WEEK 10: Implement the non-parametric Locally Weighted Regression algorithm in order to fit data points. Select appropriate data set for your experiment and draw graphs.
Locally
Weighted Regression Algorithm
Regression:
·
Regression is a technique from statistics that are used to predict
values of the desired target quantity when the target quantity is continuous.
o
In regression, we seek to identify (or estimate) a continuous variable y
associated with a given input vector x.
§
y is called the dependent variable.
§ x is called the independent variable.
Loess/Lowess
Regression:
Loess
regression is a nonparametric technique that uses local weighted regression to
fit a smooth curve through points in a scatter plot.
Lowess
Algorithm:
·
Locally weighted
regression is a very powerful nonparametric model used in statistical learning.
·
Given a dataset X, y, we
attempt to find a model parameter β(x) that minimizes residual sum of weighted
squared errors.
·
The weights are given by
a kernel function (k or w) which can be chosen arbitrarily
Algorithm
1.
Read the Given data Sample to X and the curve (linear or nonlinear) to Y
2.
Set the value for Smoothening parameter or Free parameter say τ
3. Set
the bias /Point of interest set x0 which is a subset of X
4.
Determine the weight matrix using:
5.
Determine the value of model term parameter β using:
6.
Prediction = x0*β
Python
Program to Implement and Demonstrate Locally Weighted Regression Algorithm
