Homework A Let us use the log-likelihood function to derive an on-line adaptation rule analogous to LMS. Our goal is to update our estimate of weights.

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Homework A Let us use the log-likelihood function to derive an on-line adaptation rule analogous to LMS. Our goal is to update our estimate of weights and our estimate of noise variance sigma with each new data point. Find the first and second derivative of the log-likelihood with respect to the weights and using Newton-Raphson write an update rule for w. Use the same technique to derive an update rule for estimate of hint: take derivatives with respect to

Homework B Using simulations, determine whether ML estimate of s is unbiased or not. The “true” underlying process What you measure Your model of the process Start with n=5 data points. Compute for a given batch of data and then repeat for another batch. Do this a number of times to get an average value for . Now increase n and repeat the procedure.