Assume that we are training a linear model optimizing a squared loss function, which is defined as (y – )², with l2-norm regularizer. Write pseudo code that shows how both w and b are updated using gradient descent given one training example (Xn, Yn).
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- Suppose you are using a Linear SVM classifier with 2 class classification problem. Now you have been given the following data in which some points are circled red that are representing support vectors. a) Draw the decision boundary of linear SVM. Give a brief explanation. b) Suppose instead of SVM, we use regularized logistic regression to learn the classifier circle the points such that removing that example from the training set and running regularized logistic regression, we would get a different decision boundary than training with regularized logistic regression on the full sample . why ?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?4 the task is to estimate two models1. Cobduglus (after taking log to convert it into log-linear)2. Estimate the linear model without log
- When performing Naive Bayes operation especially for text classification, why is there a requirement for Laplace Smoothing or Additive Smoothing? Explain with considering an example of training and the test set and show how not having additive smoothing leads to undesirable outcomes.Consider a real random variable X with zero mean and variance σ2X . Suppose that we cannot directly observe X, but instead we can observe Yt := X + Wt, t ∈ [0, T ], where T > 0 and {Wt : t ∈ R} is a WSS process with zero mean and correlation function RW , uncorrelated with X.Further suppose that we use the following linear estimator to estimate X based on {Yt : t ∈ [0, T ]}:ˆXT =Z T0h(T − θ)Yθ dθ,i.e., we pass the process {Yt} through a causal LTI filter with impulse response h and sample theoutput at time T . We wish to design h to minimize the mean-squared error of the estimate.a. Use the orthogonality principle to write down a necessary and sufficient condition for theoptimal h. (The condition involves h, T , X, {Yt : t ∈ [0, T ]}, ˆXT , etc.)b. Use part a to derive a condition involving the optimal h that has the following form: for allτ ∈ [0, T ],a =Z T0h(θ)(b + c(τ − θ)) dθ,where a and b are constants and c is some function. (You must find a, b, and c in terms ofthe…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
- 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.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…Given a two-category classification problem under the univariate case, where there are two training sets (one for each category) as follows: D₁ = (-3,-1,0,4} D₂ = {-2,1,2,3,6,8} Given the test example x = 5, please answer the following questions: have and a) Assume that the likelihood function of each category has certain paramétric form. Specifically, we p(x | w₁) N, 07) p(x₂)~ N(μ₂, 02). Which category should we decide on when maximum-likelihood estimation is employed to make the prediction?
- give answer of all subparts in clear handwitten- For the model P + L ⇋ PL, what does each variable represent? Explain. The following questions refer to the variable θ.a. What is the definition of θ in words?b. What is the maximum value of θ? Explain your answer.Explain why linear predictor condition in predictor transformation is necessary.We are given the following training examples in 2D ((-3,5), +), ((-4, –2), +), ((2,1), -), ((4,3),–) Use +1 to map positive (+) examples and -1 to map negative (-) examples. We want to apply the learning algorithm for training a perceptron using the above data with starting weights wo = w1 = w2 = 0 and learning rate 7 = 0.1. In each iteration process the training examples in the order given above. Complete at most 3 iterations over the above training examples. What are the weights at the end of each iteration? Are these weights final