Consider a logistic regression classifier that implements the 2-input OR gate. At iteration t, the parameters are given by w0=0, w1=0, w2=0. Given binary input (x1,x2), output of logistic regression is given by 1/(1+exp(-
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- 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.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.Implement a simple linear regression model using Python without using any machine learning libraries like scikit-learn. Your model should take a dataset of input features X and corresponding target values y, and it should output the coefficients w and b for the linear equation y =wX + b
- the logit function(given as l(x)) is the log of odds function. what could be the range of logit function in the domain x=[0,1]?The task is to implement density estimation using the K-NN method. Obtain an iidsample of N ≥ 1 points from a univariate normal (Gaussian) distribution (let us callthe random variable X) centered at 1 and with variance 2. Now, empirically obtain anestimate of the density from the sample points using the K-NN method, for any valueof K, where 1 ≤ K ≤ N. Produce one plot for each of the following cases (each plotshould show the following three items: the N data points (instances or realizations ofX) and the true and estimated densities versus x for a large number – e.g., 1000, 10000– of discrete, linearly-spaced x values): (i) K = N = 1, (ii) K = 2, N = 10, (iii) K = 10,N = 10, (iv) K = 10, N= 1000, (v) K = 100, N= 1000, (vi) K = N = 50,000. Pleaseprovide appropriate axis labels and legends. Thus there should be a total of six figures(plots),Use Matlab scripts to simulate the following experiment. Computer A sends a message to computer B over an unreliable radio link. The message is encoded so that B can detect when errors have been introduced into the message during transmission. If B detects an error, it requests A to retransmit it. If the probability of a message transmission error is q = .1. (1) Plot the PMF of the resulting geometric random variable. (2) What is the probability that a message needs to be transmitted more than two times? (3)
- 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. =• Simplify the Boolean functions by means of the tabulation matching method: a. F(w,x,y,z) = Σm(2,3,12,13,14,15) b. P(m,n,o,p,q,r) =Em(6,9,13,18,19,25,27,29,41,45,57,61) c. P(A,B,C,D,E,F,G) =Σm(20,28,38,39,52,60,102,103)Solve in R programming language: Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3. (a) Find p(X<1.25). (b) Find EX. (c) Find the variance of X.
- We have that y*n+1=y*n=y*. Using the given model: yn+1 = byn(1-yn), we find that y* = 1-1/b and y* = 0 are fixed points. I have the function:def main(b,yInit,n): out=np.zeros((n,1)) y = yInit for i in range(n): out[i] = y y = b*(1-y)*y return out The graph model of this would depend both on the value of the initial population (y*) and choice of b. I need to graph this in python using interactive sliders widget [from matplotlib.widgets import slider], where one slider will control b value (x-axis) and another for y value (y-axis). I have the skeleton code for the sliders but have no idea how to graph this equation with it. (y* = between 0 to 1, b = 0 to 4)Computer Science A way to avoid overfitting in Deep Neural Networks is to add an additional term R to the loss function L (for example L can be the cross entropy loss) as follows: L(w) + λR(w). (1) You know that one choice for R is the L2 norm, i.e. R(w) = ||w||2 2 . One friend of yours from the School of Maths told you however that there’s no need to use squares (i.e. powers of two) and that you can achieve the same effect by using absolute values, i.e. the L1 norm: R(w) = ||w||1. Would you agree with him? i.e. is the use of the L2 norm equivalent to using the L1 norm for regularization purposes? Justify your answerUse the two methods to simulate a Poisson process: For fix t(sayt = 10) , and rate lambda = 2 simulate N(t) and the arrival times S_1. Upload a r-script file if you did it in r or a pdf file with the code and plot(s) if you did it in another other programming language.