2. Suppose you are given the following classification task using Logistic Regression: predict the target Y = {0,1} given two real valued features X₁ and X₂. After some training, you learn the following decision rule: [f_W₁X₁ +W₂X₂ +Wo ≥ 0 Predict Y = 1, otherwise predict Y = 0; where model parameters are tuned to w₁ = 3, W₂ = 5, and wo_ - 15. With these values the model is: 3X₁ +5X₂ - 15 = 0 Plot the decision boundary and label the region where we would predict Y = 1 and Y = 0. Hint: Determine the intercept by setting either X₁ = 0 or X₂ = 0
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- Question 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.NoneAssume 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…
- 2. Take a bivariate normal distribution with two random variables X and Y, with mean value = (1, -1), var(X) = 3, var(Y) = 6, and cor(X,Y) = -0.5. %3! (a) create a contour plot for this data (b) plot 1,000 simulations of this distribution (c) Using 1,000,000 simulations, find (1) the expected value of Y (ii) the expected value of Y, given that X> 2 (ii) the expected value of Y, given that X = 2give the steps by steps answerAssume an attribute (feature) has a normal distribution in a dataset. Assume the standard deviation is S and the mean is M. Typically: Group of answer choices, multiple choice: Then the outliers usually lie below -3*M or above +3*M Then the outliers usually lie above -3*S or below +3*S Then the outliers usually lie below -3*S or above +3*S Then the outliers usually lie above -3*M or below +3*M
- In this section we create the model object and define the loss function and optimizer. For the loss function use nn.CrossEntropyLoss() instead of the mean-squared loss done in class. Use the same optimizer as in class. learning_rate = 0.001 num_epochs = 5 device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu") #this is to use gpu if available # **create your neural net model here, call the variable 'model'** # ** complete following lines of code to define loss function and optimizer #criterion = **complete this** #optimizer = **complete this**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.)Machine Learning Evaluation measures. Consider a dataset with 90 negative examples and 10 positive examples. Suppose a model built using this data predicts 30 of the examples as positive (only 10 of them are actually positive) and 70 as negative. What are the numbers of True Positives (TP), False Positives (FP), True Negatives (TN), False Negatives (FN), Accuracy, Precision, Recall, and Specificity? Show all your steps