WEEK 5: • Build an Artificial Neural Network by implementing the Backpropagation algorithm and test the same using appropriate data sets.
WEEK 5: • Build an Artificial Neural Network by implementing the Backpropagation algorithm and test the same using appropriate data sets.
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.
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
WEEK 8: Write a program to implement k-Nearest Neighbors algorithm to classify the iris data set. Print both correct and wrong predictions.
WEEK 8: Write a program to implement k-Nearest Neighbors algorithm to classify the iris data set. Print both correct and wrong predictions.
K-Nearest Neighbor Algorithm
Training algorithm:
·
For each training example (x, f
(x)), add the example to the list training examples Classification algorithm:
o Given
a query instance xq to be classified,
§ Let
x1 . . .xk denote the k instances from training examples that are nearest to xq
§ Return
Where, f(xi) function to calculate the mean value of the k nearest
training examples.

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