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In class, we derived linear regression and various learning algorithms based on gradient descent. In addition to the least square objective, we also learned its probabilistic perspective where each observation is assumed to have a Gaussian noise. (i.e., Noise of each example is an independent and identically distributed sample from a normal distribution) In this problem, you are supposed to deal with the following regression model that includes one feature x1 that relates linearly/quadratically and another linear feature x2. y = 00 + 01x1+02x2+ 03xi+ € where e ~ N(0, o²) You are provided with a training observations D = {(x{", x2", y(?)|1 < i < m}.Derive the conditional log-likelihood that will be later maximized to make D most likely. m 1 m log 1 Ozx – 0zx")? - - - - 202 i=1

In class, we derived linear regression and various learning algorithms based on gradient descent. In addition to the least square objective, we also learned its probabilistic perspective where each observation is assumed to have a Gaussian noise. (i.e., Noise of each example is an independent and identically distributed sample from a normal distribution) In this problem, you are supposed to deal with the following regression model that includes one feature x1 that relates linearly/quadratically and another linear feature x2. y = 00 + 01x1+02x2+ 03xi+ € where e ~ N(0, o²) You are provided with a training observations D = {(x{", x2", y(?)|1 < i < m}.Derive the conditional log-likelihood that will be later maximized to make D most likely. m 1 m log 1 Ozx – 0zx")? - - - - 202 i=1

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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In class, we derived linear regression and various learning algorithms based on gradient descent. In addition to the least square objective, we also learned its probabilistic perspective where each observation is assumed to have a Gaussian noise. (i.e., Noise of each example is an independent and identically distributed sample from a normal distribution) In this problem, you are supposed to deal with the following regression model that includes one feature x1 that relates linearly/quadratically and another linear feature x2. y = 00 + 01x1+02x2+ 03xi+ € where e ~ N(0, o²) You are provided with a training observations D = {(x{", x2", y(?)|1 < i < m}.Derive the conditional log-likelihood that will be later maximized to make D most likely. m 1 m log- 1 (y® – 0o – O1rf° – 62x2" - - - 202 i=1 (y() – 6o – 0,xfº – 02x – Ozxf1²)², m 1 log- exp(- 202 i=1 m 1 m log 2no 1 (y) – 0o – O,x – 02x – Ozxf?)² | - 202 i=1
Transcribed Image Text:In class, we derived linear regression and various learning algorithms based on gradient descent. In addition to the least square objective, we also learned its probabilistic perspective where each observation is assumed to have a Gaussian noise. (i.e., Noise of each example is an independent and identically distributed sample from a normal distribution) In this problem, you are supposed to deal with the following regression model that includes one feature x1 that relates linearly/quadratically and another linear feature x2. y = 00 + 01x1+02x2+ 03xi+ € where e ~ N(0, o²) You are provided with a training observations D = {(x{", x2", y(?)|1 < i < m}.Derive the conditional log-likelihood that will be later maximized to make D most likely. m 1 m log- 1 (y® – 0o – O1rf° – 62x2" - - - 202 i=1 (y() – 6o – 0,xfº – 02x – Ozxf1²)², m 1 log- exp(- 202 i=1 m 1 m log 2no 1 (y) – 0o – O,x – 02x – Ozxf?)² | - 202 i=1
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