From e45319ddecb6d80d32982b5eb76fe30d77e6516f Mon Sep 17 00:00:00 2001 From: mhjensen Date: Mon, 31 Aug 2020 13:44:42 +0200 Subject: [PATCH] correcting project --- doc/src/Projects/2020/Project1/Project1.do.txt | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/doc/src/Projects/2020/Project1/Project1.do.txt b/doc/src/Projects/2020/Project1/Project1.do.txt index 1f6d053fd..df0765b42 100644 --- a/doc/src/Projects/2020/Project1/Project1.do.txt +++ b/doc/src/Projects/2020/Project1/Project1.do.txt @@ -9,7 +9,7 @@ DATE: today The main aim of this project is to study in more detail various regression methods, including the Ordinary Least Squares (OLS) method, Ridge regression and finally Lasso regression. -The methods are in turn combined with resampling techniques. +The methods are in turn combined with resampling techniques like the bootstrap method and cross validation. We will first study how to fit polynomials to a specific two-dimensional function called "Franke's @@ -33,8 +33,8 @@ f(x,y) &= \frac{3}{4}\exp{\left(-\frac{(9x-2)^2}{4} - \frac{(9y-2)^2}{4}\right)} The function will be defined for $x,y\in [0,1]$. Our first step will be to perform an OLS regression analysis of this function, trying out a polynomial fit with an $x$ and $y$ dependence of the form $[x, y, -x^2, y^2, xy, \dots]$. We will also include cross-validation (or bootstrap) as -resampling technique. As in homeworks 1 and 2, we can use a uniform +x^2, y^2, xy, \dots]$. We will also include bootstrap first as +a resampling technique. After that we will include the cross-validation technique. As in homeworks 1 and 2, we can use a uniform distribution to set up the arrays of values for $x$ and $y$, or as in the example below just a set of fixed values for $x$ and $y$ with a given step @@ -100,7 +100,7 @@ plt.show() We will generate our own dataset for a function $\mathrm{FrankeFunction}(x,y)$ with $x,y \in [0,1]$. The function $f(x,y)$ is the Franke function. You should explore also the addition -an added stochastic noise to this function using the normal +of an added stochastic noise to this function using the normal distribution $\cal{N}(0,1)$. Write your own code (using either a matrix inversion or a singular