r"""
    Compute the expectation:
    expectation[n] = <(\Sum_i K1_i_{Z1, x_n}) (\Sum_j K2_j_{x_n, Z2})>_p(x_n)
        - \Sum_i K1_i_{.,.}, \Sum_j K2_j_{.,.} :: Sum kernels

    :return: NxM1xM2
977586
def _expectation(p, kern1, feat1, kern2, feat2, nghp=None):
    
    """
    crossexps = []

    if kern1 == kern2 and feat1 == feat2:  # avoid duplicate computation by using transposes
        for i, k1 in enumerate(kern1.kernels):
            crossexps.append(expectation(p, (k1, feat1), (k1, feat1), nghp=nghp))

            for k2 in kern1.kernels[:i]:
                eKK = expectation(p, (k1, feat1), (k2, feat2), nghp=nghp)
                eKK += tf.matrix_transpose(eKK)
                crossexps.append(eKK)
    else:
        for k1, k2 in it.product(kern1.kernels, kern2.kernels):
            crossexps.append(expectation(p, (k1, feat1), (k2, feat2), nghp=nghp))

    return functools.reduce(tf.add, crossexps)
850299
public function compute(Tensor $expected, Tensor $output) : float
    {
        return $output->subtract($expected)->square()->sum()->mean();
    }
935018
def _nbinom_ztrunc_p(mu, k_agg):
        

        p_eq = lambda p, mu, k_agg: (k_agg * p) / (1 - (1 + p)**-k_agg) - mu

        # The upper bound needs to be large. p will increase with increasing mu
        # and decreasing k_agg
        p = optim.brentq(p_eq, 1e-10, 1e10, args=(mu, k_agg))
        return p
728607
def sse(mean, estimator):
    
    return np.sum((np.asarray(estimator) - np.asarray(mean)) ** 2, axis=0)
557383
def _build_likelihood(self):
        
        pX = DiagonalGaussian(self.X_mean, self.X_var)

        num_inducing = len(self.feature)
        psi0 = tf.reduce_sum(expectation(pX, self.kern))
        psi1 = expectation(pX, (self.kern, self.feature))
        psi2 = tf.reduce_sum(expectation(pX, (self.kern, self.feature), (self.kern, self.feature)), axis=0)
        Kuu = features.Kuu(self.feature, self.kern, jitter=settings.jitter)
        L = tf.cholesky(Kuu)
        sigma2 = self.likelihood.variance
        sigma = tf.sqrt(sigma2)

        # Compute intermediate matrices
        A = tf.matrix_triangular_solve(L, tf.transpose(psi1), lower=True) / sigma
        tmp = tf.matrix_triangular_solve(L, psi2, lower=True)
        AAT = tf.matrix_triangular_solve(L, tf.transpose(tmp), lower=True) / sigma2
        B = AAT + tf.eye(num_inducing, dtype=settings.float_type)
        LB = tf.cholesky(B)
        log_det_B = 2. * tf.reduce_sum(tf.log(tf.matrix_diag_part(LB)))
        c = tf.matrix_triangular_solve(LB, tf.matmul(A, self.Y), lower=True) / sigma

        # KL[q(x) || p(x)]
        dX_var = self.X_var if len(self.X_var.get_shape()) == 2 else tf.matrix_diag_part(self.X_var)
        NQ = tf.cast(tf.size(self.X_mean), settings.float_type)
        D = tf.cast(tf.shape(self.Y)[1], settings.float_type)
        KL = -0.5 * tf.reduce_sum(tf.log(dX_var)) \
             + 0.5 * tf.reduce_sum(tf.log(self.X_prior_var)) \
             - 0.5 * NQ \
             + 0.5 * tf.reduce_sum((tf.square(self.X_mean - self.X_prior_mean) + dX_var) / self.X_prior_var)

        # compute log marginal bound
        ND = tf.cast(tf.size(self.Y), settings.float_type)
        bound = -0.5 * ND * tf.log(2 * np.pi * sigma2)
        bound += -0.5 * D * log_det_B
        bound += -0.5 * tf.reduce_sum(tf.square(self.Y)) / sigma2
        bound += 0.5 * tf.reduce_sum(tf.square(c))
        bound += -0.5 * D * (tf.reduce_sum(psi0) / sigma2 -
                             tf.reduce_sum(tf.matrix_diag_part(AAT)))
        bound -= KL
        return bound
674713
def gaussian1(height, x0, y0, a, b, c):
    

    return lambda x, y: height * np.exp(-0.5* (a*(x-x0)**2 + b*(x-x0)*(y-y0) + c*(y-y0)**2))
542295
def _expectation(p, kern, none1, none2, none3, nghp=None):
    
    return kern.Kdiag(p.mu)
413608
def variance
            expected = self.expectation
            @map.reduce(0) {|sum, (value,p)| 
                tmp = (value.to_f - expectation)
                sum + tmp * tmp * p 
            }
        end
424756
def _m_to_e(cls, e, M):
        

        k1 = 3 * np.pi + 2
        k2 = np.pi - 1
        k3 = 6 * np.pi - 1
        A = 3 * k2 ** 2 / k1
        B = k3 ** 2 / (6 * k1)

        m1 = float(M)
        if abs(m1) < 1 / 6:
            E = m1 + e * (6 * m1) ** (1 / 3) - m1
        elif m1 < 0:
            w = np.pi + m1
            E = m1 + e * (A * w / (B - w) - np.pi - m1)
        else:
            w = np.pi - m1
            E = m1 + e * (np.pi - A * w / (B - w) - m1)

        e1 = 1 - e
        risk_disabler = (e1 + E ** 2 / 6) >= 0.1

        for i in range(2):
            fdd = e * sin(E)
            fddd = e * cos(E)

            if risk_disabler:
                f = (E - fdd) - m1
                fd = 1 - fddd
            else:
                f = cls._e_e_sin_e(e, E) - m1
                s = sin(E / 2)
                fd = e1 + 2 * e * s ** 2
            dee = f * fd / (0.5 * f * fdd - fd ** 2)

            w = fd + 0.5 * dee * (fdd + dee * fddd / 3)
            fd += dee * (fdd + 0.5 * dee * fddd)
            E -= (f - dee * (fd - w)) / fd

        E += M - m1

        return E
992713
def gaussian(x,  a, b, c, d=0):
    '''
    
    '''
    return a * np.exp(  -(((x-b)**2 )/ (2*(c**2)))  ) + d
936737
def add_expectation(self, caller):
        

        expectation = Expectation(self._target, self._method_name, caller)
        self._expectations.insert(0, expectation)
        return expectation
394483
def stochastic_kl_builder(posterior, prior, sample):
  """"""
  return tf.subtract(
      tf.reduce_sum(posterior.log_prob(sample)),
      tf.reduce_sum(prior.log_prob(sample)))
774414
def _build_likelihood(self):
        

        """

        # Get prior KL.
        KL = gauss_kl(self.q_mu, self.q_sqrt)

        # Get conditionals
        K = self.kern.K(self.X) + tf.eye(self.num_data, dtype=settings.float_type) * \
            settings.numerics.jitter_level
        L = tf.cholesky(K)

        fmean = tf.matmul(L, self.q_mu) + self.mean_function(self.X)  # NN,ND->ND

        q_sqrt_dnn = tf.matrix_band_part(self.q_sqrt, -1, 0)  # D x N x N

        L_tiled = tf.tile(tf.expand_dims(L, 0), tf.stack([self.num_latent, 1, 1]))

        LTA = tf.matmul(L_tiled, q_sqrt_dnn)  # D x N x N
        fvar = tf.reduce_sum(tf.square(LTA), 2)

        fvar = tf.transpose(fvar)

        # Get variational expectations.
        var_exp = self.likelihood.variational_expectations(fmean, fvar, self.Y)

        return tf.reduce_sum(var_exp) - KL
150046
def predict(self, X):
        """"""
        return self.__cost(self.__unroll(self.__thetas), 0, np.matrix(X))
1189157
def cluster(self, X):
        """"""

        # Initialize the gaussians randomly
        self._init_random_gaussians(X)

        # Run EM until convergence or for max iterations
        for _ in range(self.max_iterations):
            self._expectation(X)    # E-step
            self._maximization(X)   # M-step

            # Check convergence
            if self._converged(X):
                break

        # Make new assignments and return them
        self._expectation(X)
        return self.sample_assignments
554548
def _build_likelihood(self):
        

        """
        K = self.kern.K(self.X)
        L = tf.cholesky(
            K + tf.eye(tf.shape(self.X)[0], dtype=settings.float_type) * settings.numerics.jitter_level)
        F = tf.matmul(L, self.V) + self.mean_function(self.X)

        return tf.reduce_sum(self.likelihood.logp(F, self.Y))
822115
def compute(cls, observation, prediction):
        """"""
        assert isinstance(observation, dict)
        assert isinstance(prediction, dict)
        p_mean = prediction['mean']  # Use the prediction's mean.
        p_std = prediction['std']
        o_mean = observation['mean']
        o_std = observation['std']
        try:  # Try to pool taking samples sizes into account.
            p_n = prediction['n']
            o_n = observation['n']
            s = (((p_n-1)*(p_std**2) + (o_n-1)*(o_std**2))/(p_n+o_n-2))**0.5
        except KeyError:  # If sample sizes are not available.
            s = (p_std**2 + o_std**2)**0.5
        value = (p_mean - o_mean)/s
        value = utils.assert_dimensionless(value)
        return CohenDScore(value)