Gaussian Naive Bayes

In [112]:

    

from collections import defaultdict
import numpy as np


    

In [271]:

    

class GaussianNaiveBayes:
    def __init__(self):
        self.trained = defaultdict(bool)
        self.stats = defaultdict(dict)
        
    def _update_stats(self, datum, label):
        if len(datum) > len(self.stats[label]):
            self.stats[label]['n'] = 1
            self.stats[label]['sum'] = datum
            self.stats[label]['sum_squared'] = datum ** 2
            self.stats[label]['mean'] = datum
            self.stats[label]['std'] = np.zeros(len(datum))
        else:
            stats = self.stats[label]
            self.stats[label]['n'] += 1
            self.stats[label]['sum'] += datum
            self.stats[label]['sum_squared'] += datum ** 2
            self.stats[label]['mean'] =  stats['sum'] / stats['n']
            self.stats[label]['std'] = (stats['sum_squared'] - (stats['sum'] ** 2 / stats['n'])) / stats['n']
            self.trained[label] = True
        
    def train_incremental(self, data, labels):
        data_array = np.array(data)
        labels_array = np.array(labels)
        
        for datum, label in zip(data_array, labels_array):
            self._update_stats(datum, label)    
                
    def train_batch(self, data, labels):
        pass
    
    def _gaussian(self, x, mu, sigma):
        num = (x - mu) ** 2
        denum = 2 * sigma ** 2
        norm = 1 / np.sqrt(2 * np.pi * sigma ** 2)
        return norm * np.exp(-num / denum)
        
    def predict(self, data):
        if len(data) == 1:
            data = [data]
            
        output = []
        
        for datum in data:
            best = (-1, None)
            for label in self.stats.keys():
                if self.trained[label]:
                    value = self._gaussian(np.array(datum), self.stats[label]['mean'], self.stats[label]['std'])
                    likelihood = np.nanprod(value)
                    if likelihood > best[0]:
                        best = (likelihood, label)
                else:
                    print('Not even training data for {}'.format(label))
                
            output.append(best[1])    
                
        return output


    

In [272]:

    

data = [
    [1, 2, 3, 4],
    [10, 20, 30, 40],
    [1.2, 1.9, 3.1, 4.5],
    [10.1, 20.2, 29.8, 42]
]

labels = ['x', 'y', 'x', 'y']


    

In [273]:

    

nb = GaussianNaiveBayes()


    

In [274]:

    

nb.train_incremental(data, labels)


    

In [275]:

    

nb.stats


    

    
Out[275]:





defaultdict(dict,
            {'x': {'mean': array([ 1.1 ,  1.95,  3.05,  4.25]),
              'n': 2,
              'std': array([ 0.01  ,  0.0025,  0.0025,  0.0625]),
              'sum': array([ 2.2,  3.9,  6.1,  8.5]),
              'sum_squared': array([  2.44,   7.61,  18.61,  36.25])},
             'y': {'mean': array([ 10.05,  20.1 ,  29.9 ,  41.  ]),
              'n': 2,
              'std': array([ 0.0025,  0.01  ,  0.01  ,  1.    ]),
              'sum': array([ 20.1,  40.2,  59.8,  82. ]),
              'sum_squared': array([  202.01,   808.04,  1788.04,  3364.  ])}})

In [276]:

    

nb.predict(data)


    

    
Out[276]:





['x', 'y', 'x', 'y']

In [277]:

    

nb.train_incremental([[100, 200, 300, 400]], ['z'])


    

In [278]:

    

nb.stats


    

    
Out[278]:





defaultdict(dict,
            {'x': {'mean': array([ 1.1 ,  1.95,  3.05,  4.25]),
              'n': 2,
              'std': array([ 0.01  ,  0.0025,  0.0025,  0.0625]),
              'sum': array([ 2.2,  3.9,  6.1,  8.5]),
              'sum_squared': array([  2.44,   7.61,  18.61,  36.25])},
             'y': {'mean': array([ 10.05,  20.1 ,  29.9 ,  41.  ]),
              'n': 2,
              'std': array([ 0.0025,  0.01  ,  0.01  ,  1.    ]),
              'sum': array([ 20.1,  40.2,  59.8,  82. ]),
              'sum_squared': array([  202.01,   808.04,  1788.04,  3364.  ])},
             'z': {'mean': array([100, 200, 300, 400]),
              'n': 1,
              'std': array([ 0.,  0.,  0.,  0.]),
              'sum': array([100, 200, 300, 400]),
              'sum_squared': array([ 10000,  40000,  90000, 160000])}})

In [279]:

    

nb.predict([[101, 198, 305, 401]])


    

    




Not even training data for z






    
Out[279]:





['x']

In [280]:

    

nb.train_incremental([[103, 205, 299, 412]], ['z'])


    

In [281]:

    

nb.predict([[101, 198, 305, 401]])


    

    
Out[281]:





['z']

In [282]:

    

nb.predict([[1,2,3,4]])


    

    
Out[282]:





['x']

In [283]:

    

nb.stats


    

    
Out[283]:





defaultdict(dict,
            {'x': {'mean': array([ 1.1 ,  1.95,  3.05,  4.25]),
              'n': 2,
              'std': array([ 0.01  ,  0.0025,  0.0025,  0.0625]),
              'sum': array([ 2.2,  3.9,  6.1,  8.5]),
              'sum_squared': array([  2.44,   7.61,  18.61,  36.25])},
             'y': {'mean': array([ 10.05,  20.1 ,  29.9 ,  41.  ]),
              'n': 2,
              'std': array([ 0.0025,  0.01  ,  0.01  ,  1.    ]),
              'sum': array([ 20.1,  40.2,  59.8,  82. ]),
              'sum_squared': array([  202.01,   808.04,  1788.04,  3364.  ])},
             'z': {'mean': array([ 101.5,  202.5,  299.5,  406. ]),
              'n': 2,
              'std': array([  2.25,   6.25,   0.25,  36.  ]),
              'sum': array([203, 405, 599, 812]),
              'sum_squared': array([ 20609,  82025, 179401, 329744])}})