Create a data based on the linear model with dummy (0,1) variables y = Xb + e, and this model not of full rank Again, y is an 6 x 1 vector of observations yi, b is a 3 × 1 vector of parameters, X is an 6 x 3 matrix of known values (in most cases O's and 1's) and e is a vector of random error terms
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- let P matrix with dimension (1x6) . write code in matlab to change P dimension to P(2x3) then write code to change it back to P(1x6).Represent the images of “space invaders” in Figure 5.16 by quantitative vectors and compute the distances between them (i.e. their similarity) using Manhattan distance measures.1. The impulse response of a causal system is: h(t) = A cos(wt) e¯¹/¹u(t) where u(t) is the Heaviside step function. The response is measured experimentally with a sampling interval of T. a. Write an expression for the sampled impulse response h[n]. b. Calculate the z transform of h[n] and write an expression for H[z]. Use the tables provided below as necessary. c. Does the system have an infinite impulse response (IIR) or finite impulse response (FIR)? Justify your answer. d. What is the DC gain of H[z]? e. Write a difference equation that describes the output y[n] in terms of input x[n].
- Appendix A 10-Fold Cross Validation for Parameter Selection Cross Validation is the standard method for evaluation in empirical machine learning. It can also be used for parameter selection if we make sure to use the training set only. To select parameter A of algorithm A(X) over an enumerated range d E [A1,..., A] using dataset D, we do the following: 1. Split the data D into 10 disjoint folds. 2. For each value of A e (A1,..., Ar]: (a) For i = 1 to 10 Train A(A) on all folds but ith fold Test on ith fold and record the error on fold i (b) Compute the average performance of A on the 10 folds. 3. Pick the value of A with the best average performance Now, in the above, D only includes the training data and the parameter A is chosen without the knowledge of the test data. We then re-train on the entire train set D using the chosen A and evaluate the result on the test set.Write a MATLAB function that implements Gaussian Elimination with support for both partial pivoting and full pivoting for use in computing the inverse of a matrix. Do not use MATLAB-provided functions that directly implement Gaussian Elimination or compute inverses. Demonstrate the use of your function to invert a matrix A of your choice. You function should return a matrix B that is the inverse of matrix A. Your function should take the following input parameters: the matrix A, and an integer indicating the mode of operation with 0=no pivoting, 1=partial pivoting, and 2=full pivoting.In R, write a function that produces plots of statistical power versus sample size for simple linear regression. The function should be of the form LinRegPower(N,B,A,sd,nrep), where N is a vector/list of sample sizes, B is the true slope, A is the true intercept, sd is the true standard deviation of the residuals, and nrep is the number of simulation replicates. The function should conduct simulations and then produce a plot of statistical power versus the sample sizes in N for the hypothesis test of whether the slope is different than zero. B and A can be vectors/lists of equal length. In this case, the plot should have separate lines for each pair of A and B values (A[1] with B[1], A[2] with B[2], etc). The function should produce an informative error message if A and B are not the same length. It should also give an informative error message if N only has a single value. Demonstrate your function with some sample plots. Find some cases where power varies from close to zero to near…
- a. Write down the factorization of P(D, I, G, S, L) based on the Bayesian network.Let A be the n x n matrix with n = 1000 and entries A(i, i) = i, A(i, i + 1) = A(i + 1, i) = 1/2, A(i, i + 2) = A(i + 2, i) = 1/2 for all i that fit within the matrix.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.
- Which of the following are true about principal components analysis (PCA)? Assume that no two eigenvectorsof the sample covariance matrix have the same eigenvalue. A: Appending a 1 to the end of every sample point doesn’t change the results of performing PCA (except thatthe useful principal component vectors have an extra 0 at the end, and there’s one extra useless component witheigenvalue zero). B: If you use PCA to project d-dimensional points down to j principal coordinates, and then you run PCA againto project those j-dimensional coordinates down to k principal coordinates, with d > j > k, you always get the sameresult as if you had just used PCA to project the d-dimensional points directly down to k principle coordinates. C: If you perform an arbitrary rigid rotation of the sample points as a group in feature space before performingPCA, the principal component directions do not change. D: If you perform an arbitrary rigid rotation of the sample points as a group in…Please implement Multinomial Logistic Regression on the following data. Please continue from the given code:This is a Machine Learning question : Given a dataset, (1,+), (7, - ), (2, +), (6, -), (5, +), (9, -), (11, +) You are supposed to find a threshold function that minimizes the error in the given dataset. Threshold functions look like this: f( x | a,b ) = sign(a-x).b where a is a real number and b is in {1,-1}. How many possible values should you consider to solve this problem? What is the value of a and b in the case that minimizes the error? What is the minimum error? Show how you found it. Note: Please first sort the dataset, and use the mid-point between two adjacent points as the threshold value to identify the misclassified points. Explain in detail how you have identified the misclassified points using the threshold value and the values of b.