The following distribution 7(x|o,q) 2(202)/4r(1/9) is a generalization of the univariate Gaussian distribution, where I denotes...

  

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The following distribution 7(x|o²,q) 2(202)¹/4r(1/9) is a generalization of the univariate Gaussian distribution, where I denotes the Gamma function (see https://en.wikipedia.org/wiki/Gamma_function for details, but you only need to know r(1/2) = √7 for this problem). Show that this distribution reduces to the Gaussian distribution when q = 2. Consider a regression model in which that target variable is given by t = y(x, w) + € and e is a random noise variable drawn from the distribution (2). Show that the log likelihood log (tx, w, ²) = Al 681-001 CS 695-001 | Assignment 1 Fall 2022 function over w and ², for an observed data set of input vectors x = [x₁,...,xN] € RN and corresponding target variables t = [t₁...,tN] RN, is given by 202 -exp(- 1 N N y(x₁, w) -til-log(20²) + cst, 9 i=1 where 'cst' denotes terms independent of both w and ². The following distribution 7(x|o²,q) 2(202) ¹/4r(1/9) is a generalization of the univariate Gaussian distribution, where I denotes the Gamma function (see https://en.wikipedia.org/wiki/Gamma_function for details, but you only need to know r(1/2) = √ for this problem). Show that this distribution reduces to the Gaussian distribution when q = 2. Consider a regression model in which that target variable is given by t = y(x, w) + € and e is a random noise variable drawn from the distribution (2). Show that the log likelihood -exp(- 1 Al 681-001 CS 695-001 | Assignment 1 Fall 2022 function over w and ², for an observed data set of input vectors x = [x₁,...,XN] € RN and corresponding target variables t = [₁,...,t] RN, is given by log (tx, w, ²) = N N 202 ly (x₁, w) -t-log(20²) + cst, i=1 9 where 'cst' denotes terms independent of both w and ². The following distribution 7(x|o²,q) 2(202)¹/4r(1/9) is a generalization of the univariate Gaussian distribution, where I denotes the Gamma function (see https://en.wikipedia.org/wiki/Gamma_function for details, but you only need to know r(1/2) = √7 for this problem). Show that this distribution reduces to the Gaussian distribution when q = 2. Consider a regression model in which that target variable is given by t = y(x, w) + € and e is a random noise variable drawn from the distribution (2). Show that the log likelihood log (tx, w, ²) = Al 681-001 CS 695-001 | Assignment 1 Fall 2022 function over w and ², for an observed data set of input vectors x = [x₁,...,xN] € RN and corresponding target variables t = [t₁...,tN] RN, is given by 202 -exp(- 1 N N y(x₁, w) -til-log(20²) + cst, 9 i=1 where 'cst' denotes terms independent of both w and ². The following distribution 7(x|o²,q) 2(202) ¹/4r(1/9) is a generalization of the univariate Gaussian distribution, where I denotes the Gamma function (see https://en.wikipedia.org/wiki/Gamma_function for details, but you only need to know r(1/2) = √ for this problem). Show that this distribution reduces to the Gaussian distribution when q = 2. Consider a regression model in which that target variable is given by t = y(x, w) + € and e is a random noise variable drawn from the distribution (2). Show that the log likelihood -exp(- 1 Al 681-001 CS 695-001 | Assignment 1 Fall 2022 function over w and ², for an observed data set of input vectors x = [x₁,...,XN] € RN and corresponding target variables t = [₁,...,t] RN, is given by log (tx, w, ²) = N N 202 ly (x₁, w) -t-log(20²) + cst, i=1 9 where 'cst' denotes terms independent of both w and ².

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