<SYSTEM_TASK:>
Given the following text description, write Python code to implement the functionality described below step by step
<END_TASK>
<USER_TASK:>
Description:
 Depression Identification
Step1:  1. State assumptions about your data
X are i.i.d. random variables.
y ~ Bern(p)
2. Formally define classification problem
Feature matrix X
Step2:  5. Compute accuracy
Step3:  6. Plot accuracy vs. sample size in simulation
Step4:  7. Apply method directly on real data
<ASSISTANT_TASK:>
Python Code:
import pandas as pd
import numpy as np
# Our data is cleaned by cleaning utility code
df = pd.read_csv('Clean_Data_Adults_1.csv')
# Separate labels and Features
df_labels = df['Depressed']
df_feats = df.drop(['Depressed', 'Unnamed: 0'], axis=1, inplace=False)
X = df_feats.get_values()  # features
y = df_labels.get_values() # labels
'''
Get rid of the negative values of the race_id columns
W.L.O.G., subtract the minimum negative from the entire column 
'''
def clean_negs(X):
    # Get indices of columns that contain negative values
    neg_col_inds = np.unique(np.where(X<0)[1])
    # Subtract minimum negative for each column
    for neg_i in neg_col_inds:
        neg_col = X[:, neg_i]
        min_neg = np.min(neg_col)
        new_col = [c - min_neg for c in neg_col] 
        X[:, neg_i] = new_col
        
    return X
# Preprocess training features
X = clean_negs(X)
Explanation: Depression Identification
End of explanation
'''
Data Preparation
'''
from sklearn.cross_validation import train_test_split
# Split the simulated data into training set and test set
# Randomly sample 20% data as the test set
train_X, test_X, train_y, test_y = train_test_split(X, y, test_size=0.2, random_state=42)
print 'Training set size is', train_X.shape
print 'Testing set size is', test_X.shape
max_n = len(train_X)
# Train the given classifier
def train_clf(clf, train_feats, train_labels):
    # Supervised training
    clf.fit(train_feats, train_labels)
    
# Test the given classifier anc calculate accuracy
def test_clf(clf, test_feats, test_labels):
    # Predict using test set
    predicted = clf.predict(test_feats)
    # Compute accuracy
    acc = np.mean(predicted == test_labels)
    return predicted, acc
Explanation: 1. State assumptions about your data
X are i.i.d. random variables.
y ~ Bern(p)
2. Formally define classification problem
Feature matrix X: R<sup>n x m</sup>
Each sample X<sub>i</sub> ∈ R<sup>m</sup>, i ∈ [1, n]
Label y<sub>i</sub> ∈ {0, 1}, i ∈ [1, n]
g(X) → y
G := { g: R → {0, 1} }
Goal: g<sup>*</sup> = argmin<sub>g ∈ G</sub> E[L(g(X), y)], where L denotes loss function.
The loss function L differs for different classifiers and is speficied in the classfication context below:
Multinomial Naive Bayes: negative joint likelihood
L = -log p(X, y)
Logistic Regression:  logistic loss (cross-entropy loss)
L = -log P(y|g(X)) = -(y · log(g(X)) + (1 - y) · log(1 - g(X))
K Nearest Neighbors
L = ∑<sub>i</sub> D(X<sub>i</sub>|y<sub>i</sub>=1, X|y=1) + ∑<sub>i</sub> D(X<sub>i</sub>|y<sub>i</sub>=0, X|y=0)
D(a, b) = (a - b)<sup>2</sup>
Support Vector Machine: squared hinge loss
L = (max{0, 1 − y · g(x)})<sup>2</sup>
Random Forest
L = ∑<sub>i</sub> (g(X<sub>i</sub>) - y<sub>i</sub>)<sup>2</sup>
3. Provide algorithm for solving problem (including choosing hyperparameters as appropriate)
Multinomial Naive Bayes
alpha: default =1.0 (Laplace smoothing parameter)
fit_prior: default = True (learn class prior probabilities)
Logistic Regression
penalty = 'l1' (l1 norm for penalization)
K Nearest Neighbors
n_neighbors = 10
Support Vector Machine (Linear Kernel)
C: default = 1.0 (penalty parameter of the error term)
Random Forest
n_estimators = 60 (number of trees)
criterion: default = 'gini'
4. Sample data from a simulation setting inspired by your data
End of explanation
# Compute accuracy of a model trained with a specific number of samples
def compute_acc(clf, n):
    train_clf(clf, train_X[:n], train_y[:n])
    predict_y, acc = test_clf(clf, test_X, test_y)
    return acc
from sklearn.naive_bayes import MultinomialNB
from sklearn.linear_model import LogisticRegression
from sklearn.neighbors import KNeighborsClassifier
from sklearn.svm import LinearSVC
from sklearn.ensemble import RandomForestClassifier
[acc_NB, acc_LG, acc_KNN, acc_SVM, acc_RF] = [[]  for i in xrange(5)] 
for n in xrange(100, max_n, 100):
    # Multinomial Naive Bayes
    multiNB = MultinomialNB()
    acc_NB.append(compute_acc(multiNB, n))
    
    # Logistic Regression
    lg = LogisticRegression(penalty='l1')
    acc_LG.append(compute_acc(lg, n))
    
    # K Nearest Neighbors
    knn = KNeighborsClassifier(n_neighbors=10)
    acc_KNN.append(compute_acc(knn, n))
    
    # Support Vector Machine
    svc = LinearSVC()
    acc_SVM.append(compute_acc(svc, n)) 
    
    # Random Forest
    rf = RandomForestClassifier(n_estimators=60) 
    acc_RF.append(compute_acc(rf, n))
Explanation: 5. Compute accuracy
End of explanation
%matplotlib inline
import matplotlib.pyplot as plt
sizes = range(100, max_n, 100)
fig = plt.figure(1)
fig.set_size_inches(9, 6.5)
plt.plot(sizes, acc_NB, label='Multinomial NB')
plt.plot(sizes, acc_LG, label='Logistic Regression')
plt.plot(sizes, acc_KNN, label='K Nearest Neighbors')
plt.plot(sizes, acc_SVM, label='Support Vector Machine')
plt.plot(sizes, acc_RF, label='Random Forest')
plt.legend(loc='best')
plt.xlabel('sample size')
plt.ylabel('Simulation Accuracy')
Explanation: 6. Plot accuracy vs. sample size in simulation
End of explanation
'''
Train models with all the training data
Evaluate using the test data
'''
# Multinomial Naive Bayes
multiNB = MultinomialNB()
train_clf(multiNB, train_X, train_y)
predict_y, acc_nb = test_clf(multiNB, test_X, test_y)
# Logistic Regression
lg = LogisticRegression(penalty='l1')
train_clf(lg, train_X, train_y)
predict_y, acc_lg = test_clf(lg, test_X, test_y)
# K Nearest Neighbors
knn = KNeighborsClassifier(n_neighbors=10)
train_clf(knn, train_X, train_y)
predict_y, acc_knn = test_clf(knn, test_X, test_y)
# Support Vector Machine
svc = LinearSVC()
train_clf(svc, train_X, train_y)
predict_y, acc_svc = test_clf(svc, test_X, test_y)
# Random Forest
rf = RandomForestClassifier(n_estimators=60)
train_clf(rf, train_X, train_y)
predict_y, acc_rf = test_clf(rf, test_X, test_y)
print 'Multinomial Naive Bayes accuracy is', acc_nb
print 'Logistic Regression accuracy is', acc_lg
print 'K Nearest Neighbors accuracy is', acc_knn
print 'Support Vector Machine (Linear Kernel) accuracy is', acc_svc
print 'Random Forest accuracy is', acc_rf
# Visualize classifier performance
x = range(5)
y = [acc_nb, acc_lg, acc_knn, acc_svc, acc_rf]
clf_names = ['Multinomial Naive Bayes', 'Logistic Regression', \
             'K Nearest Neighbors', 'Support Vector Machine', 'Random Forest']
width = 0.6/1.2
plt.bar(x, y, width)
plt.title('Classifier Performance')
plt.xticks(x, clf_names, rotation=25)
plt.ylabel('Accuracy')
Explanation: 7. Apply method directly on real data
End of explanation
<END_TASK>