Suppose you have a training set S of data points in R², with each data point x; being labeled 1 or -1. You would like to use SGD to find a line that comes as close as possible to separating the positive points from the negative points. (a) Say that your starting line is x + y = 0, so Wo = (1,1,0). Explain the first step in SGD to get W₁, using n = 0.5.
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- please try to simulate the probability of rolling a Die with Sample Space* S={1,2,3,4,5,6} and the probability of each sample point has a 1/6 chance of occurring, i.e., you need to verify that your simulation converges to 1/6 when you select one point of sample space. When X is a random variable for sample point of rolling a Die, Pr(X<=4)=2/3. Please verify this result by simulation. Please let me know how to make an Excel file as stated above.You are given a N*N maze with a rat placed at maze[0][0]. Find whether any path exist that rat can follow to reach its destination i.e. maze[N-1][N-1]. Rat can move in any direction ( left, right, up and down).Value of every cell in the maze can either be 0 or 1. Cells with value 0 are blocked means rat cannot enter into those cells and those with value 1 are open.Input FormatLine 1: Integer NNext N Lines: Each line will contain ith row elements (separated by space)Output Format :The output line contains true if any path exists for the rat to reach its destination otherwise print false.Sample Input 1 :31 0 11 0 11 1 1Sample Output 1 :trueSample Input 2 :31 0 11 0 10 1 1Sample Output 2 : false Solution: //// public class Solution { public static boolean ratInAMaze(int maze[][]){ int n = maze.length; int path[][] = new int[n][n]; return solveMaze(maze, 0, 0, path); } public static boolean solveMaze(int[][] maze, int i, int j, int[][] path) {//…Generate 100 synthetic data points (x,y) as follows: x is uniform over [0,1]10 and y = P10 i=1 i ∗ xi + 0.1 ∗ N(0,1) where N(0,1) is the standard normal distribution. Implement full gradient descent and stochastic gradient descent, and test them on linear regression over the synthetic data points. Subject: Python Programming
- Your training set is made up of the following 2-dimensional points: A={a', a², a³, a², a³} {(1,0), (1,3), (3,0), (0,-2), (-2,0)}, where a', a², and a³ belong to class 1, and at, a5 to class 2. (a) Plot all samples into a 2-dimensional Cartesian axis system Calculate the Manhattan distance 1 between the test sample b=(0,0) and every a of the (b) training set (c) Use the K- Nearest Neighbor algorithm with K=1 to assign a class to 'b'. Explain (d) Classify 'b' using K=5. Explain 'Manhattan(a, b) = E; la² – b' , Vi = 1,2We can specify the PageRank algorithm's convergence threshold using proc networks. This figure has to be positive. Default value is 1E-9. When the difference between the PageRank scores of the current iteration and the previous iteration is less than or equal to the tolerance set, the PageRank algorithm ceases iterating. We can use the PAGERANKTOLERANCE= parameter to specify the convergence tolerance. Write The example code demonstrates how to calculate PageRank centrality using a proc network built on a directed graph with unweighted links.Classify the 1’s, 2’s, 3’s for the zip code data in R. (a) Use the k-nearest neighbor classification with k = 1, 3, 5, 7, 15. Report both the training and test errors for each choice. (b) Implement the LDA method and report its training and testing errors. Note: Before carrying out the LDA analysis, consider deleting variable 16 first from the data, since it takes constant values and may cause the singularity of the covariance matrix. In general, a constant variable does not have a discriminating power to separate two classes.
- 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,…Design and explain a generic m-round winner tournament, Round-Winner-Tournament(P,m), for players P, in which the participants are matched randomly in each round 0, 1,...,m 1, and the winners advance to the next round. Following round m 1, the champion is chosen at random from among the remaining participants. This tournament structure, interestingly, contains the following special cases: m = 0 is a random selection tournament, m = 1 is a random pairing tournament, and m = lg |P| is a single elimination seeding tournament.Correct answer will be upvoted else downvoted. There are n focuses on an endless plane. The I-th point has facilitates (xi,yi) to such an extent that xi>0 and yi>0. The directions are not really integer. In one maneuver you play out the accompanying activities: pick two focuses an and b (a≠b); move point a from (xa,ya) to either (xa+1,ya) or (xa,ya+1); move point b from (xb,yb) to either (xb+1,yb) or (xb,yb+1); eliminate focuses an and b. Notwithstanding, the move must be performed if there exists a line that goes through the new organizes of, another directions of b and (0,0). If not, the move can't be performed and the focuses stay at their unique directions (xa,ya) and (xb,yb), individually. Input The main line contains a solitary integer n (1≤n≤2⋅105) — the number of focuses. The I-th of the following n lines contains four integers ai,bi,ci,di (1≤ai,bi,ci,di≤109). The directions of the I-th point are xi=aibi and yi=cidi. Output :In the primary…
- Design an adjacency Matrix of the alphabets of Uzair Bhatti . In accordance with the following conditions: If your name has repeated characters (e.g. character E, 2 times) then you will consider only 1 time. If your Name contains both G and S, then there will be an edge between them and one additional edge from W to each if W is also in your name. If N is the alphabet in your name, it will have an edge to A and S if it available in your name. If P is available then it will have an edge with L if it is available. If there is a blank space in full Name then it will be represented by “_”, and it must have an edge with all alphabets. (Note: Place on in 1 for Edge and 0 for No Edge) Sketch an undirected graph of the above designed adjacency matrixConsider the elliptic curve group based on the equation where a = 1405, b = 2011, and p = 2531. We will use these values as the parameters for a session of Elliptic Curve Diffie-Hellman Key Exchange. We will use P = (0,98) as a subgroup generator. You may want to use mathematical software to help with the computations, such as the Sage Cell Server (SCS). On the SCS you can construct this group as: G=EllipticCurve(GF(2531),[1405,2011]) Here is a working example. (Note that the output on SCS is in the form of homogeneous coordinates. If you do not care about the details simply ignore the 3rd coordinate of output.) 62 Alice selects the private key 41 and Bob selects the private key 20. What is A, the public key of Alice? y² = x³ + ax+b mod p What is B, the public key of Bob? 2472 After exchanging public keys, Alice and Bob both derive the same secret elliptic curve point TAB. The shared secret will be the x-coordinate of TAB. What is it?If we add a positive constant to each of the array of values, then the z-score of an observation will also rise. [T or F]. Explain the answer.