An introduction to statistical learning: with applications in R
13th Edition
ISBN: 9781461471387
Author: James, Gareth, Witten, Daniela, Hastie, Trevor, TIBSHIRANI, Robert
Publisher: MPS (CC)
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Chapter 4, Problem 5E
a.
Explanation of Solution
Baye’s decision boundary
- If the Bayes decision boundary is linear, then QDA is expected to perform better on the training set.
- Because of its higher flexibility, it may yield a closer fit...
b.
Explanation of Solution
Baye’s decision boundary
- If the Bayes decision boundary is non-linear, QDA...
c.
Explanation of Solution
Baye’s decision boundary
- QDA is more flexible than LDA and so has higher variance...
d.
Explanation of Solution
Baye’s decision boundary
- With fewer sample points, the variance from using a more flexible method s...
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Students have asked these similar questions
2. Can you design a binary classification experiment with 100 total population (TP+TN+FP+ FN), with precision (TP/(TP+FP)) of 1/2, with sensitivity (TP/(TP+FN)) of 2/3, and specificity (TN/(FP+TN)) of 3/5? (Please consider the population to consist of 100 individuals.)
given the observed data (obsX,obsY), learning rate (alpha), error change threshold, and delta from the huber loss model,write a function returns theta0 and theta1 that minimizes the error.
Use pseudo huber loss function
In a case where there is multicollinearity in the model
A.
Independent variables have strong linear relationships with each other
B.
The variance of the estimates increases when we have multicollinearity.
C.
Multicollinearity will lead to bias.
D.
Both A and B
E.
Both A and C
Chapter 4 Solutions
An introduction to statistical learning: with applications in R
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- Imagine a regression model on a single feature, defined by the function f (x) = wx + b where X, W, and b are scalars. We will use the MSE loss loss(w, b) = E;(f(x;) – t;)² . n Work out the gradient with respect to b. Which is the correct answer? Read the four equations carefully, so you notice all the differences. 1. E:(f(x;) – t;)x; 2.E(f(x;) – t;) n 3.- E;(wx; + b – t;)x; n 4. E: (wa; +b - t;) n 4arrow_forwardNow suppose that you have two versions of your model with different parameters(e.g., different regularization) or even different model families (e.g., logistic regression versus random forest). Which one is better?arrow_forwardAssume that your hypothesis function is of the form f(x) = w0 + w1x and that the current values of w0 and w1 are 1 and 2 respectively. Further assume that you are using a learning rate (alpha) of 0.001 What is the gradient update for w0 (only the change) associated with the point (1, 12)?arrow_forward
- In python, for a sample data with 4 columns and 60 rows how do you find the parameters for the regression with the feature map (see attached) where we consider the loss function to be the square of residuals. Once this is done, how do you compute the empirical risk? I've attached some of the data below, it would be sufficient to see how you get results for the question using the above dataset. 1 14 25 620 -1 69 29 625 0 83 27 850 0 28 25 1315 1 41 25 2120 -1 153 31 1315 0 55 25 2600 0 55 31 490 1 69 25 3110 1 83 25 3535arrow_forwardSay that you have the following initial settings for binary logistic regression: x = [1, 1, 3] w = [0, -2, 0.75] b = 0.5 2. Given that x's label is 1, what is the value of w_1, w_2, and w_3 at time t + 1 if the learning rate is 1? For this problem, you may ignore the issue of updating the bias term. 3. What is the value of P(y = 1 | x) given your updated weights from the previous question? 4. Given that x's label is 1, what is the value of the bias term at time t + 1 if the learning rate is 1? 5. What is the value of P(y = 1 | x) given both your updated weights and your updated bias term? 6. Given that x's label is 0, what is the value of P(y = 0| x) at time t + 1 if the learning rate is 0.1? Round your answer to the nearest 1000th as a number [0, 1].arrow_forwardIn a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where O represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of 5.3 and a standard deviation of 1.9. Answer parts (a)-(d) below. (a) Find the probability that a randomly selected study participant's response was loss than 4. The probability that a randomly selected study participant's response was lons than 4 is (Round to four decimal placos as needed.)arrow_forward
- Review the Stata do-file written below thatsimulates the omitted variable bias. 1. Discuss the step-by-step procedure for the OVB simulation as written in the Stata do-file. In the regression of Y on T. is the estimated coefficient for T biased? why? 2. Does adding variable S on the regression of Y on T change the estimated coefficient T? why? 3.Reproduce the empirical density figure and explain your finding. * ============================================================================== * * Title : OLS simulation: ommitted variable bias (OVB) * Authors : Gumilang Aryo Sahadewo * Stata version : 12 * Date created : December 4th 2017 * Last modified : December 7th 2017 * * ============================================================================== ** INITIALIZATION version 12 set more off clear all cap log close // use this command if you are used to using log files ** SET NUMBER OF OBSERVATIONS set obs 1000 ** PART A: MULTIPLE LINEAR REGRESSION //…arrow_forwardThe task is to implement density estimation using the K-NN method. Obtain an iidsample of N ≥ 1 points from a univariate normal (Gaussian) distribution (let us callthe random variable X) centered at 1 and with variance 2. Now, empirically obtain anestimate of the density from the sample points using the K-NN method, for any valueof K, where 1 ≤ K ≤ N. Produce one plot for each of the following cases (each plotshould show the following three items: the N data points (instances or realizations ofX) and the true and estimated densities versus x for a large number – e.g., 1000, 10000– of discrete, linearly-spaced x values): (i) K = N = 1, (ii) K = 2, N = 10, (iii) K = 10,N = 10, (iv) K = 10, N= 1000, (v) K = 100, N= 1000, (vi) K = N = 50,000. Pleaseprovide appropriate axis labels and legends. Thus there should be a total of six figures(plots),arrow_forwardWe want to build a regression model and have many observations and many predictors. (a) From a computational point of view, which of these two model building algorithms are preferable: best subset selection or forward stepwise selection? (b) True or false and explain: Best subset selection will result in a smaller prediction error than forward stepwise selection because every model that is considered in forward stepwise selection is also considered in best subset searrow_forward
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