8. Assume our hypothesis class is the set of lines, and we use a line to separatethe positive and negative examples, instead of bounding the positive exam-ples as in a rectangle, leaving the negatives outside (see figure 2.13). Showthat the VC dimension of a line is 3.DŒX1Figure 2.13 A line separating positive and negative instances.9. Show that the VC dimension of the triangle hypothesis class is 7 in two di-mensions. (Hint: For best separation, it is best to place the seven pointsequidistant on a circle.)10. Assume as in exercise 8 that our hypothesis class is the set of lines. Writedown an error function that not only minimizes the number of misclassifica-tions but also maximizes the margin.11. One source of noise is error in the labels. Can you propose a method to finddata points that are highly likely to be mislabeled?

Question:8. The VC dimension of a line in two dimensions is 3.9. The VC dimension of the triangle…

Answered: 8. Assume our hypothesis class is the…

Similar questions

Your task is simple: use machine learning to create a model that predicts which passengers survived the Titanic shipwreck. Implement and train a classification model for the Titanic dataset (the dataset can be found here: https://www.kaggle.com/c/titanic). Please ignore the test set (i.e., test.csv) and consider the given train set (i.e., train.csv) as the dataset. What you need to do: 1. Data cleansing 2. Split the dataset (i.e., train.csv) into a training set (80% samples) and a testing set (20% samples) 3. Train your model (see details below) 4. Report the overall classification accuracies on the training and testing sets 5. Report the precision, recall, and F-measure scores on the testing set 1. Required Model (100 pts): Implement and train a logistic regression as your classification model. • You have to use Sklearn deep learning library. • You may want to refer to this tutorial: https://bit.ly/37anOxi
Map coloring problem with {Red, Green, Blue). Assume that Arizona and Colorado do not share any border, and Utah and New Mexico do not share any border. Southwestern States Pacific Ocean ܞ W Key Oregon Sacramento ★ State Capital Carson State Boundary Water CEnchantedLearning.com City Névada California Idaho Salt Lake City Utah Arizona Phoenix MEXICO Wyoming Denver Colorado Santa Fe New Mexico Texas Kansas Nebraska Oklahoma Texas Please answer the following questions. 1. Which state should be selected to color first based on the heuristic of most constraining variable (degree heuristic)? 2. Assume our current assignment is {Nevada= Red, Arizona = Green}, which state(s) should be selected to color next based on the heuristic of minimum remaining value? 3. Assume our current assignment is {Arizona = Blue, Utah = Red} and we select California to color next, which color should we select based on the heuristic of least constraining value? 4. Assume our current assignment is {California =…
1. Prove that IR2 of the Armstrong Inference Rules is correct (sound). We did that for IR3 in class. Consider F = {BC -> D, B -> E, CE -> D, E -> CA, BF -> G}and R(A,B,C,D,E,F,G) for the next 6 questions. 2. Use all three of Armstrong Rules to "infer" one new FD. 3. Find a minimal cover for F. 4. Find all many keys for R. 5. Find a 3NF decomposition for R that is dependency preserving and has lossless join. 6. Find a BCNF decomposition for R that has lossless join. 7. Apply the lossless join test algorithm on the decomposition of Q6 or the decomposition of Q7 to verify that the decomposition is a lossless join decomposition. You do not need to do that for both Q6 and Q7.
Suppose we are trying to model a classification problem with two labels: 'sick' and 'healthy.' For the purpose of this test, we consider a positive result to be testing sick and a negative to test as healthy. After fitting the model with LDA in R, we compare predicted values from the actual values, as shown below: > lda. fit = 1da (test.result x1 + x2, data-mydata) > lda. pred > lda.class=lda.pred$class > table (lda.class, mydata$test.result) = predict (1da.fit) mydata lda.pred sick healthy sick 40 healthy 25 32 121
Consider the following claim for any sets A, B, C: (B �� A) n (C − A) = (B^C) – A. Consider the proof that supposes show that a € Bn C and True or False: This is a valid proof approach that would prove the claim. (This is not asking whether this is an actual proof of the result. It's asking whether this general, high-level approach would suffice to prove the result.) True False EB-A and EC-A, and wants to A.
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.
2. Prove the validity of this argument: Premises: Conclusion: (p^t) → (rVs) q→ (u^t) u p S q→r Hint: Check the method in the slides used to show validity of an argument when the conclusion is an implicati- on. CS Scanned with CamScanner
1. Consider the method m1() in Question 2. Consider the AOR[1] and the ROR[2] mutation operators. a. What is the minimum number of mutants necessary for coverage comparable to the strongest graph coverage criteria? Justify. b. List such minimum set of mutants. c. Pick one of your mutants and provide the reachability conditions, infection conditions, propagation conditions, and test case values to kill that mutant. 1. public int m1() { 2. 3. outVal = 1; 4. 5. 6. 7. 8. 9. 10. } 11. 12. } 13. 14. 02 = new C2(); GPA 02.m2(); (stub) if GPA > 3.5 { outVal outVal * 10 + 10%; www wwwwwwwwww if major "ICS" { outVal = outVal * 2; wwwwwwwww outVal outVal / 2; wwwwwwww wwwwwwwwwwww elsif GPA 2.5 { wwwwww outVal = 60 30 ✶ outVal; wwwwwww - wwwwwwwww 15. } 16. else { 17. 18. } 19. outVal = 20 outVal + 20; wwwwwwww return outVal; wwwwwwwwww wwwwww 20. }
Consider a concept class C formed by orthogonal rectangles (boxes). We have received the following labelled sample. True or False:There is an infinite number of rectangles in C that are consistent with this sample.
The PDDL describes a fictional jungle. This universe has three predicates with up to four parameters and five constants. JUNGLE should have fewer states. Must justify.