1. Maximum Likelihood Estimation. Assume we have a dataset with N pairs of (inpu

Question

1. Maximum Likelihood Estimation. Assume we have a dataset with N pairs of (input,output) samples in which the i-th sample has one real-valued input feature r and one real-valued output y'. We have the following model with one unknown parameter w which we want to learn from data yN(exp(wr'), 1), where N(, *) denotes a normal distribution with mean and variance 2. 1. Determine if the task of estimating w is a linear or a nonlinear regression? Explain 2. Assume you decide to do a maximum likelihood estimation of w. Which of the followin;g equations you need to solve to determine w (exactly one)? Provide all your derivations of the maximum likelihood estimation to arrive at this solution exp (wc Tj exp wx

Explanation / Answer

Answer: See the answer below:

1. For the given problem, the relationship between dependent (y) and independent (x) variables is non-linear (as evident from exponential function). For such a relationship, use of linear regression technique will not be adequately able to represent the relationship between variables. Hence, for such a scenario, use of non-linear regression will be appropriate.

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