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1262 votes
27 answers

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 ...
  • 12.9k
766 votes
11 answers

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 ...
  • 53.2k
625 votes
12 answers

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 ...
545 votes
11 answers

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 ...
  • 6,969
540 votes
3 answers

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 ...
  • 96.3k
539 votes
15 answers

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 ...
  • 9,550
531 votes
23 answers

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 ...
  • 5,555
482 votes
20 answers

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 ...
432 votes
5 answers

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 ...
  • 6,537
419 votes
14 answers

Bayesian and frequentist reasoning in plain English

How would you describe in plain English the characteristics that distinguish Bayesian from Frequentist reasoning?
399 votes
11 answers

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 ...
  • 4,969
394 votes
9 answers

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?
  • 5,738
392 votes
18 answers

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 $(...
386 votes
7 answers

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 ...
  • 4,271
378 votes
26 answers

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 ...
375 votes
7 answers

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 ...
  • 4,131
373 votes
80 answers

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 ...
372 votes
12 answers

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 ...
  • 6,044
365 votes
16 answers

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 ...
351 votes
5 answers

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 ...
342 votes
8 answers

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 ...
  • 3,637
325 votes
13 answers

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 ...
  • 18.2k
323 votes
9 answers

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 ...
  • 81.2k
303 votes
10 answers

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 ...
  • 5,707
294 votes
8 answers

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?
  • 3,049
290 votes
16 answers

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 ...
286 votes
6 answers

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 ...
  • 3,791
284 votes
15 answers

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 ...
  • 4,206
281 votes
6 answers

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.
  • 3,189
278 votes
153 answers

Famous statistical quotations

What is your favorite statistical quote? This is community wiki, so please one quote per answer.
277 votes
6 answers

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 ...
  • 9,380
276 votes
2 answers

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. ...
275 votes
13 answers

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 ...
272 votes
10 answers

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 ...
  • 13.8k
267 votes
11 answers

How would you explain Markov Chain Monte Carlo (MCMC) to a layperson?

Maybe the concept, why it's used, and an example.
266 votes
3 answers

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 ...
  • 120k
257 votes
8 answers

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 ...
  • 4,435
255 votes
15 answers

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 ...
250 votes
46 answers

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 ...
245 votes
4 answers

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 ...
235 votes
9 answers

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 ...
  • 2,341
234 votes
38 answers

What is the best introductory Bayesian statistics textbook?

Which is the best introductory textbook for Bayesian statistics? One book per answer, please.
233 votes
8 answers

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 ...
  • 2,480
228 votes
4 answers

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 ...
  • 13.8k
227 votes
4 answers

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? ...
  • 18.8k
223 votes
13 answers

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 ...
  • 53.2k
222 votes
13 answers

What is the difference between data mining, statistics, machine learning and AI?

What is the difference between data mining, statistics, machine learning and AI? Would it be accurate to say that they are 4 fields attempting to solve very similar problems but with different ...
219 votes
5 answers

Which "mean" to use and when?

So we have arithmetic mean (AM), geometric mean (GM) and harmonic mean (HM). Their mathematical formulation is also well known along with their associated stereotypical examples (e.g., Harmonic mean ...
  • 13.8k
218 votes
17 answers

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 ...
  • 20.4k
211 votes
8 answers

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 ...
  • 11.9k

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