我们从Python开源项目中，提取了以下8个代码示例，用于说明如何使用scipy.stats.norm.logcdf()。
def compute_log_lik_exp(self, m, v, y): if m.ndim == 2: gh_x, gh_w = self._gh_points(GH_DEGREE) gh_x = gh_x[:, np.newaxis, np.newaxis] gh_w = gh_w[:, np.newaxis, np.newaxis] / np.sqrt(np.pi) v_expand = v[np.newaxis, :, :] m_expand = m[np.newaxis, :, :] ts = gh_x * np.sqrt(2 * v_expand) + m_expand logcdfs = norm.logcdf(ts * y) prods = gh_w * logcdfs loglik = np.sum(prods) pdfs = norm.pdf(ts * y) cdfs = norm.cdf(ts * y) grad_cdfs = y * gh_w * pdfs / cdfs dts_dm = 1 dts_dv = 0.5 * gh_x * np.sqrt(2 / v_expand) dm = np.sum(grad_cdfs * dts_dm, axis=0) dv = np.sum(grad_cdfs * dts_dv, axis=0) else: gh_x, gh_w = self._gh_points(GH_DEGREE) gh_x = gh_x[:, np.newaxis, np.newaxis, np.newaxis] gh_w = gh_w[:, np.newaxis, np.newaxis, np.newaxis] / np.sqrt(np.pi) v_expand = v[np.newaxis, :, :, :] m_expand = m[np.newaxis, :, :, :] ts = gh_x * np.sqrt(2 * v_expand) + m_expand logcdfs = norm.logcdf(ts * y) prods = gh_w * logcdfs prods_mean = np.mean(prods, axis=1) loglik = np.sum(prods_mean) pdfs = norm.pdf(ts * y) cdfs = norm.cdf(ts * y) grad_cdfs = y * gh_w * pdfs / cdfs dts_dm = 1 dts_dv = 0.5 * gh_x * np.sqrt(2 / v_expand) dm = np.sum(grad_cdfs * dts_dm, axis=0) / m.shape[0] dv = np.sum(grad_cdfs * dts_dv, axis=0) / m.shape[0] return loglik, dm, dv
def __init__(self, K, Y, init=None, threshold=1e-9): N = np.shape(K)[0] f = np.zeros((N,1)) converged = False k = 0 innerC = 0 for i in xrange(N): pdfDiff = norm.logpdf(f) - norm.logcdf(Y*f) W = np.exp(2*pdfDiff) + Y*f*np.exp(pdfDiff) Wsqrt = np.sqrt(W) Wdiag= np.diag(Wsqrt.flatten()) B = np.identity(N) + np.dot(Wdiag, np.dot(K, Wdiag)) grad = Y*np.exp(pdfDiff) b = W*f + grad interim = np.dot(Wdiag, np.dot(K, b)) cgRes = Cg(B, interim, threshold=threshold) s1 = cgRes.result innerC = innerC + cgRes.iterations a = b - Wsqrt*s1 if(converged): break f_prev = f f = np.dot(K, a) diff = f - f_prev if (np.dot(diff.T,diff).flatten() < threshold*N or innerC>15000): converged = True k = k+1 self.result = f self.iterations = k + innerC
def __init__(self, K, Y, P, init=None, threshold=1e-9, precon=None): N = np.shape(K)[0] f = np.zeros((N,1)) converged = False k = 0 innerC = 0 for i in xrange(N): pdfDiff = norm.logpdf(f) - norm.logcdf(Y*f) W = np.exp(2*pdfDiff) + Y*f*np.exp(pdfDiff) Wsqrt = np.sqrt(W) Wdiag= np.diag(Wsqrt.flatten()) B = np.identity(N) + np.dot(Wdiag, np.dot(K, Wdiag)) grad = Y*np.exp(pdfDiff) b = W*f + grad interim = np.dot(Wdiag, np.dot(K, b)) pcgRes = RegularPcg(B, interim, None, threshold=threshold, preconInv=P.get_laplace_inversion(W,Wsqrt)) s1 = pcgRes.result innerC = innerC + pcgRes.iterations a = b - Wsqrt*s1 if(converged): break f_prev = f f = np.dot(K, a) diff = f - f_prev if (np.dot(diff.T,diff).flatten() < threshold*N or innerC>15000): converged = True k = k+1 self.result = f self.iterations = k + innerC
def integrateNormalDensity(lb,ub,mu = 0,sigma = 1): from scipy.stats import norm assert not (ub < lb) lessThanUpper = norm.logcdf(ub,loc = mu,scale = sigma) lessThanLower = norm.logcdf(lb,loc = mu,scale = sigma) #print lessThanUpper,lessThanLower,lessThanUpper-lessThanLower,1 - math.exp(lessThanLower - lessThanUpper) return lessThanUpper + np.log1p(-math.exp(lessThanLower - lessThanUpper))
def _scores(self, range_, k, cumsum, m_log_combs, n_log_combs): """Calculates the score function for all possible numbers of rows (or columns).""" avgs = cumsum / (range_ * k) log_probs = norm.logcdf(-avgs * np.sqrt(range_ * k)) return - log_probs - m_log_combs - n_log_combs[k-1]
def _setup(self): super(MinValueEntropySearch, self)._setup() # Apply Gumbel sampling m = self.models[0] valid = self.feasible_data_index() # Work with feasible data X = self.data[0][valid, :] N = np.shape(X)[0] Xrand = RandomDesign(self.gridsize, self._domain).generate() fmean, fvar = m.predict_f(np.vstack((X, Xrand))) idx = np.argmin(fmean[:N]) right = fmean[idx].flatten()# + 2*np.sqrt(fvar[idx]).flatten() left = right probf = lambda x: np.exp(np.sum(norm.logcdf(-(x - fmean) / np.sqrt(fvar)), axis=0)) i = 0 while probf(left) < 0.75: left = 2. ** i * np.min(fmean - 5. * np.sqrt(fvar)) + (1. - 2. ** i) * right i += 1 # Binary search for 3 percentiles q1, med, q2 = map(lambda val: bisect(lambda x: probf(x) - val, left, right, maxiter=10000, xtol=0.01), [0.25, 0.5, 0.75]) beta = (q1 - q2) / (np.log(np.log(4. / 3.)) - np.log(np.log(4.))) alpha = med + beta * np.log(np.log(2.)) # obtain samples from y* mins = -np.log(-np.log(np.random.rand(self.num_samples).astype(np_float_type))) * beta + alpha self.samples.set_data(mins)
