# Neural Networks for Regression

• Szeliski 2022 Chapter 5

# Exercise 3. Regression.

One in-house project is to classify images of remote galaxies, which are often distorted due to the gravity of dark matter. This effect is known as gravitational lensing.

A sample dataset can be found at github. This directory contains

• A data file, sphere-pm.csv
• 10000 images of distorted galaxies
• A python file Dataset.py defining a subclass of Dataset to manage these data

The CSV file has the form

index,filename,source,lens,chi,x,y,einsteinR,sigma,sigma2,theta,nterms
"00001",image-00001.png,s,p,50,30,40,19,31,0,0,16

The interesting columns are the filename which points to the input image, and the four output variables $$x$$, $$y$$, einsteinR, and $$\sigma$$. These variables are integers or floating point values, and make a case for regression The other columns are associated with more advanced problem instances and should be ignored.

1. Study the Dataset class Dataset.py. How does it compare to how you have managed datasets in PyTorch so far? How is the dataset managed?
2. Use this class to test if you can train a network to determine the four outputs for an image.

# Exercise 4. Own Data (Optional)

Making your own training data may be difficult, because of the large quantity of data that you need, but if you want to give it a try, I would recommend this.

1. Team up with everybody else who wants to do this problem.
2. Each team member makes a set of hand-drawn digits or letters, at least ten versions of each digit each.
3. Digitise the digits into image files. Make sure that everybody uses the same resolution (image size in pixels).
• The resolution must be large enough to make digits recognisable, but small enough to save computational power.
• Somewhere between $$28\times28$$ (same as the MIST dataset) and $$64\times64$$ sounds reasonable.
4. Gather the images into a dataset with their labels (digit value). You may use Exercise 3 as an example.
5. Merge and share the dataset.
6. Train and test a neural network to read the digits.
7. Try different networks, at least the ones you have used in previous exercises.