In this project we will write a series of solvers for the following linear
classifiers: 

1. Least squares
2. Regularized least squares
3. Hinge loss
4. Regularized hinge loss
5. Logistic regression

The outline of the project is given in the file project1_startingpoint.py on the course
website. You may use this as a starting point. The code for input and output
are already given in the course site. Your task would be to complete the five 
functions in this file. 

The input to your program is the data file and the train labels given in the datasets
posted course on the website. For example to run your project on the breast cancer
data with trainlabels.0 you would type

python project1.py <traindata> <testdata>

where <traindata> and <testdata> are in the same format as the
datasets *.train.0 and *.test.0 given on the course website. For
example see https://web.njit.edu/~usman/courses/cs675_fall20/bc.train.0
and https://web.njit.edu/~usman/courses/cs675_fall20/bc.test.0

The output of your project are just the predicted labels of each
datapoint in the test file. Each predicted label is either +1 or -1.
For each classifier you will output a separate file:

1. Least squares output is "least_squares_prediction"
2. Regularized least squares is "reg_least_squares_prediction"
3. Hinge loss is "hinge_prediction"
4. Regularized hinge loss is "regularized_hinge_prediction"
5. Logistic regression is "logistic_prediction"

Use eta=0.001 and stop condition of .001. For the regularized versions
keep lambda=0.01.

For logistic regression convert the labels from -1 and 1 to 0 and 1.
To predict the test datapoints we use 0 as the cutoff for least squares and
hinge and 0.5 for logistic.

Submit your assignment by copying it into the directory
/afs/cad/courses/ccs/f20/cs/675/101/<ucid>.
For example if your ucid is abc12 then copy your solution into 
/afs/cad/courses/ccs/f20/cs/675/101/abc12.

Your completed assignment is due by 1:30pm June 26th