Consider a concept learning problem in which each instance is a real number, and in which each hypothesis is an interval over the reals. More precisely, each hypothesis in the hypothesis space H is of the form a
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- Discrete mathematics. What is wrong with this proof?1. Suppose we are in the middle of a proof and our current goal is: S(c)→(∀d)(M(d)→R(d,c)) Suppose the next line of the proof is "Assume S(c)." Which of the following does the goal change to? (∀d)(M(d)→R(d,c)) S(c)→(∀d)(M(d)→R(d,c)) M(d)→R(d,c) S(c)→M(c) 2. Suppose we are in the middle of a proof and our current goal is: (∀d)(R(d,c)→R(c,d)) Suppose the next line of the proof is "Let d be an arbitrary (whatever its type is)." Which of the following does the goal change to? Group of answer choices R(d,c)→R(c,d) (∀d)(R(d,c)→R(c,d)) R(d,c) R(c,d)Let's revisit our first problem, where we want to set up a series of chess matches so we can rank six players in our class. As we did before, we will assume that everyone keeps their chess rating a private secret; however, when two players have a chess match, the person with the higher rating wins 100% of the time. But this time, we are only interested in identifying the BEST of these six players and the WORST of these six players. (We don't care about the relative ordering or ranking of the middle four players.) Your goal is to devise a comparison-based algorithm that is guaranteed to identify the player with the highest rating and the player with the lowest rating. Because you are very strong at Algorithm Design, you know how to do this in the most efficient way. Here are five statements. A. There exists an algorithm to solve this problem using 6 matches, but there does not exist an algorithm using only 5 matches. B. There exists an algorithm to solve this problem using 7 matches,…
- Why is an RNN (Recurrent Neural Network) used for machine translation, say translating English to French? (Check all that apply.) It can be trained as a supervised learning problem. It is strictly more powerful than a Convolutional Neural Network (CNN). It is applicable when the input/output is a sequence (e.g. a sequence of words). ⒸRNNs represent the recurrent process of Idea->Code-> Experiment->Idea->....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. =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.
- Considering the problem of performing rapid COVID test among a large group of people. Assuming there are exactly 1 positive case among N people, and you are asked to find the positive case with the least number tests. 1. A straight forward approach is to test every single person, which requires N tests in total. Can you design a testing framework that works better than the greedy one under, even under the worst-case scenario? Write the pseudo code for your approach and briefly explain the time complexity of your approach. 2. Based on your framework, if there are 1,000 people, what are the maximum number of tests that need to be performed in order to identify the positive case (number of tests required in the worst case)?In this assignment, you will develop a multiclass classifier that predicts the most probable hashtagstweets. We consider a supervised learning setting where a small number of trainingand validation tweets and their corresponding hashtags are provided. Note that hashtags are user-generatedcontent and may not be precise or comprehensive. However, hashtags of test tweets areprecise and comprehensive as they are verified by human annotators in the hashtag space of thisassignment. (make in python language)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.A machine learning model is learning parameters w₁ and w₂. It turns out that for the latest data inputted, the error function is: E=(w₁-1)²+(W₂-1)² The current values of the parameters are w₁-2 and w₂=0.9. Gradient descent is applied to update the parameters. Which statement is true? 7 0 w1 2 W2 3 4 0 W2 W1 decreases and decreases, change in w₁ is bigger. W₁ decreases and w₂ increases, change in w₂ is bigger. W₁ decreases and w₂ increases, change in w₁ is bigger. W₁ decreases and w₂ increases, both by the same amount. 18 16 14 12 10 8 6 4 HH +++ 2