More Python, numpy and sklearn

We will use the following data sets:

titanic = sns.load_dataset("titanic")
iris = sns.load_dataset("iris")

Q1 (20 pts) Working with numpy.random.

Part 1 (10 pts) Consider a sequence of \(n\) Bernoulli trials with success probabilty \(p\) per trial. A string of consecutive successes is known as a success run. Write a function that returns the counts for runs of length \(k\) for each \(k\) observed in a dictionary.

For example: if the trials were [0, 1, 0, 1, 1, 0, 0, 0, 0, 1], the function should return

{1: 2, 2: 1})

In [1]:

Part 2 (10 pts) Continuing from Part 1, what is the probability of observing at least one run of length 5 or more when \(n=100\) and \(p=0.5\)?. Estimate this from 100,000 simulated experiments. Is this more, less or equally likely than finding runs of length 7 or more when \(p=0.7\)?

In [1]:

Q2. (30 pts)

Using RandomForestClassifier from sklearn, find the 5 most important predictors of survival on the Titanic. Compare the accuracy of prediction using only these 5 predictors and using all non-redundant predictors. Some intial pre-processing code is provided. Hint: check out the pandas.get_dummies() function.

In [1]:

titanic = sns.load_dataset("titanic")
titanic.head()

Out[1]:

	survived	pclass	sex	age	sibsp	parch	fare	embarked	class	who	adult_male	deck	embark_town	alive	alone
0	0	3	male	22.0	1	0	7.2500	S	Third	man	True	NaN	Southampton	no	False
1	1	1	female	38.0	1	0	71.2833	C	First	woman	False	C	Cherbourg	yes	False
2	1	3	female	26.0	0	0	7.9250	S	Third	woman	False	NaN	Southampton	yes	True
3	1	1	female	35.0	1	0	53.1000	S	First	woman	False	C	Southampton	yes	False
4	0	3	male	35.0	0	0	8.0500	S	Third	man	True	NaN	Southampton	no	True

In [2]:

titanic.drop(['alive', 'embarked', 'class', 'who', 'adult_male'], axis=1, inplace=True)
titanic.dropna(axis=0, inplace=True)
titanic.head()

Out[2]:

	survived	pclass	sex	age	sibsp	parch	fare	deck	embark_town	alone
1	1	1	female	38.0	1	0	71.2833	C	Cherbourg	False
3	1	1	female	35.0	1	0	53.1000	C	Southampton	False
6	0	1	male	54.0	0	0	51.8625	E	Southampton	True
10	1	3	female	4.0	1	1	16.7000	G	Southampton	False
11	1	1	female	58.0	0	0	26.5500	C	Southampton	True

In [3]:

Q2. (25 pts)

Using sklearn, perform unsupervised learning of the iris data using 2 different clustering methods. Do NOT assume you know the number of clusters - rather the code should either determine it from the data or compare models with different numbers of components using some appropriate test statistic. Make a pairwise scatter plot of the four predictor variables indicating cluster by color for each unsupervised learning method used.

In [3]:

Q3. (50 pts)

Write code to generate a plot similar to the following using the explanation for generation of 1D Cellular Automata found here. You should only need to use standard Python, numpy and matplotllib.

To make it simpler, I have provided the code for plotting below. All you need to do is to supply the make_ca function (which may of course use as many ohter custom functons as you deem necessary). As you can see from the code below, the make_ca function takes 3 arguments

rule - an integer e.g. 30
init - an initial state i.e. the first row of the image
niter - the number of iterations i.e. the number of rows in the image

In [3]:

In [3]:

from matplotlib.ticker import NullFormatter, IndexLocator

def plot_grid(rule, grid, ax=None):
    if ax is None:
        ax = plt.subplot(111)
    ax.grid(True, which='major', color='grey', linewidth=0.5)
    ax.imshow(grid, interpolation='none', cmap='Greys', aspect=1, alpha=0.8)
    ax.xaxis.set_major_locator(IndexLocator(1, 0))
    ax.yaxis.set_major_locator(IndexLocator(1, 0))
    ax.xaxis.set_major_formatter( NullFormatter() )
    ax.yaxis.set_major_formatter( NullFormatter() )
    ax.set_title('Rule %d' % rule)

In [4]:

niter = 15
width = niter*2+1
init = np.zeros(width, 'int')
init[width//2] = 1
rules = np.array([30, 54, 60, 62, 90, 94, 102, 110, 122, 126,
                  150, 158, 182, 188, 190, 220, 222, 250]).reshape((-1, 3))

nrows, ncols = rules.shape
fig, axes = plt.subplots(nrows, ncols, figsize=(ncols*3, nrows*2))
for i in range(nrows):
    for j in range(ncols):
        grid = make_ca(rules[i, j], init, niter)
        plot_grid(rules[i, j], grid, ax=axes[i,j])
plt.tight_layout()

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-4-add074bebf92> in <module>()
     10 for i in range(nrows):
     11     for j in range(ncols):
---> 12         grid = make_ca(rules[i, j], init, niter)
     13         plot_grid(rules[i, j], grid, ax=axes[i,j])
     14 plt.tight_layout()

NameError: name 'make_ca' is not defined