ways of building neural ...
- 55.3k
653
votes
12
answers
479k
views
What is the difference between "likelihood" and "probability"?
The wikipedia page claims that likelihood and probability are distinct concepts.
In non-technical parlance, "likelihood" is usually a synonym for "probability," but in statistical usage there is a ...
- 7,391
578
votes
4
answers
463k
views
Relationship between SVD and PCA. How to use SVD to perform PCA?
Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix ...
- 101k
560
votes
11
answers
650k
views
What is the difference between test set and validation set?
I found this confusing when I use the neural network toolbox in Matlab.
It divided the raw data set into three parts:
training set
validation set
test set
I notice in many training or learning ...
- 7,149
557
votes
15
answers
238k
views
What is the intuition behind beta distribution?
Disclaimer: I'm not a statistician but a software engineer. Most of my knowledge in statistics comes from self-education, thus I still have many gaps in understanding concepts that may seem trivial ...
- 9,820
552
votes
23
answers
313k
views
Why square the difference instead of taking the absolute value in standard deviation?
In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute ...
- 5,775
491
votes
20
answers
174k
views
The Two Cultures: statistics vs. machine learning?
Last year, I read a blog post from Brendan O'Connor entitled "Statistics vs. Machine Learning, fight!" that discussed some of the differences between the two fields. Andrew Gelman responded favorably ...
441
votes
5
answers
172k
views
How to understand the drawbacks of K-means
K-means is a widely used method in cluster analysis. In my understanding, this method does NOT require ANY assumptions, i.e., give me a dataset and a pre-specified number of clusters, k, and I just ...
- 6,799
432
votes
14
answers
279k
views
Bayesian and frequentist reasoning in plain English
How would you describe in plain English the characteristics that distinguish Bayesian from Frequentist reasoning?
- 4,429
416
votes
9
answers
849k
views
What is the difference between fixed effect, random effect and mixed effect models?
In simple terms, how would you explain (perhaps with simple examples) the difference between fixed effect, random effect and mixed effect models?
- 5,998
410
votes
11
answers
180k
views
Explaining to laypeople why bootstrapping works
I recently used bootstrapping to estimate confidence intervals for a project. Someone who doesn't know much about statistics recently asked me to explain why bootstrapping works, i.e., why is it that ...
- 5,089
403
votes
7
answers
402k
views
When conducting multiple regression, when should you center your predictor variables & when should you standardize them?
In some literature, I have read that a regression with multiple explanatory variables, if in different units, needed to be standardized. (Standardizing consists in subtracting the mean and dividing ...
- 4,441
401
votes
19
answers
165k
views
What happens if the explanatory and response variables are sorted independently before regression?
Suppose we have data set $(X_i,Y_i)$ with $n$ points. We want to perform a linear regression, but first we sort the $X_i$ values and the $Y_i$ values independently of each other, forming data set $(...
- 3,691
398
votes
7
answers
1.6m
views
How to normalize data to 0-1 range?
I am lost in normalizing, could anyone guide me please.
I have a minimum and maximum values, say -23.89 and 7.54990767, respectively.
If I get a value of 5.6878 how can I scale this value on a scale ...
- 4,395
386
votes
12
answers
375k
views
Difference between logit and probit models
What is the difference between Logit and Probit model?
I'm more interested here in knowing when to use logistic regression, and when to use Probit.
If there is any literature which defines it using ...
- 6,264
381
votes
5
answers
433k
views
What is the trade-off between batch size and number of iterations to train a neural network?
When training a neural network, what difference does it make to set:
batch size to $a$ and number of iterations to $b$
vs. batch size to $c$ and number of iterations to $d$
where $ ab = cd $?
To ...
- 45.5k
378
votes
80
answers
181k
views
What is your favorite "data analysis" cartoon?
Data analysis cartoons can be useful for many reasons: they help communicate; they show that quantitative people have a sense of humor too; they can instigate good teaching moments; and they can help ...
378
votes
26
answers
136k
views
Python as a statistics workbench
Lots of people use a main tool like Excel or another spreadsheet, SPSS, Stata, or R for their statistics needs. They might turn to some specific package for very special needs, but a lot of things can ...
372
votes
15
answers
143k
views
Is normality testing 'essentially useless'?
A former colleague once argued to me as follows:
We usually apply normality tests to the results of processes that,
under the null, generate random variables that are only
asymptotically or ...
- 14.3k
351
votes
9
answers
334k
views
What should I do when my neural network doesn't learn?
I'm training a neural network but the training loss doesn't decrease. How can I fix this?
I'm not asking about overfitting or regularization. I'm asking about how to solve the problem where my ...
- 87.6k
348
votes
8
answers
150k
views
Why is Euclidean distance not a good metric in high dimensions?
I read that 'Euclidean distance is not a good distance in high dimensions'. I guess this statement has something to do with the curse of dimensionality, but what exactly? Besides, what is 'high ...
- 3,697
335
votes
13
answers
194k
views
How to understand degrees of freedom?
From Wikipedia, there are three interpretations of the degrees of freedom of a statistic:
In statistics, the number of degrees of freedom is the number of
values in the final calculation of a ...
- 18.9k
318
votes
10
answers
188k
views
What's the difference between a confidence interval and a credible interval?
Joris and Srikant's exchange here got me wondering (again) if my internal explanations for the difference between confidence intervals and credible intervals were the correct ones. How you would ...
- 5,887
299
votes
6
answers
676k
views
What is batch size in neural network?
I'm using Python Keras package for neural network. This is the link. Is batch_size equals to number of test samples? From ...
- 3,941
299
votes
8
answers
212k
views
Bagging, boosting and stacking in machine learning
What's the similarities and differences between these 3 methods:
Bagging,
Boosting,
Stacking?
Which is the best one? And why?
Can you give me an example for each?
- 3,099
298
votes
15
answers
107k
views
Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
It seems that through various related questions here, there is consensus that the "95%" part of what we call a "95% confidence interval" refers to the fact that if we were to exactly replicate our ...
- 13.2k
291
votes
15
answers
548k
views
What is the meaning of p values and t values in statistical tests?
After taking a statistics course and then trying to help fellow students, I noticed one subject that inspires much head-desk banging is interpreting the results of statistical hypothesis tests. It ...
- 4,296
289
votes
7
answers
454k
views
What does AUC stand for and what is it?
Searched high and low and have not been able to find out what AUC, as in related to prediction, stands for or means.
- 3,249
284
votes
13
answers
242k
views
Is there any reason to prefer the AIC or BIC over the other?
The AIC and BIC are both methods of assessing model fit penalized for the number of estimated parameters. As I understand it, BIC penalizes models more for free parameters than does AIC. Beyond a ...
- 17.9k
284
votes
8
answers
207k
views
How to choose a predictive model after k-fold cross-validation?
I am wondering how to choose a predictive model after doing K-fold cross-validation.
This may be awkwardly phrased, so let me explain in more detail: whenever I run K-fold cross-validation, I use K ...
- 4,745
282
votes
6
answers
46k
views
Is $R^2$ useful or dangerous?
I was skimming through some lecture notes by Cosma Shalizi (in particular, section 2.1.1 of the second lecture), and was reminded that you can get very low $R^2$ even when you have a completely linear ...
- 9,560
281
votes
153
answers
147k
views
Famous statistical quotations
What is your favorite statistical quote?
This is community wiki, so please one quote per answer.
281
votes
11
answers
162k
views
How would you explain covariance to someone who understands only the mean?
...assuming that I'm able to augment their knowledge about variance in an intuitive fashion ( Understanding "variance" intuitively ) or by saying: It's the average distance of the data ...
- 14.4k
279
votes
2
answers
230k
views
Interpretation of R's lm() output
The help pages in R assume I know what those numbers mean, but I don't.
I'm trying to really intuitively understand every number here. I will just post the output and comment on what I found out. ...
- 4,271
277
votes
3
answers
30k
views
How to know that your machine learning problem is hopeless?
Imagine a standard machine-learning scenario:
You are confronted with a large multivariate dataset and you have a
pretty blurry understanding of it. What you need to do is to make
predictions ...
Tim♦
- 134k
276
votes
12
answers
185k
views
How would you explain Markov Chain Monte Carlo (MCMC) to a layperson?
Maybe the concept, why it's used, and an example.
- 9,742
262
votes
11
answers
183k
views
What exactly are keys, queries, and values in attention mechanisms?
How should one understand the keys, queries, and values that are often mentioned in attention mechanisms?
I've tried searching online, but all the resources I find only speak of them as if the reader ...
- 3,346
261
votes
15
answers
291k
views
What are the differences between Factor Analysis and Principal Component Analysis?
It seems that a number of the statistical packages that I use wrap these two concepts together. However, I'm wondering if there are different assumptions or data 'formalities' that must be true to use ...
- 6,942
254
votes
46
answers
27k
views
What are common statistical sins?
I'm a grad student in psychology, and as I pursue more and more independent studies in statistics, I am increasingly amazed by the inadequacy of my formal training. Both personal and second hand ...
253
votes
5
answers
121k
views
ROC vs precision-and-recall curves
I understand the formal differences between them, what I want to know is when it is more relevant to use one vs. the other.
Do they always provide complementary insight about the performance of a ...
- 18.9k
248
votes
9
answers
122k
views
Why is Newton's method not widely used in machine learning?
This is something that has been bugging me for a while, and I couldn't find any satisfactory answers online, so here goes:
After reviewing a set of lectures on convex optimization, Newton's method ...
- 2,471
246
votes
38
answers
151k
views
What is the best introductory Bayesian statistics textbook?
Which is the best introductory textbook for Bayesian statistics?
One book per answer, please.
245
votes
8
answers
122k
views
Algorithms for automatic model selection
I would like to implement an algorithm for automatic model selection.
I am thinking of doing stepwise regression but anything will do (it has to be based on linear regressions though).
My problem ...
- 2,618
240
votes
4
answers
358k
views
When (and why) should you take the log of a distribution (of numbers)?
Say I have some historical data e.g., past stock prices, airline ticket price fluctuations, past financial data of the company...
Now someone (or some formula) comes along and says "let's take/use ...
- 14.4k
239
votes
4
answers
469k
views
How to interpret a QQ plot?
I am working with a small dataset (21 observations) and have the following normal QQ plot in R:
Seeing that the plot does not support normality, what could I infer about the underlying distribution? ...
- 19.6k
237
votes
14
answers
202k
views
How should I transform non-negative data including zeros?
If I have highly skewed positive data I often take logs. But what should I do with highly skewed non-negative data that include zeros? I have seen two transformations used:
$\log(x+1)$ which has the ...
- 55.3k
233
votes
18
answers
259k
views
Intuitive explanation for dividing by $n-1$ when calculating standard deviation?
I was asked today in class why you divide the sum of square error by $n-1$ instead of with $n$, when calculating the standard deviation.
I said I am not going to answer it in class (since I didn't ...
- 21k
228
votes
10
answers
125k
views
Why is accuracy not the best measure for assessing classification models?
This is a general question that was asked indirectly multiple times in here, but it lacks a single authoritative answer. It would be great to have a detailed answer to this for the reference.
...
Tim♦
- 134k
227
votes
8
answers
273k
views
What are the advantages of ReLU over sigmoid function in deep neural networks?
The state of the art of non-linearity is to use rectified linear units (ReLU) instead of sigmoid function in deep neural network. What are the advantages?
I know that training a network when ReLU is ...
- 12.5k