Manually train a hypothesis function h(x) = g(Ō¹x) based on the following training instances using stochastic gradient ascent rule. The initial values of parameters are 0o = 0.1,0₁ = 0.1,0₂ = 0.1. The learning rate a is 0.1. Please update each parameter at least five times. X1 0 0 1 1 X2 0 1 0 1 y 1 1 0 0
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Please write this out by hand and not by code. I would be so grateful.
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- 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(-w0-w1*x1-w2*x2)). What will be value of the loss function at t? What will be the values of w0, w1 and w2 at (t+1) with learning rate ɳ=1?Given access to a robot's motion model and prior belief distribution, how can we compute the probability P(x|u) where x is the latest robot's state and u is the control applied at a previous state x'?When a temperature gauge surpasses a threshold, your local nuclear power station sounds an alarm. Core temperature is gauged. Consider the Boolean variables A (alarm sounds), FA (faulty alarm), and FG (faulty gauge) and the multivalued nodes G (gauge reading) and T (real core temperature). Since the gauge is more likely to fail at high core temperatures, draw a Bayesian network for this domain.
- The room temperature x in Fahrenheit (F) is converted to y in Celsius (C) through the function y = f(x) = 5(x-32)/9. Let a fuzzy set B1 (in Fahrenheit) be defined by B1 = 0.15/76 + 0.42/78 + 0.78/80 + 1.0/82 + 1.0/84 What is the induced fuzzy set of B1 in terms of the extension principle? B2 = ?A model is used to obtain a prediction by accepting features as inputs and returning a prediction in the is.... subset of machine learning. The following are some new cutting-edge models that have become feasible: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)?
- 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 ProgrammingIn the context of evolutionary computing the goal function is known as the fitnessfunction and the problem is to maximize it. The typical formulation has to be changedin a simple way.min f (x) = − max[− f (x)] (4.9)Another requirement is that the goal function is positive.Phenotype evolution treats x as a phenotype and the goal function as the fitnessfunction. The typical framework for the method is as follows:The room temperature x in Fahrenheit is converted to y in Celsius through the function y = f(x) = 5(x-32)/9. Let a fuzzy set B1 (in Fahrenheit) be defined by B1 = 0.15/76 + 0.42/78 + 0.78/80 + 1.0/82 + 1.0/84 What is the induced fuzzy set of B1 in terms of the extension principle? B2 = ?
- I need help to solve problem Manually fit a linear function h_(\theta )(vec(x))=vec(\theta )^(T)*vec(x) based on the following training instances using the stochastic gradient descent algorithm. The initial values of parameters are \theta _(0)=0.1,\theta _(1)=0.1,\theta _(2)=0.1. The learning rate \alpha is 0.1. Please update each parameter at least five times.X_1,X_2,Y 0 0 20 1 31 0 31 1 4Show the operation of all the bin-packing strategies discussed in our classes: Next fit, First fit, Best fit, and First fit decreasing, on the input 0.42, 0.25, 0.27, 0.07, 0.72, 0.86, 0.09, 0.44, 0.50, 0.68, 0.73, 0.31, 0.78, 0.17, 0.79, 0.37, 0.73, 0.23, 0.30.Subject: Machine Learning Given the neural network below, calculate and show the weight changes that would be made by one step of BACKPROPAGATION for the training instance (X1,X2)=(0,05,0.10) and (Y1, Y2)=(0.01,0.99). Assume that the hidden (H1 & H2) and output (Y1 & Y2) units use sigmoid functions, the network is being trained to minimize squared error, and the learning rate is 1. Edges from constant b1 and b2 on the side indicate bias parameters.