Assume we are trained two models using linear SVM with soft margins. One with C = 1 and another with C = 10. Which of the following statements are true? C=1 has larger margin than C=10 C=10 has larger margin than C=1 If data is linearly separable, C=1 training error is lower than or equal to C=10 If data is linearly separable, C=10 training error is lower than or equal to C=1 If data is linearly separable, C=10 and C=1 both training error of zero
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- You have trained a logistic regression classifier and planned to make predictions according to: Predict y=1 if ho(x) 2 threshold Predict y=0 if ho (x) < threshold For different threshold values, you get different values of precision (P) and recall (R). Which of the following is a reasonable way to pick the threshold value? O a Measure precision (P) and recall (R) on the test set and choose the value of P+R threshold which maximizes 2 Ob Measure precision (P) and recall (R) on the cross validation set and choose the P+R value of threshold which maximizes 2 Measure precision (P) and recall (R) on the cross validation set and choose the PR value of threshold which maximizes 2 P+R Measure precision (P) and recall (R) on the test set and choose the value of PR threshold which maximizes 2 P+R2. Using Scikit-learn fit a linear regression model on the test dataset and predict on the testing dataset. Compare the model’s prediction to the ground truth testing data by plotting the prediction as a line and the ground truth as data points on the same graph. Examine the coef_ and intercept_ attributes of the trained model, what do the values mean? Note: Linear Regression Reference: https://scikit-learn.org/stable/modules/linear_model.htmlYou decide to run a simpler model to predict churn, using only the variables tenure (in months) and TotalCharges (in US$). The output is given below. The AIC of this model is 4727.6 (in contrast to the AIC of 4240 for the full model). On the basis of this which model would be expected to give superior predictive performance? Actual ## Coefficients: ## Estimate Std. Error z value Pr(>|z|) ## (Intercept) 2.471e-01 5.360e-02 4.611 4.01e-06 *** ## tenure < 2e-16 *** -1.124e-01 5.816e-03 -19.334 ## TotalCharges 8.236e-04 5.618e-05 14.660 < 2e-16 *** ## No --- ## Signif. codes: 0 ## Yes Yes ## Null deviance: 5701.5 on 4921 ## Residual deviance: 4721.6 on 4919 ## AIC: 4727.6 515 345 ## (Dispersion parameter for binomial family taken to be 1) ## Predicted ***** No 795 3267 0.001 Confusion Matrix (Training) **** Actual 0.01 Yes No degrees of freedom degrees of freedom Yes The simpler model (with just tenure and TotalCharges) The full model (with all variables) 0.05 0.1 220 145 Predicted No 339…
- You are working on a spam classification system using regularized logistic regression. "Spam" is a positive class (y = 1)and "not spam" is the negative class (y=0). You have trained your classifier and there are m= 1000 examples in the cross-validation set. The chart of predicted class vs. actual class is: Predicted class: 1 Predicted class: 0 Actual class: 1 85 15 For reference: Accuracy = (true positives + true negatives)/(total examples) Precision = (true positives)/(true positives + false positives) Recall = (true positives)/ (true positives + false negatives) F1 score = (2* precision * recall)/(precision + recall) What is the classifier's F1 score (as a value from 0 to 1)? Write all steps Use the editor to format your answer Actual class: 0 890 10Question 48. Let us return to the Titanic data set. We now have learned several models and want to choose the best one. We used three different methods to validate these models: The training error rate (apparent error rate), the error rate on an external test set and the error rate estimated by a 10-fold cross validation. Training Error | Error on the test set | Cross Validation Error 0.18 Learner Decision Tree 0.22 0.21 Random Forest 0.01 0.10 0.12 1-Nearest-Neighbour 0.18 0.19 Which of the following statements are correct? a) 1-Nearest-Neighbour has a perfect training error and hence it should be used here. b) Random Forests outperforms both 1-Nearest-Neighbour and the Decision Tree in terms of prediction error. c) Not just in this case, but in general, Cross Validation is the better validation strategy and should always be preferred over the error on a single test set. d) Not just in this case, but in general, Decision Trees always perform worse than Random Forests.Assume the following simple regression model, Y = β0 + β1X + ϵ ϵ ∼ N(0, σ^2 ) Now run the following R-code to generate values of σ^2 = sig2, β1 = beta1 and β0 = beta0. Simulate the parameters using the following codes: Code: # Simulation ## set.seed("12345") beta0 <- rnorm(1, mean = 0, sd = 1) ## The true beta0 beta1 <- runif(n = 1, min = 1, max = 3) ## The true beta1 sig2 <- rchisq(n = 1, df = 25) ## The true value of the error variance sigmaˆ2 ## Multiple simulation will require loops ## nsample <- 10 ## Sample size n.sim <- 100 ## The number of simulations sigX <- 0.2 ## The variances of X # # Simulate the predictor variable ## X <- rnorm(nsample, mean = 0, sd = sqrt(sigX)) Q1 Fix the sample size nsample = 10 . Here, the values of X are fixed. You just need to generate ϵ and Y . Execute 100 simulations (i.e., n.sim = 100). For each simulation, estimate the regression coefficients (β0, β1) and the error variance (σ 2 ). Calculate the mean of…
- A threshold of total variability explained has been set at 85%. How many principal components must you select?give the steps by steps answerYou are developing a simulation model of a service system and are trying to create aninput model of the customer arrival Process, You have the following four observations of the process of interest [86, 24,9, 50] and you are considering either an exponential distributionOf a uniform distribution for the model. Using the data to estimate any necessary distributionParameters, write the steps to plot Q-Q plots for both cases.