Assume the following data generative model: y = f(x) + , where follows a standard...

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Assume the following data generative model: y = f(x) + €, where € follows a standard Gaussian distribution, i.e., € ~ N (0, 1). Assume a linear model for f(x) = wx. We now modify the data generative model by assuming that € follows a Laplacian distribution whose probability density function is p(e) = A/ 2 exp(-^|E|), where A is a positive constant. Based on the above noise model about €, derive the log-likelihood for the observed training data {(x1, y1), . ..,(xn, yn)) and the objective function for computing the solution w. Does the problem have a closed form solution such as the Least Sqaure Regression? Assume the following data generative model: y = f(x) + €, where € follows a standard Gaussian distribution, i.e., € ~ N (0, 1). Assume a linear model for f(x) = wx. We now modify the data generative model by assuming that € follows a Laplacian distribution whose probability density function is p(e) = A/ 2 exp(-^|E|), where A is a positive constant. Based on the above noise model about €, derive the log-likelihood for the observed training data {(x1, y1), . ..,(xn, yn)) and the objective function for computing the solution w. Does the problem have a closed form solution such as the Least Sqaure Regression?