0. This document

This is an Rmarkdown (.Rmd) document, and you may be reading the HTML version (after its compilation). Please get the .Rmd version in our website, in order to:

edit it (with RStudio),
write down the solutions to the problems (code & comments),
and compile it (with RStudio) using [CTRL+SHIFT+K].

In case of errors, look for help or contact your instructor.

PROBLEM 1: a neural network for regression

Creating simulated data

The following lines create a dataset in an independent variable called x and a dependent variable called y.

set.seed(123)
x = rnorm(n=100, mean=0, sd=0.5)
y = 4.1 - 1.3*x - 1.5*x^2 + rnorm(n=100, mean=0, sd=0.3)
m = data.frame(x=x, y=y)

Here I don’t ask you to pay attention to how the data has been generated.

1.1. Fit the data to a neural network of a single neuron in the input layer (variable `x`), 5 neurons in the hidden layer, and variable `y` in the output layer. Write the list of weights defining the fitted network.

# Here just launch the fitting and make many
# attemps in order to get close to the real minimum

The fitted network has weights: …

1.2. Plot original data, and add in red colour the predictions the net would do over the sampled data.

# Code for plotting data (x,y)
# Code for adding points in red color to plot

1.3. Repeat exercices 1.1 and 1.2 for a network with 3 neurons in the hidden layer.

# Here your code with final plot

1.3. Explain “in a few words” how to perform “cross-validation” in order to choose the best of those two types of network (5 neurons vs 3 neurons).

Here your explanation.

Neural networks (evaluation problems)

Data Mining (SIQ022-SIQ522)

Put your name here

0. This document

PROBLEM 1: a neural network for regression

Creating simulated data

1.1. Fit the data to a neural network of a single neuron in the input layer (variable `x`), 5 neurons in the hidden layer, and variable `y` in the output layer. Write the list of weights defining the fitted network.

1.2. Plot original data, and add in red colour the predictions the net would do over the sampled data.

1.3. Repeat exercices 1.1 and 1.2 for a network with 3 neurons in the hidden layer.

1.3. Explain “in a few words” how to perform “cross-validation” in order to choose the best of those two types of network (5 neurons vs 3 neurons).

Neural networks (evaluation problems)

Data Mining (SIQ022-SIQ522)

Put your name here

0. This document

PROBLEM 1: a neural network for regression

Creating simulated data

1.1. Fit the data to a neural network of a single neuron in the input layer (variable x), 5 neurons in the hidden layer, and variable y in the output layer. Write the list of weights defining the fitted network.

1.2. Plot original data, and add in red colour the predictions the net would do over the sampled data.

1.3. Repeat exercices 1.1 and 1.2 for a network with 3 neurons in the hidden layer.

1.3. Explain “in a few words” how to perform “cross-validation” in order to choose the best of those two types of network (5 neurons vs 3 neurons).

1.1. Fit the data to a neural network of a single neuron in the input layer (variable `x`), 5 neurons in the hidden layer, and variable `y` in the output layer. Write the list of weights defining the fitted network.