In logistic regression, if the probability of an instance is = 0.6, and it actually belongs to class '1' (positive class), what is the value of its cost function?
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- 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 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 10A Ridge Linear Regression adds the sum of the squared values of the coefficients to the loss function to penalize large coefficients. Group of answer choices True False
- The following is true about sensitivity: Group of answer choices a) The output of the model is said to be inversely sensitive if the output of the model changes a small amount for a large change in an input variable b) Sensitivity is not an important concept in modeling c) It can help the modeler tell, on a relative basis, what are the important variables d) A variable is considered NOT very sensitive if a small change in the variable results `in a large change in the output of the model.You are given the true labels and the predicted probabilities from logistic regression model for N test examples. Approximately compute the AUC scores for ROC and PR curves.In the simple linear regression equation ŷ = bo + b₁x, how is b₁ interpreted? it is the change in that occurs with a one-unit change in y O It is the estimated value of ŷ when x = 0 O It is the change in ŷ that occurs when bo increases O it is the change in ŷ that occurs with a one-unit change in
- 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…In bivariate regression, the regression coefficient will be equal to rXY when:What is the mean of Linear Correlation ? if r = 0 has strong linear correlation it does mean has strong linear relationship?