tfb_rational_quadratic_spline: A piecewise rational quadratic spline, as developed in Conor...

In tfprobability: Interface to 'TensorFlow Probability'

A piecewise rational quadratic spline, as developed in Conor et al.(2019).

Description

This transformation represents a monotonically increasing piecewise rational quadratic function. Outside of the bounds of knot_x/knot_y, the transform behaves as an identity function.

Usage

tfb_rational_quadratic_spline(
  bin_widths,
  bin_heights,
  knot_slopes,
  range_min = -1,
  validate_args = FALSE,
  name = NULL
)

Arguments

bin_widths	The widths of the spans between subsequent knot x positions, a floating point Tensor. Must be positive, and at least 1-D. Innermost axis must sum to the same value as bin_heights. The knot x positions will be a first at range_min, followed by knots at range_min + cumsum(bin_widths, axis=-1).
bin_heights	The heights of the spans between subsequent knot y positions, a floating point Tensor. Must be positive, and at least 1-D. Innermost axis must sum to the same value as bin_widths. The knot y positions will be a first at range_min, followed by knots at range_min + cumsum(bin_heights, axis=-1).
knot_slopes	The slope of the spline at each knot, a floating point Tensor. Must be positive. 1s are implicitly padded for the first and last implicit knots corresponding to range_min and range_min + sum(bin_widths, axis=-1). Innermost axis size should be 1 less than that of bin_widths/bin_heights, or 1 for broadcasting.
range_min	The x/y position of the first knot, which has implicit slope 1. range_max is implicit, and can be computed as range_min + sum(bin_widths, axis=-1). Scalar floating point Tensor.
validate_args	Logical, default FALSE. Whether to validate input with asserts. If validate_args is FALSE, and the inputs are invalid, correct behavior is not guaranteed.
name	name prefixed to Ops created by this class.

Details

Typically this bijector will be used as part of a chain, with splines for trailing x dimensions conditioned on some of the earlier x dimensions, and with the inverse then solved first for unconditioned dimensions, then using conditioning derived from those inverses, and so forth.

For each argument, the innermost axis indexes bins/knots and batch axes index axes of x/y spaces. A RationalQuadraticSpline with a separate transform for each of three dimensions might have bin_widths shaped [3, 32]. To use the same spline for each of x's three dimensions we may broadcast against x and use a bin_widths parameter shaped [32].

Parameters will be broadcast against each other and against the input x/ys, so if we want fixed slopes, we can use kwarg knot_slopes=1. A typical recipe for acquiring compatible bin widths and heights would be:

nbins <- unconstrained_vector$shape[-1]
range_min <- 1
range_max <- 1
min_bin_size = 1e-2
scale <- range_max - range_min - nbins * min_bin_size
bin_widths = tf$math$softmax(unconstrained_vector) * scale + min_bin_size

Value

a bijector instance.

References

• Conor Durkan, Artur Bekasov, Iain Murray, George Papamakarios. Neural Spline Flows. arXiv preprint arXiv:1906.04032, 2019.

See Also

For usage examples see tfb_forward(), tfb_inverse(), tfb_inverse_log_det_jacobian().

Other bijectors: tfb_absolute_value(), tfb_affine_linear_operator(), tfb_affine_scalar(), tfb_affine(), tfb_ascending(), tfb_batch_normalization(), tfb_blockwise(), tfb_chain(), tfb_cholesky_outer_product(), tfb_cholesky_to_inv_cholesky(), tfb_correlation_cholesky(), tfb_cumsum(), tfb_discrete_cosine_transform(), tfb_expm1(), tfb_exp(), tfb_ffjord(), tfb_fill_scale_tri_l(), tfb_fill_triangular(), tfb_glow(), tfb_gompertz_cdf(), tfb_gumbel_cdf(), tfb_gumbel(), tfb_identity(), tfb_inline(), tfb_invert(), tfb_iterated_sigmoid_centered(), tfb_kumaraswamy_cdf(), tfb_kumaraswamy(), tfb_lambert_w_tail(), tfb_masked_autoregressive_default_template(), tfb_masked_autoregressive_flow(), tfb_masked_dense(), tfb_matrix_inverse_tri_l(), tfb_matvec_lu(), tfb_normal_cdf(), tfb_ordered(), tfb_pad(), tfb_permute(), tfb_power_transform(), tfb_rayleigh_cdf(), tfb_real_nvp_default_template(), tfb_real_nvp(), tfb_reciprocal(), tfb_reshape(), tfb_scale_matvec_diag(), tfb_scale_matvec_linear_operator(), tfb_scale_matvec_lu(), tfb_scale_matvec_tri_l(), tfb_scale_tri_l(), tfb_scale(), tfb_shifted_gompertz_cdf(), tfb_shift(), tfb_sigmoid(), tfb_sinh_arcsinh(), tfb_sinh(), tfb_softmax_centered(), tfb_softplus(), tfb_softsign(), tfb_split(), tfb_square(), tfb_tanh(), tfb_transform_diagonal(), tfb_transpose(), tfb_weibull_cdf(), tfb_weibull()

tfprobability documentation built on Sept. 1, 2022, 5:07 p.m.