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Question: <p>Can you please name some major and minor journals publishing articles in the field of statistical learning / machine learning. </p>
Answer: <p>Some influential journals in machine learning:</p>
<ul>
<li><a href="http://www.computer.org/portal/web/tpami" rel="nofollow">IEEE TPAMI</a></li>
<li><a href="htt... | https://stats.stackexchange.com/questions/88330/journals-in-statistical-learning-machine-learning |
Question: <p>I have seen posts about the difference between ML and Statistics. And I have also seen posts explaining that Statistical Learning is a statistical approach to ML. But then, this is confusing because what is the difference between Statistics and Statistical Learning anyways?</p>
<p>To finally resolve this ... | https://stats.stackexchange.com/questions/442128/machine-learning-vs-statistical-learning-vs-statistics |
Question: <p>I'm majoring industrial engineering on a master's course. Recently, I've realized that I need to study statistical perspective on M.L.</p>
<p>So I'm studying the book Introduction to statistical learning with myself. But it seems to lack of mathematical background. On the other hand, Element of statistica... | https://stats.stackexchange.com/questions/392814/easier-than-element-of-statistical-learning-and-harder-than-introduction-to-stat |
Question: <p>I'm currently reading the book 'An Introduction to Statistical Learning with application in R(ISLR)', it is very helpful for learning the applications of statistical model, but less complement of theoreotical content or mathematical proof/derivation of formulas. I'm often confused with some conclusion/form... | https://stats.stackexchange.com/questions/468321/statistical-learning-book-with-theoretical-content |
Question: <p><a href="https://hastie.su.domains/ISLR2/ISLRv2_website.pdf" rel="nofollow noreferrer">An Introduction to Statistical Learning
with Applications in R</a> 2nd edition by Hastie et al. says that</p>
<blockquote>
<p><em>Statistical learning</em> refers to a set of tools for making sense of complex datasets.</... | https://stats.stackexchange.com/questions/617771/what-is-the-difference-between-statistical-learning-and-machine-learning |
Question: <p>What relations and differences are between <a href="http://en.wikipedia.org/wiki/Statistical_learning_theory" rel="nofollow noreferrer">statistical learning theory</a> and <a href="http://en.wikipedia.org/wiki/Computational_learning_theory" rel="nofollow noreferrer">computational learning theory</a>?</p>
... | https://stats.stackexchange.com/questions/63077/statistical-learning-theory-vs-computational-learning-theory |
Question: <p>Elements of Statistical Learning (ESL) is a book that has fantastic breadth and depth. It covers the essentials to the very modern methods by citing the papers where these original studies come about. However, I really find the language of the book very very prohibitive. I believe there is an easier way to... | https://stats.stackexchange.com/questions/154788/elements-of-statistical-learning-alternatives |
Question: <p>For those that have read the book <a href="http://faculty.marshall.usc.edu/gareth-james/ISL/ISLR%20Seventh%20Printing.pdf" rel="nofollow noreferrer">Introduction to Statistical Learning</a>, I'm having a problem understanding a certain line: </p>
<p><a href="https://i.sstatic.net/2eTms.png" rel="nofollow ... | https://stats.stackexchange.com/questions/438143/introduction-to-statistical-learning |
Question: <p>Any recommendations for good literature on statistical learning theory? I mean, something what goes into more details than Elements of Statistical Learning, in terms of losses, empirical error estimation etc.</p>
Answer: | https://stats.stackexchange.com/questions/441192/a-good-literature-for-statistical-learning-theory |
Question: <p>My interests in statistics centre around statistical learning, including Bayesian inference, inference in combinatorial spaces, Monte Carlo methods, Markov decision processes, modeling stochastic processes and so on. It is mandatory at my university’s program that we take an experiment design course, which... | https://stats.stackexchange.com/questions/422186/motivations-for-experiment-design-in-statistical-learning |
Question: <p>I've recently been working through <em>Statistical Learning with Sparsity</em> (SLS) by Hastie, Tibshirani and Hastie.</p>
<p>I found some exercises very hard, and think I found some mistakes. A set of solutions would be very helpful.</p>
<p>I've recently discovered that <em>Elements of Statistical Learnin... | https://stats.stackexchange.com/questions/583137/solutions-to-statistical-learning-with-sparsity |
Question: <p>I'm studying some statistical learning theory. If i have <span class="math-container">$X$</span>, <span class="math-container">$Y$</span> as random variables representing the data-labels samples drawn from a certain distribution and a loss function, it is right to say that:
<span class="math-container">$$ ... | https://stats.stackexchange.com/questions/521720/statistical-learning-and-expected-value |
Question: <p><a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.115.9500&rep=rep1&type=pdf" rel="nofollow">This</a> paper attempts to contrast the basic elements of statistical learning theory and statistical decision theory, but I'm still confused about how the two are related.</p>
Answer: <p>H... | https://stats.stackexchange.com/questions/135923/how-are-statistical-decision-theory-and-statistical-learning-theory-related |
Question: <p>I used to hear some Statistics professor complaining about Machine Learning theories: "It is just Non-parametric Statistics". And, when I read Vapnik's book "Statistical Learning Theory", it seems he has been influenced a lot by non-parametric statistics. So, would anybody explain the similarity and differ... | https://stats.stackexchange.com/questions/258417/relation-between-nonparametric-statistics-and-statistical-learning-theory |
Question: <p>Quick question I guess, but is there a perceivable difference between the terms <em>Statistical Learning</em> and <em>Machine Learning</em>, or is it simply area jargon? I gather the computer scientists like to refer to machine learning while statisticians might refer to statistical learning (no less influ... | https://stats.stackexchange.com/questions/271027/is-there-a-difference-between-the-terms-statistical-learning-and-machine-learnin |
Question: <p>I know it's a rather debated question on Stack Exchange communities but let me explain the points of this question.</p>
<p>I'm writing my capstone on Machine Learning and I need to clarify deeply, giving valid references, the differences among Data Mining, Big Data, Statistical Learning and Machine Learni... | https://stats.stackexchange.com/questions/179021/valid-references-on-origins-of-machine-learning-statistical-learning-and-data-m |
Question: <p>I am reading Vapnik's "Statistical Learning Theory" and I am confused about his use of Q(z,alpha). On page 23 he explains that Q is the loss function which takes as argument a function g, the function used by the learning algorithm to generate predictions:</p>
<p>Q(z,alpha) = L(z,g(z,alpha))</p>
<p>Howev... | https://stats.stackexchange.com/questions/247373/statistical-learning-theory-loss-function |
Question: <p>I'm looking for books similar to Introduction to Statistical Learning with Applications in R (ISLR), which is not too rigorous in terms of the mathematical treatment, but still able to provide you the intuition about the methods? I'm particularly looking at this topics:</p>
<ul>
<li>Generalized Linear Mode... | https://stats.stackexchange.com/questions/476270/books-similar-to-introduction-to-statistical-learning |
Question: <p>I have a question, how to prove formula (2.12) in book 《Elements of Statistical Learning》</p>
<p><a href="https://i.sstatic.net/XfiOD.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/XfiOD.png" alt="enter image description here" /></a></p>
Answer: | https://stats.stackexchange.com/questions/618307/elements-of-statistical-learning-2-4-statistical-decision-theory-how-to-prove-f |
Question: <p>I've been working my way through the problems in the book "Introduction to Statistical Learning". I have a question about the notation in Question 5 from Chapter 3 (screenshot below). What does $x_{i'}$ mean exactly, in comparison to $x_{i}$.</p>
<p><img src="https://i.sstatic.net/KnJdH.png" alt="enter im... | https://stats.stackexchange.com/questions/135468/question-about-notation-in-introduction-to-statistical-learning |
Question: <p>I was asked the following 2 questions in an interview. I wasn't selected which means my answers were wrong. </p>
<p>Now I need to learn from my mistakes. I have though quite a bit since the interview and still not got anywhere concrete so need your help..</p>
<p>Question 1 : It is raining during evening ... | https://stats.stackexchange.com/questions/197044/data-modelling-statistical-learning-interview-questions |
Question: <p>I am trying to read the Elements of Statistical Learning Tibshirani, Hastie and Friedman, however I have a problem with understanding the expected (squared) prediction error (<span class="math-container">$EPE$</span>) formula that they provide on page <span class="math-container">$26$</span>:</p>
<p>The s... | https://stats.stackexchange.com/questions/372525/elements-of-statistical-learning-training-set |
Question: <p>Recently, I have been reading the 《Elements of Statistical Learning》book . Now,I have three question in chapter 2 formula(2.10).
(1)What does <span class="math-container">$pr(dx,dy)$</span> in Formula 2.10 mean?</p>
<p>(2)how to derivate this (2.10)formula?</p>
<p>(3)Can <span class="math-container">$pr(dx... | https://stats.stackexchange.com/questions/618301/elements-of-statistical-learning-statistical-decision-theory-formula-2-10-ep |
Question: <p>In statistical learning (many textbooks), we assume that the data $Y$ is generated by $Y=f(X)+\epsilon$, where $X$ are predictors and $\epsilon$ is some random noise. Then the problem becomes: using various methods to find an estimates of $f$, i.e., $\hat{f}$ such that the expected mean square error on the... | https://stats.stackexchange.com/questions/189583/a-fundamental-question-about-statistical-learning |
Question: <p>I'm a little puzzled by a formula presented in Hastie's "Introduction to Statistical Learning". In Chapter 6, page 212 (sixth printing, available <a href="http://www-bcf.usc.edu/~gareth/ISL/ISLR%20Sixth%20Printing.pdf">here</a>), it is stated that:</p>
<p>$AIC = \frac{RSS}{n\hat\sigma^2} + \frac{2d}{n} $<... | https://stats.stackexchange.com/questions/181539/aic-formula-in-introduction-to-statistical-learning |
Question: <p>Based on <a href="https://quant.stackexchange.com/questions/111/how-can-i-go-about-applying-machine-learning-algorithms-to-stock-markets">this post</a>, I want to digest Elements of Statistical Learning. Fortunately it is available for free and I started reading it.</p>
<p>I don't have enough knowledge to... | https://stats.stackexchange.com/questions/18973/book-for-reading-before-elements-of-statistical-learning |
Question: <p>I'm reading <em>Introduction to Statistical Learning</em>, currently Chapter 2 about the Bias-Variance trade-off. </p>
<p>In all examples the irreducible error is 1, i.e. $Var(\epsilon) = 1$. I read in <a href="https://stats.stackexchange.com/questions/228896/why-is-the-variance-of-the-error-term-a-k-a-th... | https://stats.stackexchange.com/questions/285750/statistical-learning-how-to-determine-the-irreducible-error |
Question: <p>Currently I am re-reading some chapters of: <em>An Introduction to Statistical Learning with Applications in R</em> by Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani (Springer, 2015). Now, I have some doubts about what is said there.</p>
<p>Above all it seems to me relevant to note that ... | https://stats.stackexchange.com/questions/493564/statistical-learning-contradictions |
Question: <p>This picture is from the book "the elements of statistical learning":</p>
<p><a href="https://i.sstatic.net/3gmgr.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/3gmgr.png" alt="enter image description here" /></a></p>
<p>I am wondering how the test-error rate is calculated based o... | https://stats.stackexchange.com/questions/645621/the-error-rate-in-the-elements-of-statistical-learning |
Question: <p>I'm currently studying Vapnik's theory of statistical learning. I rely on <a href="https://statisticalsupportandresearch.files.wordpress.com/2017/05/vladimir-vapnik-the-nature-of-statistical-learning-springer-2010.pdf" rel="nofollow noreferrer">Vapnik (1995)</a> and some secondary literature that is more a... | https://stats.stackexchange.com/questions/478351/what-is-alpha-in-vapniks-statistical-learning-theory |
Question: <p>I am a Pure Maths PhD student specialising in functional analysis.</p>
<p>I would like to work as a data scientist after my PhD graduation, particularly in the field of machine learning, deep learning and artificial intelligence. </p>
<p>I have some backgrounds on machine learning such as linear regressi... | https://stats.stackexchange.com/questions/468483/what-is-next-after-finished-reading-elements-of-statistical-learning |
Question: <p>I am reading An Introduction to Statistical Learning with Applications in R (ISLR) and I wonder what would be the answer for exercise 2.1 part (d). The question is, If the variance of the error terms <span class="math-container">$$\sigma^2 = \mathrm{Var}(\epsilon)$$</span> is extremely high, a more flexibl... | https://stats.stackexchange.com/questions/539362/intro-to-statistical-learning-solutions-for-2-1 |
Question: <p>If I understand correctly, statistical learning theory is just <em>one</em> approach to machine learning,</p>
<p>What machine learning isn't statistical?</p>
<p>Based on my very limited understanding, I thought that things like PAC-learning or Empirical Risk minimization pretty much cover everything. Isn't... | https://stats.stackexchange.com/questions/497986/what-machine-learning-isnt-statistical |
Question: <p>I can't figure out how formula 7.14 on page 224 of <em>The Elements of Statistical Learning</em> is derived. Can anyone help me figure it out? </p>
<p>$$\textrm{Average squared bias} = \textrm{Average}[\textrm{model bias}]^2 + \textrm{Average}[\textrm{estimation bias}]^2$$</p>
<p><a href="https://i.ssta... | https://stats.stackexchange.com/questions/201779/decomposition-of-average-squared-bias-in-elements-of-statistical-learning |
Question: <p>In Hasties book "statistical learning", just above equation 2.28, it says that <span class="math-container">$\mathbf{X}^T\mathbf{X} \rightarrow NCov(X)$</span> (when <span class="math-container">$N$</span> is large and <span class="math-container">$E(X)=0$</span>).</p>
<p>Why is this true?</p>
<p... | https://stats.stackexchange.com/questions/641539/hastie-statistical-learning-2-28-least-squares-and-covariance |
Question: <p>I am trying to reproduce a table 3.3 in Elements of statistical learning. Specifically, I am trying to get the coefficient estimates for ridge regression and lasso. I know that the estimate can be a bit off depending on the seeding value, but I personally think it is significantly off. The code is below, a... | https://stats.stackexchange.com/questions/161517/reproducing-table-3-3-from-elements-of-statistical-learning |
Question: <p>I am taking a class in statistics which uses The Elements of Statistical Learning: Data Mining, Inference, and Prediction as a textbook. However, I find this book very terse. </p>
<p>Could anyone please recommend a book which has similar topic coverage but contains more examples and detailed explanations ... | https://stats.stackexchange.com/questions/332842/alternative-to-the-elements-of-statistical-learning-data-mining-inference-and |
Question: <p>I am almost finished reading ESL; Elements of Statistical Learning.
I come from a strong mathematical and statistical background, and that was my first book about Machine Learning.</p>
<p><strong>What other books would be good to go over now?</strong></p>
<p>I am aware of books such as:</p>
<ul>
<li>Mac... | https://stats.stackexchange.com/questions/460411/books-to-read-on-ml-after-esl-elements-of-statistical-learning |
Question: <p>In statistical learning, we split the data into three parts for training, validation, and test, separately. With training data we can get a model <span class="math-container">$T$</span>, then we seem to optimize or change the model by validation data. How does that happen (since the model <span class="math... | https://stats.stackexchange.com/questions/500236/how-validation-set-in-statistical-learning-works |
Question: <p>My main source on statistical learning theory has been <a href="https://www.cs.huji.ac.il/%7Eshais/UnderstandingMachineLearning/" rel="nofollow noreferrer">Shwartz/Ben-David</a>. This is a good book but it's a little vague from a measure-theoretic point of view. For example, in the definition of PAC learna... | https://stats.stackexchange.com/questions/552709/measure-theoretically-rigorous-treatment-of-statistical-learning-theory |
Question: <p>I am producing a research statement to be sent to a statistics department and I was trying to avoid the term Machine learning in favour of the more friendly one of Statistical learning. Probably I could not avoid such use.</p>
Answer: <p>The classic <a href="https://web.stanford.edu/%7Ehastie/ElemStatLear... | https://stats.stackexchange.com/questions/524205/is-it-allowed-to-refer-to-artificial-neural-networks-as-statistical-learning |
Question: <p>Is there a good book/pdf similar to "Elements of Statistical Learning" that's available for free online, that deals with Bayesian statistics, ideally with code for <code>R</code>?</p>
Answer: <p>Well, given that you asked for something similar to the elements, I'm going to assume that you are of a machine... | https://stats.stackexchange.com/questions/47442/free-pdf-for-bayes-with-r-similar-to-elements-of-statistical-learning |
Question: <p>I am having a hard time understanding Bootstrap method. In the book <a href="http://faculty.marshall.usc.edu/gareth-james/ISL/ISLR%20Seventh%20Printing.pdf" rel="nofollow noreferrer"><em>Introduction to Statistical Learning</em></a> (pp. 187-190) the Bootstrap method is explained by first using "simu... | https://stats.stackexchange.com/questions/475693/understanding-the-bootstrap-method-in-introduction-to-statistical-learning |
Question: <p>I'm self-studying <em>Introduction to Statistical Learning</em>. Page 19 of the book states the following:</p>
<blockquote>
<p>Consider a given estimate $\hat{f}$ and a set of predictors $X$, which yields the prediction $\hat{Y} = \hat{f}(X)$. Assume for a moment that both $\hat{f}$ and $X$ are fixed. T... | https://stats.stackexchange.com/questions/206645/justifying-an-early-equation-from-introduction-to-statistical-learning |
Question: <p>I'm really confused about equation 2.7 on page 34 in the Introduction to Statistical Learning with R text book found here: <a href="http://faculty.marshall.usc.edu/gareth-james/ISL/ISLR%20Seventh%20Printing.pdf" rel="nofollow noreferrer">http://faculty.marshall.usc.edu/gareth-james/ISL/ISLR%20Seventh%20Pri... | https://stats.stackexchange.com/questions/451021/introduction-to-statistical-learning-with-r-equation-2-7 |
Question: <p>I'm a non-stats person trying to learn more about statistical learning methods, and to organize my thinking I am trying to construct a mental taxonomy of the methods I'm learning about. For instance: </p>
<blockquote>
<p>Statistical learning methods can be divided into supervised and unsupervised catego... | https://stats.stackexchange.com/questions/320664/where-do-artificial-neural-networks-belong-in-the-taxonomy-of-statistical-lear |
Question: <p>I am currently trying to read the "<a href="http://amzn.to/2yXDxdf" rel="nofollow noreferrer">Elements of Statistical Learning</a>", by Efron, Hastie, and Tibshirani, and already at the beginning there is a bit above my level in mathematics.
I have 3 questions regarding the move from (2.9) to (2.... | https://stats.stackexchange.com/questions/314517/derivation-of-epe-in-the-elements-of-statistical-learning |
Question: <p>I was listening to the first session of society of Minds by Minsky (2011) and he mentions at some point around minute 48 the following:</p>
<p>"...lots of statistical learning tools is good for lots of applications, but they won't cut it to solve hard problems, where the hypothesis more complicated than s... | https://stats.stackexchange.com/questions/134857/explanation-on-a-minskys-critique-on-statistical-learning-related-to-xor |
Question: <p>In the book Statistical Learning with Sparsity: The Lasso and Generalizations, in section 2.4.1, they mention that the absolute value of <span class="math-container">$\beta$</span> has no derivative at <span class="math-container">$\beta=0$</span>, therefore they proceed by direct inspection to determine t... | https://stats.stackexchange.com/questions/432403/statistical-learning-with-sparsity-direct-inspection-of-the-lasso-function |
Question: <p>In order to define what <a href="https://www.deeplearningbook.org" rel="nofollow noreferrer">deep learning</a> is, the learning portion is often listed with <a href="https://en.wikipedia.org/wiki/Backpropagation" rel="nofollow noreferrer">backpropagation</a> as a requirement without alternatives in the mai... | https://stats.stackexchange.com/questions/559251/simulated-annealing-for-deep-learning-why-is-gradient-free-statistical-learning |
Question: <p>I'm learning about the Statistical learning and in the section comparing Lasso and Ridge Regression it shows that the main difference between these two problems is the way the constraint/penalty is formulated. </p>
<p>In Lasso, the penalty is $\ell_1$ norm: $\lambda \sum |\beta_j|$, while in regression, t... | https://stats.stackexchange.com/questions/151954/sparsity-in-lasso-and-advantage-over-ridge-statistical-learning |
Question: <p>I am trying to recreate FIGURE 3.6 from Elements of Statistical Learning. The only information about the figure is included in the caption.
<a href="https://i.sstatic.net/XiK3l.png" rel="noreferrer"><img src="https://i.sstatic.net/XiK3l.png" alt=""></a></p>
<p>To recreate the forward stepwise line my pro... | https://stats.stackexchange.com/questions/411327/recreating-figure-3-6-from-elements-of-statistical-learning |
Question: <p>For example, I don't see a lot come up in my search for "non-learnability" ... is there another term? Specifically I'm imagining that similar to the Learning Guarantees from statistical learning theory there might be some results concerning non-learnability guarantees. Or are these equivalent in some simpl... | https://stats.stackexchange.com/questions/463034/are-there-any-good-references-regarding-non-learnability-in-statistical-learning |
Question: <p>Table 18.1 in the <a href="http://www-stat.stanford.edu/~tibs/ElemStatLearn/" rel="noreferrer">Elements of Statistical Learning</a> summarizes the performance of several classifiers on a 14 class data set. I am comparing a new algorithm with the lasso and elastic net for such multiclass classification prob... | https://stats.stackexchange.com/questions/12360/reproducing-table-18-1-from-elements-of-statistical-learning |
Question: <p>Elements of Statistical Learning 4.3.2 elaborates on computation for Linear Discriminant Analysis. <a href="https://web.stanford.edu/~hastie/Papers/ESLII.pdf" rel="nofollow noreferrer">https://web.stanford.edu/~hastie/Papers/ESLII.pdf</a></p>
<p>Procedure is said to be </p>
<blockquote>
<p>• Sphere the... | https://stats.stackexchange.com/questions/405541/computation-of-lda-in-elements-of-statistical-learning-4-3-2 |
Question: <p>In <em>Elements of Statistical Learning</em>, they state on p. 11 that all vectors are column vectors and start developing the least squares idea.</p>
<p>So if we have
$$\mathbf{X} = \begin{bmatrix}
1 \\
X_1 \\
X_2 \\
\vdots \\
X_p\end{bmatrix}$$
and $$\hat{\boldsymbol{\beta}} = \begin{bmatrix}
\hat{\beta... | https://stats.stackexchange.com/questions/181648/least-squares-definition-in-elements-of-statistical-learning |
Question: <p>With reference to Expected Prediction Error derivation - page 18, section 2.4 in Elements of Statistical Learning. Please refer text below: </p>
<p><a href="https://i.sstatic.net/ZJbWz.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ZJbWz.gif" alt="Please Refer below:"></a></p>
<p>I have b... | https://stats.stackexchange.com/questions/286290/elements-of-statistical-learning-statistical-decision-theory-doubt-regarding |
Question: <p>I am currently reading the book "Introduction to statistical learning" and on <a href="https://books.google.co.in/books?id=qcI_AAAAQBAJ&lpg=PR2&pg=PA3#v=onepage&q&f=false" rel="nofollow noreferrer">Page 3</a> there is a problem statement regarding the SMarket data (stock exchange data) fig ... | https://stats.stackexchange.com/questions/300097/what-does-this-figure-in-introduction-to-statistical-learning-mean |
Question: <p>I am reading exercise 6.4 from <a href="https://web.stanford.edu/~hastie/Papers/ESLII.pdf" rel="nofollow noreferrer">The Elements of Statistical Learning</a> (Hastie, Tibshirani and Friedman) and I am having difficulty interpreting exactly what is being asked in the following question</p>
<blockquote>
<... | https://stats.stackexchange.com/questions/465439/interpreting-exercise-in-elements-of-statistical-learning |
Question: <p>I am trying to implement a Simulation from the book "Elements of Statistical Learning" by Hastie et al. </p>
<p>My Problem is that I don't understand how to generate the pseudodata as they did.
The book says </p>
<blockquote>
<p>For each of N = 100 Samples, we generated p standard Gaussian features X ... | https://stats.stackexchange.com/questions/317961/generating-pseudodata-as-in-elements-of-statistical-learning |
Question: <p>When I read "Elements of Statistical Learning", I met some difficulty in calculating the Bayes decision boundary of Figure 2.5. In the package <code>ElemStatLearn</code>, it already calculated the probability at each point and used contours to draw the boundary. Can any one tell me how to calculate the pro... | https://stats.stackexchange.com/questions/35728/bayes-decision-boundary-of-figure-2-5-in-elements-of-statistical-learning |
Question: <p>I am stuck on problem 7.3 from the book 'The Elements of Statistical Learning'. This is the problem:
<a href="https://i.sstatic.net/CoQ3s.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/CoQ3s.jpg" alt="enter image description here"></a></p>
<p>Here is my attempt to a solution for least-squa... | https://stats.stackexchange.com/questions/306777/hints-for-exercise-7-3-from-the-elements-of-statistical-learning |
Question: <p>In the book "The Elements of Statistical Learning" in chapter 2 ("Linear models and least squares; page no: 12"), it is written that </p>
<blockquote>
<p>In the (p+1)-dimensional input-output space, (X,Y) represent a hyperplane. If the constant is included in X, then the hyperplane includes the origin a... | https://stats.stackexchange.com/questions/185634/understanding-linear-projection-in-the-elements-of-statistical-learning |
Question: <p>Some resources such as <a href="https://online.stat.psu.edu/stat508/book/export/html/696" rel="nofollow noreferrer">https://online.stat.psu.edu/stat508/book/export/html/696</a>, give the following for the quadratic discriminant function; <span class="math-container">$$ln(\pi_k)-\frac{1}{2}(x-\mu_k)^T\Sigma... | https://stats.stackexchange.com/questions/490651/qda-missing-term-in-quadratic-discriminant-function-in-introduction-to-statis |
Question: <p>I was reading the book "Introduction to Statistical Learning - 2nd ed" and I can't understand the derivation of equation 6.15 on the page 247.</p>
<p><a href="https://i.sstatic.net/9m9pt.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/9m9pt.png" alt="Page 247 of ISLR" /></a></p>
<p... | https://stats.stackexchange.com/questions/590667/derivation-of-equation-6-15-of-introduction-to-statistical-learning-2nd-ed |
Question: <p>I'm working on Chapter 5 from <a href="https://web.stanford.edu/%7Ehastie/Papers/ESLII.pdf" rel="nofollow noreferrer">The elements of statistical learning</a> which describes the more general linear models that is splines. The fragment (chapter 5, page 143) below describes the alternative and more direct m... | https://stats.stackexchange.com/questions/441574/trying-to-understand-splines-according-to-the-elements-of-statistical-learning |
Question: <p>In the textbook <a href="https://static1.squarespace.com/static/5ff2adbe3fe4fe33db902812/t/6062a083acbfe82c7195b27d/1617076404560/ISLR%2BSeventh%2BPrinting.pdf" rel="nofollow noreferrer"><em>Introduction to Statistical Learning with Applications in R</em></a> by James et al. (2014), the authors give the fo... | https://stats.stackexchange.com/questions/534570/introduction-to-statistical-learning-ch-3-pages-65-66 |
Question: <p>I am struggling to understand what is meant by Equation 1.8 in Vapnik's Statistical Learning Theory. Vapnik introduces the equation below as the <em>regression</em> function.</p>
<p><span class="math-container">$ r(x) = \int y\ dF(y|x) $</span></p>
<p>I know that <span class="math-container">$x$</span> and... | https://stats.stackexchange.com/questions/605801/understanding-vapniks-regression-function-in-statistical-learning-theory |
Question: <p>This should be a simple question but I must have missed something.</p>
<p>Equation (8.52) of Section 8.7 Bagging on page 285 of Trevor Hastie, <em>The Elements of Statistical Learning: Data Mining, Inference, and Prediction</em> is equivalent to
<span class="math-container">$$\mathbf E_{\mathcal P}[(Y-f_{\... | https://stats.stackexchange.com/questions/578939/question-about-an-equation-on-bagging-in-elements-of-statistical-learning-book |
Question: <p>The underlined sentences below from p. 331 in <a href="https://www.statlearning.com/" rel="nofollow noreferrer">An Introduction to Statistical Learning</a> have me scratching my head: Given that the splitting algorithm always finds the best next split in terms of error reduction, how could it be possible f... | https://stats.stackexchange.com/questions/643222/can-you-explain-this-description-of-tree-pruning-in-intro-to-statistical-learnin |
Question: <p>From the elements of statistical learning, it was claimed that
$$
\frac{1}{N}\sum_{i=1}^N ||h(x_i) ||^2 \sigma^2_\varepsilon= \frac{p}{N}\sigma^2_\varepsilon$$</p>
<p>where $h(x_i) = X(X^TX)^{-1}x_i$. Can someone show me how to prove this ? Thanks</p>
<p>This came from the image below</p>
<p><img src="... | https://stats.stackexchange.com/questions/91766/deriving-the-in-sample-error-for-linear-model-from-the-elements-of-statistical-l |
Question: <p>In <a href="https://web.stanford.edu/%7Ehastie/Papers/ESLII.pdf" rel="nofollow noreferrer">Elements of Statistical Learning II</a> on page 349, the multinomial deviance loss function is given by <span class="math-container">$L(y,p(x))=-\sum_{k=1}^KI(y=G_k)f_k(x)+\log(\sum_{\ell=1}^Ke^{f_\ell(x)})$</span>, ... | https://stats.stackexchange.com/questions/517082/question-on-loss-function-notation-in-elements-of-statistical-learning-ii |
Question: <p>In statistical learning, implicitly or explicitly, one <em>always</em> assumes that the training set $\mathcal{D} = \{ \bf {X}, \bf{y} \}$ is composed of $N$ input/response tuples $({\bf{X}}_i,y_i)$ that are <em>independently drawn from the same joint distribution</em> $\mathbb{P}({\bf{X}},y)$ with</p>
<p... | https://stats.stackexchange.com/questions/213464/on-the-importance-of-the-i-i-d-assumption-in-statistical-learning |
Question: <p>In table 3.3 (page 63) of the elements of statistical learning book, the intercept terms for Ridge regression, lasso , pcr and PLS differ. </p>
<p>However, according to the theory in the book, these models should all have the same $\hat{\beta_0} = \bar{y}$. How are the intercepts estimated in the table ? ... | https://stats.stackexchange.com/questions/92590/the-intercept-terms-for-ridge-regression-lasso-pcr-and-pls-elements-of-stati |
Question: <p>I was reading elements of statistical learning and it mentions let <span class="math-container">$\hat{f}(x)=Ave(y_i|x_i \in N_k(x))$</span> where <span class="math-container">$N_k(x)$</span> is the neighborhood containing the k points closest to x .</p>
<p>Then it says "under mild regularity condition... | https://stats.stackexchange.com/questions/629745/show-hatfx-to-eyx-x-elements-of-statistical-learning |
Question: <p>My question is about "The elements of statistical learning" book. I would like to know how to prove that the use of the $L_1$ loss $$L_1: E\bigg[|Y-f(X)|\bigg]$$ leads to have conditional median $\hat{f}(x)=median(Y|X=x)$ as solution to the $EPF(f)$ criterion minimisation in eq(2.11): $$EPF(f)= E_X\bigg[E_... | https://stats.stackexchange.com/questions/344920/derivation-of-the-conditional-median-for-linear-regression-in-the-elements-of-s |
Question: <p>I'm trying to build a data science base from scratch. I started a book called Introduction to Statistical Learning by Gareth James and found that there are many mathematical & statistical concepts that I'm unfamiliar with. I want to bridge this gap in my knowledge. Please recommend some books that will... | https://stats.stackexchange.com/questions/486182/book-recommendations-needed-building-foundational-knowledge-for-isl-introduc |
Question: <p>I'm quite familiar with loss functions in machine learning, but am struggling to connect them to loss functions in statistical decision theory [1].</p>
<p>In machine learning, a loss function is usually only considered at <strong>training time</strong>. It's a differentiable function of two variables, <cod... | https://stats.stackexchange.com/questions/485964/loss-functions-in-statistical-decision-theory-vs-machine-learning |
Question: <p>As far as I am concerned, statistical/machine learning algorithms always suppose that data are independent and identically distributed (<span class="math-container">$iid$</span>).</p>
<p>My question is: what can we do when this assumption is clearly unsatisfied? For instance, suppose that we have a data se... | https://stats.stackexchange.com/questions/563419/statistical-learning-when-observations-are-not-iid |
Question: <p>I don't understand the equation of loglikelihood of the observed data in graphical models with hidden nodes that appears in "The Elements of Statistical Learning" (Hastie, Tibshirani, Friedmann, chapter 17.4.2)</p>
<p><a href="https://i.sstatic.net/OXyKc.jpg" rel="nofollow noreferrer"><img src="https://i.... | https://stats.stackexchange.com/questions/271376/undirected-graphical-models-with-for-discrete-variables-with-hidden-nodes-logl |
Question: <p>I want to generate the plot described in the book ElemStatLearn "The Elements of
Statistical Learning: Data Mining, Inference, and Prediction. Second Edition" by Trevor Hastie
& Robert Tibshirani& Jerome Friedman. The plot is:</p>
<p><img src="https://i.sstatic.net/oY7hr.png" alt="enter image desc... | https://stats.stackexchange.com/questions/21572/how-to-plot-decision-boundary-of-a-k-nearest-neighbor-classifier-from-elements-o |
Question: <p>In the book <em>Elements of Statistical Learning</em>, section 2.8.3 describes Basis Functions, citing an example of a radial basis function as <span class="math-container">$f_{\theta}(x) = \sum_{m=1}^M \beta_M \sigma(\alpha_m'x + b_m)$</span>, with <span class="math-container">$\sigma(x)$</span> as the ac... | https://stats.stackexchange.com/questions/487702/parameter-estimation-for-basis-function-model-in-elements-of-statistical-learnin |
Question: <p>Does learning thorough statistical theory requires learning analysis before that?
I looked at the textbook for statistical theory. So far I don't know if analysis is required, but I think I have heard analysis is a prerequisite. Should I learn analysis beforehand?</p>
Answer: <p>No, you do not need to kno... | https://stats.stackexchange.com/questions/631739/does-learning-thorough-statistical-theory-require-learning-analysis |
Question: <p>I am having trouble grokking some very elementary material regarding Bayesian Classification in <a href="http://www.stat.berkeley.edu/~rabbee/s154/ISLR_First_Printing.pdf" rel="nofollow"><em>Introduction to Statistical Learning</em></a> at the end of pg. 37 to the very top of pg. 39 (i.e., the section enti... | https://stats.stackexchange.com/questions/208795/questions-regarding-the-bayes-classifier-in-introduction-to-statistical-learnin |
Question: <p>My question is about "The elements of statistical learning" book (yup, the one).
Right now I am kinda stuck on second chapter at part, where they derive EPE for linear regression (Somewhat related to <a href="https://stats.stackexchange.com/questions/253101/confusion-about-derivation-of-regression-function... | https://stats.stackexchange.com/questions/257124/derivation-of-epe-for-linear-regression-in-the-elements-of-statistical-learning |
Question: <p>I am learning the book "Elements of Statistical Learning," but it is very hard because it requires very heavy knowledge about statistics, which I have some, but apparently not enough to understand the derivations in the book. For example,
<a href="https://i.sstatic.net/8yZ06.jpg" rel="nofollow noreferrer"... | https://stats.stackexchange.com/questions/204830/what-supplemental-resource-do-you-recommend-in-order-to-fully-comprehend-the-ele |
Question: <p>I am confused by the different definitions of Loss Function in statistical decision theory vs machine learning.</p>
<p>In statistical decision theory, a loss function is typically defined as <span class="math-container">$L(\theta, \delta(X))$</span>, where <span class="math-container">$\theta$</span> is th... | https://stats.stackexchange.com/questions/543535/loss-function-in-supervised-learning-vs-statistical-decision-theory |
Question: <p>I'm going through Elements of Statistical Learning and I'm having a bit of trouble understanding this bit of notation from Chapter 2 (this example is (2.27))</p>
<p><span class="math-container">$$EPE(x_0) = E_{y_o|x_o}E_T(y_0 - \hat{y}_0)^2$$</span></p>
<p>Here, <span class="math-container">$T$</span> is... | https://stats.stackexchange.com/questions/458620/understanding-notation-in-bias-variance-decomposition-in-elements-of-statistical |
Question: <p>In Section 6.6.2 of An Introduction to Statistical Learning, the authors do the following:</p>
<p>A) Fit a lasso model</p>
<pre><code>lasso.mod=glmnet(x[train ,],y[ train],alpha=1, lambda =grid)
</code></pre>
<p>B) Perform cross-validation</p>
<pre><code>set.seed(1)
cv.out=cv.glmnet(x[train ,],y[ train],al... | https://stats.stackexchange.com/questions/490725/is-there-an-error-section-6-6-2-of-the-book-an-introduction-to-statistical-learn |
Question: <p>On page 19 of the textbook <a href="http://www-bcf.usc.edu/%7Egareth/ISL/" rel="noreferrer">Introduction to Statistical Learning</a> (by James, Witten, Hastie and Tibshirani--it is freely downloadable on the web, and very good), the following is stated:</p>
<blockquote>
<p>Consider a given estimate <span c... | https://stats.stackexchange.com/questions/110190/proof-derivation-of-residual-sum-of-squares-based-on-introduction-to-statistica |
Question: <p>I've been really enjoying the <em><a href="http://www-bcf.usc.edu/~gareth/ISL/ISLR%20Fourth%20Printing.pdf" rel="nofollow">Introduction to Statistical Learning</a></em> textbook so far, and I'm currently working my way through chapter 6. I realize that I am very confused by the process used in lab 3 of thi... | https://stats.stackexchange.com/questions/223623/cross-validation-scheme-used-in-the-introduction-to-statistical-learning-chapte |
Question: <p>I was trying to understand the difference between statistical regression VS machine learning regression. My background is from Economics and learned regression from statistical point of view for the first time. I learned machine learning later on and it also had regression. There might not be clear distinc... | https://stats.stackexchange.com/questions/514247/statistical-regression-vs-machine-learning-regression |
Question: <p>On pg. 34 of <em>Introduction to Statistical Learning</em>: $\newcommand{\Var}{{\rm Var}}$</p>
<blockquote>
<p>Though the mathematical proof is beyond the scope of this book, it is possible to show that the expected test MSE, for a given value $x_0$, can always be decomposed into the sum of three fundam... | https://stats.stackexchange.com/questions/208672/what-is-meant-by-the-variance-of-functions-in-introduction-to-statistical-lea |
Question: <p>Online Learning also known as Online Convex Optimization has famous algorithms like Follow-the-Leader and Online Gradient Descent (See <a href="http://ocobook.cs.princeton.edu/OCObook.pdf" rel="nofollow noreferrer">OCO Book)</a></p>
<p>Now stochastic programming has algorithms like Sample Average Approxima... | https://stats.stackexchange.com/questions/392301/what-is-the-relationship-between-online-learning-and-statistical-learning |
Question: <p>Linear Discriminant Analysis (LDA) possibly operates a dimension reduction. Section 4.3.3 in Elements of Statistical Learning explicits this notion as well as a method for computing the "optimal subspace for LDA".</p>
<p><a href="https://web.stanford.edu/~hastie/Papers/ESLII.pdf" rel="nofollow noreferrer"... | https://stats.stackexchange.com/questions/405607/finding-optimal-subspace-for-linear-discriminant-analysis-elements-of-statisti |
Question: <p>In particular, I am looking for a textbook which will go over the details of derivations (including all calculus and linear algebra) for learning models and concepts such as logistic regression, Gaussian Discriminant Analysis, with full proofs for variants like Gaussian Naive Bayes.</p>
<p>Books such as "... | https://stats.stackexchange.com/questions/74908/is-there-a-textbook-handbook-with-full-derivations-for-statistical-machine-l |
Question: <p>In section 7.3 of 'The Elements of Statistical Learning', the authors have shown the expression for bias-variance decomposition of linear model fit:
<a href="https://i.sstatic.net/tvwY3.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/tvwY3.jpg" alt="enter image description here"></a></p>
<p... | https://stats.stackexchange.com/questions/307110/bias-variance-docomposition-of-linear-model-fit-in-the-elements-of-statistical |
Question: <p>My question refers to the figure 10.13 of <a href="https://web.stanford.edu/%7Ehastie/Papers/ESLII.pdf" rel="nofollow noreferrer">The Elements of Statistical Learning</a>. Test error decreases monotonically with the increase in tree iterations. However, I don't understand why the test error does not raise ... | https://stats.stackexchange.com/questions/548557/why-doesnt-test-error-increase-for-a-high-number-of-boosting-iterations-figure |
Question: <p>I built a learning model (for classification) based on a Random Forest classifier and i am asked to assess the statistical significance of its performances. </p>
<p>Up to now, i trained and tested it on two different datasets A and B, respectively.</p>
<p>What kind of test can i use?</p>
Answer: <p>You ... | https://stats.stackexchange.com/questions/79677/statistical-significance-of-a-learning-model |
Question: <p>I'm reading about AdaBoost in the <em>The Elements of Statistical Learning</em> and I don't understand the equation 10.2. Below is an excerpt from the book.</p>
<blockquote>
<p>The power of AdaBoost to dramatically increase the performance of even a very weak classifier is illustrated in Figure 10.2. The f... | https://stats.stackexchange.com/questions/545107/equation-10-2-from-the-elements-of-statistical-learning-median-of-a-chi-squared |
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