Description
Note. The goal of this assignment is for you to learn these concepts in practice. You are not
allowed to use MATLAB’s built-in functions for fitting curves. However, if you exhausted your
effort and did not manage to come up with a solution, using those functions will get you 2/5
points on this assignment.
We use wine dataset already available in Matlab. It can be accessed by
[x,t] = wine_dataset;
Alternatively, it can be downloaded from
http://www.mediafire.com/file/dfmmwxumxfh3ifv/wine.mat/file
It contains 178 different wines (observations) from 3 winery (labels) with these 13 features:
1. Alcohol
2. Malic acid
3. Ash
4. Alkalinity of ash
5. Magnesium
6. Total phenols
7. Flavonoids
8. Nonflavonoid phenols
9. Proanthocyanidins
10. Color intensity
11. Hue
12. OD280/OD315 of diluted wines
13. Proline
The last column of the wine.mat file(if downloaded), or, the variable t (if you use Matlab’s built-in
data) has the labels of each wine, meaning that it belongs to one of the three wineries.
v.2
Question-0 (Preprocessing)
Remove all row corresponding to the labeled winery 3. After this process, you should have only 2
labels on your data.
Question-1 (0.25 pts)
Load the data and plot (visualize) the data points of wines by their Alcohol (feature 1 in x axis) and
Malic acid (feature 2 in y axis).
Question-2 (1 pts)
Pick Magnesium and Color intensity as your two features and for degrees n =1, …, 10 fit a polynomial
of degree n to your data. Plot those fitting lines on the data. You can check the correctness of your
solution with MALAB’s built-in curve fitting function.
Question-3 (1 pts)
For each learned function (n=1, …, 10), compute the empirical square loss (ERM) on data and plot
it as a function of n.
Question-4 (1 pts)
Now, fix the n=10 and add a lasso regularization for your predictor of data. Vary the regularization
parameter in a loop of 20 and visualize the RLM loss. You can check the correctness of your solution
with MALAB’s built-in Lasso.
Question-5 (0.25 pts)
Now, add a third feature of Hue to your data and plot the three in a 3D plot.
Question-6 (1 pts)
For your three selected features, fit a surface to your data of a degree 10.
Question-7 (0.5 pts)
Compare the ERM loss of your surface (question 6) and line (question 3) predictors.
v.2
Question-8 (1 bonus pts)
Fit the data with a Perceptron classifier and compare the loss with respect to your fitted lines
(question-3)
