Naive bayes

numpy_ml/naive_bayes/naive_bayes.py

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+import numpy as np 
+
+class GaussianNB():
+    """
+    Gaussian Naive Bayes 
+
+    Assume each class conditional feature distribution is
+    independent and estimate the mean and variance from the
+    training data
+
+    Parameters
+    ----------
+    epsilon: float
+        a value that add to variance to prevent numerical error
+
+    Attributes
+    ----------
+    num_class : ndarray of shape (n_classes,)
+        count of each class in the training sample
+
+    mean: ndarray of shape (n_classes,)
+            mean of each variance
+
+    sigma: ndarray of shape (n_classes,)
+        variance of each class
+
+    prior :  ndarray of shape (n_classes,)
+            probability of each class
+
+    """
+    def __init__(self,eps=1e-6):
+        self.eps = eps 
+
+    def fit(self,X,y):
+        """
+        Train the model with X,y
+
+        Parameters
+        ----------
+        X: ndarray of shape (n_samples, n_features)
+            Input data
+        y: ndarray of shape (n_samples,)
+            Target
+
+        returns
+        --------
+        self: object
+        """
+
+        self.n_sample, self.n_features = X.shape
+        self.labels = np.unique(y)
+        self.n_classes = len(self.labels)
+
+        self.mean = np.zeros((self.n_classes,self.n_features))
+        self.sigma = np.zeros((self.n_classes,self.n_features))
+        self.prior = np.zeros((self.n_classes,))
+
+        for i in range(self.n_classes):
+            X_c = X[y==i,:]
+
+            self.mean[i,:] = np.mean(X_c,axis=0)
+            self.sigma[i,:] = np.var(X_c,axis=0) + self.eps
+            self.prior[i] = X_c.shape[0]/self.n_sample
+
+        return self
+
+    def predict(self,X):
+        """
+        used the trained model to generate prediction
+
+        Parameters
+        ---------
+        X: ndarray of shape (n_samples, n_features)
+            Input data
+
+        returns
+        -------
+        probs : ndarray of shape (n_samples, n_classes)
+                The model predictions for each items in X to be in each class
+        """
+
+        probs = np.zeros((X.shape[0],self.n_classes))
+        for i in range(self.n_classes):
+            probs[:,i] = self.prob(X,self.mean[i,:],self.sigma[i,:],self.prior[i])
+
+
+        return probs
+
+    def prob(self,X,mean,sigma,prior):
+        """
+        compute the joint log likelihood of data based on gaussian distribution
+
+        X: ndarray of shape (n_samples, n_features)
+            Input data
+
+        mean: ndarray of shape (n_classes,)
+            mean of each variance
+
+        sigma: ndarray of shape (n_classes,)
+            variance of each class
+
+        prior :  ndarray of shape (n_classes,)
+                probability of each class
+
+        returns
+        -------
+        joint_log_likelihood : ndarry of shape (n_samples,)
+            joint log likelihood of data
+
+        """
+
+        prob = -self.n_features / 2 * np.log(2 * np.pi) - 0.5 * np.sum(
+            np.log(sigma )
+            )
+        prob -= 0.5 * np.sum(np.power(X -mean, 2) / (sigma), 1)
+
+        joint_log_likelihood = prior + prob
+        return joint_log_likelihood
+
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