Suppose you train the following logistic regression model: h(x; w) = a(wo + W1T1 + wy#2) tofit some data, where a(2) = 1/(1 +e) is the sigmoid function, and you find the followingweights: wn = 2, wi = 0, wy = -1.itsWhich of the following figures represents the decisions made by this hypothesis function?X24Predict "y-0"2-Predict y" 4Predict "y-1Predict "y1Predict "y-1"Predict "y-gPredict y"(F)Predictyo(E)(D)(C)(B)(A)OEO AOFODO None of these.OB

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Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Consider fitting a linear regression he(x) = 0Tx = 01x1+ 02x2+ O3x3 to a training dataset D = {(x1,y1),..., (xn, Yn)}, where 0 = [01, 02, 03]T and x = [#1, x2, 83]T Q1.1 Let D = {([1,0, 0]",0), ([0, 1, 0]" , 0.5), ([0, 0, 1]", – 1)}. Our current estimate of the parameter 0 = [0, 0, 0]T. which training instance makes the smallest contribution to the gradient ? (contribution means the magnitude of gradient change) O 1 O 2 O 3 Q1.2. What is the updated parameter after one step of gradient descent (assuming step size = 1)? O [0, 0, 0]T O (0, 1, 0]" О (), 0.5, — 1]7 O [0, 0.5, 1]"
The following figure depicts the decision boundary for the logistic regression model built to predict preference for light beer vs. regular beer (PREFERENCE = Light is the success or positive class). The explanatory variables are INCOME and AGE. INCOME has a positive coefficient and AGE has a negative coefficient. Predictions are made based on the depicted decision boundary. Four observations are circled. Match them with the appropriate descriptions. Age (in years) A B C D 100 80 60 20 0 -20 SE $10 $20 $30 Beer Preference $40 $50 $60 $70 Income (in US$ thousands) L.I.TJ False negative True positive True negative False positive $80 LA $90 Regular ● Light
In R, write a function that produces plots of statistical power versus sample size for simple linear regression. The function should be of the form LinRegPower(N,B,A,sd,nrep), where N is a vector/list of sample sizes, B is the true slope, A is the true intercept, sd is the true standard deviation of the residuals, and nrep is the number of simulation replicates. The function should conduct simulations and then produce a plot of statistical power versus the sample sizes in N for the hypothesis test of whether the slope is different than zero. B and A can be vectors/lists of equal length. In this case, the plot should have separate lines for each pair of A and B values (A[1] with B[1], A[2] with B[2], etc). The function should produce an informative error message if A and B are not the same length. It should also give an informative error message if N only has a single value. Demonstrate your function with some sample plots. Find some cases where power varies from close to zero to near…
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+R
Which statements are true about LASSO linear regression? Group of answer choices has embedded variable selection by shrinking the coefficient of some variables to exactly zero. has one hyper-parameter lambda (The regularization coefficient) which needs to be tuned if there are multiple correlated predictors lasso will select all of them adds the L2 norm of the coefficients as penalty to the loss function to penalize larger coefficients
You build a model predicting blood pressure as a function of three variables: weight (numeric) age (numeric) income (categorical: low, medium, high) You first specify your model as: blood pressure ~ age * income + weight How many parameters (k) does your model have? (Remember, we do not count the grand mean in k) You change the above model specification to be: blood pressure ~ age * income + weight * income How many parameters does your model have now? You change your model to include the three-way interaction (which, remember, includes all two-way interactions and main effects, too!) Your model now looks like this: blood pressure ~ age * income * weight How many parameters does your model have now?
Logistic regression aims to train the parameters from the training set D = {(x(i),y(i)), i 1,2,...,m, y ¤ {0,1}} so that the hypothesis function h(x) = g(0¹ x) 1 (here g(z) is the logistic or sigmod function g(z) can predict the probability of a 1+ e-z new instance x being labeled as 1. Please derive the following stochastic gradient ascent update rule for a logistic regression problem. 0j = 0j + a(y(¹) — hz(x)))x; ave. =
You 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 10
This is a binary classification problem, y has two values (0 or 1), and X (feature) has three dimensions. • Use a logistic regression model to project X to y (classify X into two categories: 0 or 1). • The initialization is: w1 = 0, w2 = 0, w3 = 0, b = 0, Learning rate is 2. • You must use Gradient Descent for logistic regression in this question. • The regression should stop after one iteration. Calculation process and formulas must be included in your answer! You must answer this question by manual calculation, but not programming.
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…
An instructor who taught two sections of engineering statistics last term, the first with 25 students and the second with 40, decided to assign a term project. After all projects had been turned in, the instructor randomly ordered them before grading. Consider the first 15 graded projects. (a) What is the probability that exactly 10 of these are from the second section? (Round your answer to four decimal places.) (b) What is the probability that at least 10 of these are from the second section? (Round your answer to four decimal places.) (c) What is the probability that at least 10 of these are from the same section? (Round your answer to four decimal places.) (d) What are the mean value and standard deviation of the number among these 15 that are from the second section? (Round your mean to the nearest whole number and your standard deviation to three decimal places.) mean projectsstandard deviation projects (e) What are the mean value and standard deviation of…

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