def testBetaIncGrads(self): err_tolerance = 1e-3 with self.cached_session(): # Test gradient ga_s = np.abs(np.random.randn(2, 2) * 30) # in (0, infty) gb_s = np.abs(np.random.randn(2, 2) * 30) # in (0, infty) gx_s = np.random.rand(2, 2) # in (0, 1) tf_ga_s = constant_op.constant(ga_s, dtype=dtypes.float64) tf_gb_s = constant_op.constant(gb_s, dtype=dtypes.float64) tf_gx_s = constant_op.constant(gx_s, dtype=dtypes.float64) tf_gout_t = math_ops.betainc(tf_ga_s, tf_gb_s, tf_gx_s) err = gradient_checker.compute_gradient_error([tf_gx_s], [gx_s.shape], tf_gout_t, gx_s.shape) tf_logging.info("betainc gradient err = %g " % err) self.assertLess(err, err_tolerance) # Test broadcast gradient gx_s = np.random.rand() # in (0, 1) tf_gx_s = constant_op.constant(gx_s, dtype=dtypes.float64) tf_gout_t = math_ops.betainc(tf_ga_s, tf_gb_s, tf_gx_s) err = gradient_checker.compute_gradient_error([tf_gx_s], [()], tf_gout_t, ga_s.shape) tf_logging.info("betainc gradient err = %g " % err) self.assertLess(err, err_tolerance)
def _cdf(self, x): # we use the same notation here as in wikipedia for the t = (x - self.mu)/self.sigma x_t = self.df / (math_ops.square(t) + self.df) # The cdf is defined differently for positive and negative t positive_cdf = 1. - 0.5 * math_ops.betainc(0.5 * self.df, 0.5, x_t) negative_cdf = 0.5 * math_ops.betainc(0.5 * self.df, 0.5, x_t) return tf.where(tf.less(t, 0), negative_cdf, positive_cdf)
def _cdf(self, x): # we use the same notation here as in wikipedia for the t = (x - self.mu) / self.sigma x_t = self.df / (math_ops.square(t) + self.df) # The cdf is defined differently for positive and negative t positive_cdf = 1. - 0.5 * math_ops.betainc(0.5 * self.df, 0.5, x_t) negative_cdf = 0.5 * math_ops.betainc(0.5 * self.df, 0.5, x_t) return tf.where(tf.less(t, 0), negative_cdf, positive_cdf)
def testBetaIncFpropAndBpropAreNeverNAN(self): with self.cached_session() as sess: space = np.logspace(-8, 5).tolist() if platform.machine() == 'aarch64': space_x = np.linspace(1e-16, 1 - 1e-7).tolist() else: space_x = np.linspace(1e-16, 1 - 1e-16).tolist() ga_s, gb_s, gx_s = zip( *list(itertools.product(space, space, space_x))) # Test grads are never nan ga_s_t = constant_op.constant(ga_s, dtype=dtypes.float32) gb_s_t = constant_op.constant(gb_s, dtype=dtypes.float32) gx_s_t = constant_op.constant(gx_s, dtype=dtypes.float32) tf_gout_t = math_ops.betainc(ga_s_t, gb_s_t, gx_s_t) tf_gout, grads_x = sess.run([ tf_gout_t, gradients_impl.gradients(tf_gout_t, [ga_s_t, gb_s_t, gx_s_t])[2] ]) # Equivalent to `assertAllFalse` (if it existed). self.assertAllEqual( np.zeros_like(grads_x).astype(np.bool), np.isnan(tf_gout)) self.assertAllEqual( np.zeros_like(grads_x).astype(np.bool), np.isnan(grads_x))
def _cdf(self, positive_counts): if self.validate_args: positive_counts = math_ops.floor( distribution_util.embed_check_nonnegative_discrete( positive_counts, check_integer=False)) return math_ops.betainc(self.total_count, positive_counts + 1., math_ops.sigmoid(-self.logits))
def _cdf(self, positive_counts): if self.validate_args: positive_counts = math_ops.floor( distribution_util.embed_check_nonnegative_discrete( positive_counts, check_integer=False)) return math_ops.betainc( self.total_count, positive_counts + 1., math_ops.sigmoid(-self.logits))
def testBetaIncGrads(self): err_tolerance = 1e-3 with self.cached_session(): # Test gradient ga_s = np.abs(np.random.randn(2, 2) * 30) # in (0, infty) gb_s = np.abs(np.random.randn(2, 2) * 30) # in (0, infty) gx_s = np.random.rand(2, 2) # in (0, 1) tf_ga_s = constant_op.constant(ga_s, dtype=dtypes.float64) tf_gb_s = constant_op.constant(gb_s, dtype=dtypes.float64) tf_gx_s = constant_op.constant(gx_s, dtype=dtypes.float64) tf_gout_t = math_ops.betainc(tf_ga_s, tf_gb_s, tf_gx_s) err = gradient_checker.compute_gradient_error( [tf_gx_s], [gx_s.shape], tf_gout_t, gx_s.shape) tf_logging.info("betainc gradient err = %g " % err) self.assertLess(err, err_tolerance) # Test broadcast gradient gx_s = np.random.rand() # in (0, 1) tf_gx_s = constant_op.constant(gx_s, dtype=dtypes.float64) tf_gout_t = math_ops.betainc(tf_ga_s, tf_gb_s, tf_gx_s) err = gradient_checker.compute_gradient_error( [tf_gx_s], [()], tf_gout_t, ga_s.shape) tf_logging.info("betainc gradient err = %g " % err) self.assertLess(err, err_tolerance)
def testBetaIncFpropAndBpropAreNeverNAN(self): with self.cached_session() as sess: space = np.logspace(-8, 5).tolist() space_x = np.linspace(1e-16, 1 - 1e-16).tolist() ga_s, gb_s, gx_s = zip(*list(itertools.product(space, space, space_x))) # Test grads are never nan ga_s_t = constant_op.constant(ga_s, dtype=dtypes.float32) gb_s_t = constant_op.constant(gb_s, dtype=dtypes.float32) gx_s_t = constant_op.constant(gx_s, dtype=dtypes.float32) tf_gout_t = math_ops.betainc(ga_s_t, gb_s_t, gx_s_t) tf_gout, grads_x = sess.run( [tf_gout_t, gradients_impl.gradients(tf_gout_t, [ga_s_t, gb_s_t, gx_s_t])[2]]) # Equivalent to `assertAllFalse` (if it existed). self.assertAllEqual(np.zeros_like(grads_x).astype(np.bool), np.isnan(tf_gout)) self.assertAllEqual(np.zeros_like(grads_x).astype(np.bool), np.isnan(grads_x))
def _bdtr(k, n, p): """The binomial cumulative distribution function. Args: k: floating point `Tensor`. n: floating point `Tensor`. p: floating point `Tensor`. Returns: `sum_{j=0}^k p^j (1 - p)^(n - j)`. """ # Trick for getting safe backprop/gradients into n, k when # betainc(a = 0, ..) = nan # Write: # where(unsafe, safe_output, betainc(where(unsafe, safe_input, input))) ones = array_ops.ones_like(n - k) k_eq_n = math_ops.equal(k, n) safe_dn = array_ops.where(k_eq_n, ones, n - k) dk = math_ops.betainc(a=safe_dn, b=k + 1, x=1 - p) return array_ops.where(k_eq_n, ones, dk)
def _cdf(self, x): return math_ops.betainc(self.a, self.b, x)
def _cdf(self, x): return math_ops.betainc(self.concentration1, self.concentration0, x)
def _cdf(self, x): if self.validate_args: x = distribution_util.embed_check_nonnegative_integer_form(x) return math_ops.betainc(self.total_count, 1. + x, math_ops.sigmoid(-self.logits))
def _testBetaInc(self, a_s, b_s, x_s, dtype): try: from scipy import special # pylint: disable=g-import-not-at-top np_dt = dtype.as_numpy_dtype # Test random values a_s = a_s.astype(np_dt) # in (0, infty) b_s = b_s.astype(np_dt) # in (0, infty) x_s = x_s.astype(np_dt) # in (0, 1) tf_a_s = constant_op.constant(a_s, dtype=dtype) tf_b_s = constant_op.constant(b_s, dtype=dtype) tf_x_s = constant_op.constant(x_s, dtype=dtype) tf_out_t = math_ops.betainc(tf_a_s, tf_b_s, tf_x_s) with self.cached_session(): tf_out = self.evaluate(tf_out_t) scipy_out = special.betainc(a_s, b_s, x_s, dtype=np_dt) # the scipy version of betainc uses a double-only implementation. # TODO(ebrevdo): identify reasons for (sometime) precision loss # with doubles rtol = 1e-4 atol = 1e-5 self.assertAllCloseAccordingToType(scipy_out, tf_out, rtol=rtol, atol=atol) # Test out-of-range values (most should return nan output) combinations = list( itertools.product([-1, 0, 0.5, 1.0, 1.5], repeat=3)) a_comb, b_comb, x_comb = np.asarray(list(zip(*combinations)), dtype=np_dt) with self.cached_session(): tf_comb = math_ops.betainc(a_comb, b_comb, x_comb).eval() scipy_comb = special.betainc(a_comb, b_comb, x_comb, dtype=np_dt) self.assertAllCloseAccordingToType(scipy_comb, tf_comb, rtol=rtol, atol=atol) # Test broadcasting between scalars and other shapes with self.cached_session(): self.assertAllCloseAccordingToType( special.betainc(0.1, b_s, x_s, dtype=np_dt), math_ops.betainc(0.1, b_s, x_s).eval(), rtol=rtol, atol=atol) self.assertAllCloseAccordingToType( special.betainc(a_s, 0.1, x_s, dtype=np_dt), math_ops.betainc(a_s, 0.1, x_s).eval(), rtol=rtol, atol=atol) self.assertAllCloseAccordingToType( special.betainc(a_s, b_s, 0.1, dtype=np_dt), math_ops.betainc(a_s, b_s, 0.1).eval(), rtol=rtol, atol=atol) self.assertAllCloseAccordingToType( special.betainc(0.1, b_s, 0.1, dtype=np_dt), math_ops.betainc(0.1, b_s, 0.1).eval(), rtol=rtol, atol=atol) self.assertAllCloseAccordingToType( special.betainc(0.1, 0.1, 0.1, dtype=np_dt), math_ops.betainc(0.1, 0.1, 0.1).eval(), rtol=rtol, atol=atol) with self.assertRaisesRegex(ValueError, "must be equal"): math_ops.betainc(0.5, [0.5], [[0.5]]) with self.cached_session(): with self.assertRaisesOpError("Shapes of .* are inconsistent"): a_p = array_ops.placeholder(dtype) b_p = array_ops.placeholder(dtype) x_p = array_ops.placeholder(dtype) math_ops.betainc(a_p, b_p, x_p).eval(feed_dict={ a_p: 0.5, b_p: [0.5], x_p: [[0.5]] }) except ImportError as e: tf_logging.warn("Cannot test special functions: %s" % str(e))
def _cdf(self, x): # Take Abs(scale) to make subsequent where work correctly. y = (x - self.loc) / math_ops.abs(self.scale) x_t = self.df / (y**2. + self.df) neg_cdf = 0.5 * math_ops.betainc(0.5 * self.df, 0.5, x_t) return array_ops.where(math_ops.less(y, 0.), neg_cdf, 1. - neg_cdf)
def _testBetaInc(self, a_s, b_s, x_s, dtype): try: from scipy import special # pylint: disable=g-import-not-at-top np_dt = dtype.as_numpy_dtype # Test random values a_s = a_s.astype(np_dt) # in (0, infty) b_s = b_s.astype(np_dt) # in (0, infty) x_s = x_s.astype(np_dt) # in (0, 1) tf_a_s = constant_op.constant(a_s, dtype=dtype) tf_b_s = constant_op.constant(b_s, dtype=dtype) tf_x_s = constant_op.constant(x_s, dtype=dtype) tf_out_t = math_ops.betainc(tf_a_s, tf_b_s, tf_x_s) with self.cached_session(): tf_out = tf_out_t.eval() scipy_out = special.betainc(a_s, b_s, x_s).astype(np_dt) # the scipy version of betainc uses a double-only implementation. # TODO(ebrevdo): identify reasons for (sometime) precision loss # with doubles tol = 1e-4 if dtype == dtypes.float32 else 5e-5 self.assertAllCloseAccordingToType(scipy_out, tf_out, rtol=tol, atol=0) # Test out-of-range values (most should return nan output) combinations = list(itertools.product([-1, 0, 0.5, 1.0, 1.5], repeat=3)) a_comb, b_comb, x_comb = np.asarray(list(zip(*combinations)), dtype=np_dt) with self.cached_session(): tf_comb = math_ops.betainc(a_comb, b_comb, x_comb).eval() scipy_comb = special.betainc(a_comb, b_comb, x_comb).astype(np_dt) self.assertAllCloseAccordingToType(scipy_comb, tf_comb) # Test broadcasting between scalars and other shapes with self.cached_session(): self.assertAllCloseAccordingToType( special.betainc(0.1, b_s, x_s).astype(np_dt), math_ops.betainc(0.1, b_s, x_s).eval(), rtol=tol, atol=0) self.assertAllCloseAccordingToType( special.betainc(a_s, 0.1, x_s).astype(np_dt), math_ops.betainc(a_s, 0.1, x_s).eval(), rtol=tol, atol=0) self.assertAllCloseAccordingToType( special.betainc(a_s, b_s, 0.1).astype(np_dt), math_ops.betainc(a_s, b_s, 0.1).eval(), rtol=tol, atol=0) self.assertAllCloseAccordingToType( special.betainc(0.1, b_s, 0.1).astype(np_dt), math_ops.betainc(0.1, b_s, 0.1).eval(), rtol=tol, atol=0) self.assertAllCloseAccordingToType( special.betainc(0.1, 0.1, 0.1).astype(np_dt), math_ops.betainc(0.1, 0.1, 0.1).eval(), rtol=tol, atol=0) with self.assertRaisesRegexp(ValueError, "must be equal"): math_ops.betainc(0.5, [0.5], [[0.5]]) with self.cached_session(): with self.assertRaisesOpError("Shapes of .* are inconsistent"): a_p = array_ops.placeholder(dtype) b_p = array_ops.placeholder(dtype) x_p = array_ops.placeholder(dtype) math_ops.betainc(a_p, b_p, x_p).eval( feed_dict={a_p: 0.5, b_p: [0.5], x_p: [[0.5]]}) except ImportError as e: tf_logging.warn("Cannot test special functions: %s" % str(e))