Method _maximize_alpha

numpy_ml/lda/lda.py:99–135

Optimize alpha using Blei's O(n) Newton-Raphson modification for a Hessian with special structure

(self, max_iters=1000, tol=0.1)

        return beta

    def _maximize_alpha(self, max_iters=1000, tol=0.1):
        """
        Optimize alpha using Blei's O(n) Newton-Raphson modification
        for a Hessian with special structure
        """
        D = self.D
        T = self.T

        alpha = self.alpha
        gamma = self.gamma

        for _ in range(max_iters):
            alpha_old = alpha

            #  Calculate gradient
            g = D * (digamma(np.sum(alpha)) - digamma(alpha)) + np.sum(
                digamma(gamma) - np.tile(digamma(np.sum(gamma, axis=1)), (T, 1)).T,
                axis=0,
            )

            #  Calculate Hessian diagonal component
            h = -D * polygamma(1, alpha)

            #  Calculate Hessian constant component
            z = D * polygamma(1, np.sum(alpha))

            #  Calculate constant
            c = np.sum(g / h) / (z ** (-1.0) + np.sum(h ** (-1.0)))

            #  Update alpha
            alpha = alpha - (g - c) / h

            #  Check convergence
            if np.sqrt(np.mean(np.square(alpha - alpha_old))) < tol:
                break

        return alpha

    def _E_step(self):
        """