Let D be the distribution of training data and D′ be that of test data. A key condition under which classical PAC learning results hold is that D′ = D. Give an example to show that when D′ ̸= D, any learner with access to finite training data, even with unlimited computational power, may incur a high testing error.
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5. Let D be the distribution of training data and D′ be that of test data. A key condition under which classical PAC learning results hold is that D′ = D. Give an example to show that when D′ ̸= D, any learner with access to finite training data, even with unlimited computational power, may incur a high testing error.
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- 5. Let D be the distribution of training data and D' be that of test data. A key condition under which classical PAC learning results hold is that D' = D. Give an example to show that when D' # D, any learner with access to finite training data, even with unlimited computational power, may incur a high testing error.Assume that your hypothesis function is of the form f(x) = w0 + w1x and that the current values of w0 and w1 are 1 and 2 respectively. Further assume that you are using a learning rate (alpha) of 0.001 What is the gradient update for w0 (only the change) associated with the point (1, 12)?Simulated annealing is an extension of hill climbing, which uses randomness to avoid getting stuck in local maxima and plateaux. a) As defined in your textbook, simulated annealing returns the current state when the end of the annealing schedule is reached and if the annealing schedule is slow enough. Given that we know the value (measure of goodness) of each state we visit, is there anything smarter we could do? (b) Simulated annealing requires a very small amount of memory, just enough to store two states: the current state and the proposed next state. Suppose we had enough memory to hold two million states. Propose a modification to simulated annealing that makes productive use of the additional memory. In particular, suggest something that will likely perform better than just running simulated annealing a million times consecutively with random restarts. [Note: There are multiple correct answers here.] (c) Gradient ascent search is prone to local optima just like hill climbing.…
- Construct a graph to show how the time to complete the 10th car changes as the learning curve slope parameter is varied from 75% to 95%. The Mechanical Engineering department has a student team that is designing a formula car for national competition. The time required for the team to assemble the first car is 100 hours. Their improvement (or learning rate) is 0.8, which means that as output is doubled, their time to assemble a car is reduced by 20%. Use this information to determine, Solve, (a) the time it will take the team to assemble the 10th car. (b) the total time required to assemble the first 10 cars. (c) the estimated cumulative average assembly time for the first 10 cars. Solve by hand and by spreadsheet.Computer Science Use delta rule to classify (1 ,1, -1,-1) and (-1 ,1, -1,-1) are members of class with target value 1. (1 ,1, 1,-1) and (1 ,-1, -1,1) are members of class with target value -1. Use learning rate as 1, initial weights as 0.Answer this questions True or False : Q1:lf the learning rate is too small, then gradient descent may take a very long time to converge. Q2: If 00 and 01 are initialized at a local minimum, then one iteration will not change their values Q3: If 00 and 01 are initialized so that 00=01, then by symmetry (because we do simultaneous updates to the two parameters), after one iteration of gradient descent, we will still have 00=01
- Question 47. Random forests are one of the most famous machine learning methods. They are easy to understand, easy to implement and reach good prediction performances even without a hyper-parameter tuning. Which of the following statements on random forest are correct? a) The prediction of a classification forest is made by a majority vote of the trees' predictions. b) The prediction of a regression forest is the median of the tree predictions. c) Each single tree in the forest uses only a part of the data available. d) The training time of a random forest scales linear with the number of trees used.Linear regression aims to learn the parameters 7 from the training set D = {(f(),y(i)), i {(x(i),y(i)),i = 1,2,...,m} so that the hypothesis ho(x) = ēr i can predict the output y given an input vector š. Please derive the least mean squares and stochastic gradient descent update rule, that is to use gradient descent algorithm to update Ô so as to minimize the least squares cost function JO).The world monarch in the new post-apocalyptic world is extremely worried about the birth rate. She therefore orders that every family must have at least one female or else pay hefty fines. What will the gender ratio of the next generation be if all families adhere to this policy, which requires them to keep having children until they have one girl, at which time they immediately stop? (Presume that all pregnancies have an equal chance of producing a male or a girl.) Write a computer simulation of this problem after you have rationally resolved it.
- 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. =Consider the training set given below for predicting lung cancer in patients based on their symptoms (chronic cough and weight loss) and other lifestyle and environmental attributes (tobacco smoking and expo- sure to radon). a) Draw a two-level decision tree obtained using entropy as the impurity measure. Show your steps clearly (i.e., the computation of information gain for every candidate attribute at the first and second levels of the decision tree must be shown).For each scenario, determine research design, then the independent and dependent variables. a. In a test of roughly 200 men and women, those with moderately high blood pressure did worse on tests of memory than those with normal blood pressure. b. Is diet or exercise effective in combating insomnia? Forty volunteers suffering from insomnia agreed to participate in a month-long test. Half were randomly assigned to a special no-desserts diet; the others continued desserts as usual and half to an exercise program, while the others did not exercise. Those who ate no desserts and engaged in exercise showed the most improvement.