Negative Binomial

NB

@tf.function
def tfgamma(z):
    g = tf.exp(tf.math.lgamma(z))
    return g

@tf.function
def NB(x, mu, phi):
    numerator = tfgamma(x + phi)*tf.math.pow(mu,x)*tf.math.pow(phi, phi)
    denominator = tfgamma(phi)*tfgamma(x+1) *tf.math.pow((mu + phi),(x+phi))
    return (numerator/denominator)

@tf.function
def negloglikelihood(Matrix, mu, phi):
    
    total = tf.constant(np.zeros(len(Matrix.columns)), dtype=tf.float32)
    index = 0
    for (columnName, columnData) in Matrix.iteritems():
        for x in columnData.values:
            summand = tf.math.log(NB(x, mu[index], phi[index]))
            total[index] = total[index] + summand
        total[index] = -1.0*total[index]
        index = index + 1
    return -1.0*total