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.
tfb_rational_quadratic_spline(
bin_widths,
bin_heights,
knot_slopes,
range_min = -1,
validate_args = FALSE,
name = NULL
)a bijector instance.
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).
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).
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.
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.
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 prefixed to Ops created by this class.
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
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()