Question

1. (Jupyter) Consider the function $f(x) = \frac{1}{2}x^2$. Write a simple Python program to optimize this objective function with gradient descent. Show that the function is a minimum at $x^* = 0$. 2. (Jupyter) Generate N data points \{$(y_i, x_i)$\} where $y = mx + b$ and add Gaussian noise. (a) Plot the data. (b) Fit a linear model and print the coefficients $m$ and $b$. (c) Plot the optimal model together with the data.

          1. (Jupyter) Consider the function $f(x) = \frac{1}{2}x^2$. Write a simple Python program to optimize this objective function with gradient descent. Show that the function is a minimum at $x^* = 0$.
2. (Jupyter) Generate N data points \{$(y_i, x_i)$\} where $y = mx + b$ and add Gaussian noise. (a) Plot the data. (b) Fit a linear model and print the coefficients $m$ and $b$. (c) Plot the optimal model together with the data.

$1. (Jupyter) Consider the function f(x) = (1)/(2)x^2. Write a simple Python program to optimize this objective function with gradient descent. Show that the function is a minimum at x^* = 0. 2. (Jupyter) Generate N data points {(yi, xi)} where y = mx + b and add Gaussian noise. (a) Plot the data. (b) Fit a linear model and print the coefficients m and b. (c) Plot the optimal model together with the data.$

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