- Видео 15
- Просмотров 15 898
Max Turgeon
Канада
Добавлен 14 окт 2007
Fisher's Exact Test
In this video, we briefly discuss Fisher's Exact Test. We also discuss how it connects to permutation tests, even if we don't perform any permutation of the data.
Просмотров: 66
Видео
Permutation Tests
Просмотров 792 года назад
In this video, we discuss permutation tests. Permutations are a family of resampling techniques that can be used to perform hypothesis testing under very general distributional assumptions.
Bootstrap & Linear Regression
Просмотров 3672 года назад
In this video, we discuss two different ways of using bootstrap and linear regression. It boils down to how much you trust the assumptions of the linear model: are they likely to hold for your particular model and dataset?
Residual Analysis
Просмотров 892 года назад
In this video, we discuss residual analysis and how it can be used to assess whether the assumptions of linear regression are met. I also discuss the relative importance of each assumption, following the great textbook "Regression and Other Stories" by Gelman, Hill and Vehtari. Spoiler Alert: They're not all equally important!
Review of Linear Regression
Просмотров 712 года назад
In this video, we review linear regression in preparation for our discussion of bootstrap and LR.
Bootstrap Confidence Intervals
Просмотров 5202 года назад
There are several ways of building confidence intervals using bootstrap too many to fit in a single video! Therefore, we focus on 5 main approaches: normal bootstrap, percentile, basic bootstrap, studentized, and BCa. I also give my recommendation at the end of the video.
Bootstrap
Просмотров 1442 года назад
Bootstrap can be seen as a generalization of jackknife. The main idea is: if we can't generate new datasets, then we will sample from our current dataset with replacement. Bootstrap is more general than jackknife, and for that reason that's what people typically use in practice.
Jackknife
Просмотров 8082 года назад
In this video, we discuss Jackknife, one of the earliest resampling methods. We can use Jackknife to estimate the bias and standard error of our estimators but only if they are "smooth plug-in" estimators! For that reason, Jackknife doesn't work for medians, sample quantiles, or trimmed means...
Bisection method
Просмотров 2 тыс.3 года назад
Animation of the bisection method. This was created using the manim python library: www.manim.community/ You can also find the source code in my Github repository: github.com/turgeonmaxime/num-methods-manim
Web APIs in R
Просмотров 723 года назад
Lecture on web APIs and how to interact with them using R. Part of SCI 2000-Introduction to Data Science at the University of Manitoba
Quick tour of RStudio and first steps in R
Просмотров 463 года назад
In this video, I give a quick tour of RStudio and its main panels. I also describe how to import data in R from a CSV file, how to access data from a package, and how to create simple vectors.
Reduced Rank Regression
Просмотров 2,8 тыс.3 года назад
This lecture discusses Reduced-Rank regression. It is connected to both CCA and Multivariate Linear Regression, and it also fits within our discussion of regularized regression models.
Canonical Correlation Analysis-Interpretation
Просмотров 2,7 тыс.3 года назад
We continue our discussion of CCA by looking at different ways to interpret CCA. We discuss how it generalizes many notions of correlation, and we also give a geometric interpretation.
Canonical Correlation Analysis-Inference
Просмотров 3583 года назад
In this lecture, we discuss large sample inference in the context of CCA. First, we describe the link between CCA and the test of independence that we discussed earlier in the course. Next, we discuss sequential inference.
Canonical Correlation Analysis-Introduction
Просмотров 6 тыс.3 года назад
This first video covers the basics of CCA: the population model and the sample model. We also discuss how CCA and Linear Discriminant Analysis (LDA) are related.
clean
clear visual explanation
If we standardize the data upfront on all sets, do we still need the correlation? I guess we will have correlations through the entire calculations.
If we standardize the data upfront, then the covariance and correlation matrices will be equal, and therefore both approaches become equivalent.
Thanks@@maxturgeon89
Hey thank you very much for the great video. I need to implement this via Python, but unfortunately I couldn't find any know package (like Scikitlearn) to have a function of RRR. Do you have any suggestions for me. I can do it also using R but I prefer Python.
Technical question (sorry for the spam). if (will ignore the tildes, all a,bs have them) a = M b but b = v1 (first V SVF from M = U Sig V^T), then how is a not equal to sqrt(lambda1) u1? My reasoning is simple a = M b = U Sig V v1 = sum_r sig_i u_i v^T_i v1 but v^T_i v1 = 0 for i!= 0 and 1 for i=1 so we get a is sig1 u1 where sig1=sqrt lambda_1? Btw, fantastic video! thanks in advance!
Actually, this relates to your other question above about the constant C. Remember that we want a tilde to have norm 1. So what we have is that a tilde = c sig1 u1. If we add the norm 1 constraint, we'll see that c sig1 must equal 1. In other words, we have a tilde = u1, as expected.
What is the value of C? for \tilde a = C M \tilde b when they have to be colinear. To me it results that C=1 and \tilde b = EigenValue(M^TM) should be sufficient to get maximization to work. Is that right or what value of C did you get?
what is the shape of the square root of the variance matrices?
The variance matrices are positive-definite (symmetric) matrices. Therefore, all their eigenvalues are real and positive. You can get the square root by taking the eigendecomposition Sigma = UDV^T, take the square root of the elements of D, and remultiply the matrices Sigma^{1/2} = UD^{1/2}V^T
wish you would have uploaded the rest of your videos for that class! Especially PCA, curious on your take on it.
Thanks for the comment! I never recorded the PCA lecture, so there's nothing to upload at the moment unfortunately... Maybe a future project!
Fantastic lecture! thanks, this is really appreciated! :)
Thank you for this CCA video. While it is informative, right now, I need a video that literally walks me from the original data set of p and q columns of data to the final period of the interpretation. I need a real life example without all the theoretical notation. I am proficient at EXCEL matrix operations and I am proficient with SPSS. I don't know R well enough to use it. I hope you understand. Is there a way you can communicate with me? Thank you. Kenneth
Thanks for the comment. These lectures were recorded for a course on Multivariate Analysis for graduate students in statistics, so it was definitely more on the theoretical side. But I like your suggestion of a video walking through a data analysis, I'll add it to my list of potential future videos. I don't know Excel or SPSS well enough to tell you how to perform CCA using these software. For R, the main function is "cancor", and it is available with base R (i.e. no need to install any package). There is also the package "vegan", which is a great package for multivariate analysis. It was developed by applied researchers (in this case, ecologists), so it is very much designed to be user-friendly. However, the terminology is sometimes slightly different than what statisticians use.
Hey, great video! This made it very easy to implement RRR in R using the underlying matrix operations. Could you provide the citations where you got the derivation/equations for RRR from?
The main reference I used is "Multivariate Reduced-Rank Regression: Theory and Applications", by Reinsel and Velu.
You've done an amazing job in explaining CCA and connecting it to other methods! Thanks!!
Great explanation! Will make other recordings from this course be available?
There is no plan at the moment, unfortunately! Perhaps in the future I could record my PCA lectures, they would be a good companion to the CCA ones.
This was a great explanation. Many thanks. Please upload your other videos on PCA as well.
Great explanation, many thanks!