203 lines
7.1 KiB
Python
203 lines
7.1 KiB
Python
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# adopted from https://github.com/bayesiains/nflows
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import numpy as np
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import torch
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from torch.nn import functional as F
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DEFAULT_MIN_BIN_WIDTH = 1e-3
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DEFAULT_MIN_BIN_HEIGHT = 1e-3
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DEFAULT_MIN_DERIVATIVE = 1e-3
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def piecewise_rational_quadratic_transform(
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inputs,
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unnormalized_widths,
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unnormalized_heights,
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unnormalized_derivatives,
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inverse=False,
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tails=None,
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tail_bound=1.0,
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min_bin_width=DEFAULT_MIN_BIN_WIDTH,
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min_bin_height=DEFAULT_MIN_BIN_HEIGHT,
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min_derivative=DEFAULT_MIN_DERIVATIVE,
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):
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if tails is None:
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spline_fn = rational_quadratic_spline
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spline_kwargs = {}
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else:
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spline_fn = unconstrained_rational_quadratic_spline
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spline_kwargs = {"tails": tails, "tail_bound": tail_bound}
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outputs, logabsdet = spline_fn(
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inputs=inputs,
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unnormalized_widths=unnormalized_widths,
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unnormalized_heights=unnormalized_heights,
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unnormalized_derivatives=unnormalized_derivatives,
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inverse=inverse,
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min_bin_width=min_bin_width,
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min_bin_height=min_bin_height,
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min_derivative=min_derivative,
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**spline_kwargs,
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)
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return outputs, logabsdet
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def searchsorted(bin_locations, inputs, eps=1e-6):
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bin_locations[..., -1] += eps
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return torch.sum(inputs[..., None] >= bin_locations, dim=-1) - 1
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def unconstrained_rational_quadratic_spline(
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inputs,
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unnormalized_widths,
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unnormalized_heights,
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unnormalized_derivatives,
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inverse=False,
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tails="linear",
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tail_bound=1.0,
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min_bin_width=DEFAULT_MIN_BIN_WIDTH,
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min_bin_height=DEFAULT_MIN_BIN_HEIGHT,
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min_derivative=DEFAULT_MIN_DERIVATIVE,
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):
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inside_interval_mask = (inputs >= -tail_bound) & (inputs <= tail_bound)
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outside_interval_mask = ~inside_interval_mask
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outputs = torch.zeros_like(inputs)
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logabsdet = torch.zeros_like(inputs)
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if tails == "linear":
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unnormalized_derivatives = F.pad(unnormalized_derivatives, pad=(1, 1))
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constant = np.log(np.exp(1 - min_derivative) - 1)
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unnormalized_derivatives[..., 0] = constant
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unnormalized_derivatives[..., -1] = constant
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outputs[outside_interval_mask] = inputs[outside_interval_mask]
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logabsdet[outside_interval_mask] = 0
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else:
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raise RuntimeError("{} tails are not implemented.".format(tails))
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outputs[inside_interval_mask], logabsdet[inside_interval_mask] = rational_quadratic_spline(
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inputs=inputs[inside_interval_mask],
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unnormalized_widths=unnormalized_widths[inside_interval_mask, :],
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unnormalized_heights=unnormalized_heights[inside_interval_mask, :],
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unnormalized_derivatives=unnormalized_derivatives[inside_interval_mask, :],
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inverse=inverse,
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left=-tail_bound,
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right=tail_bound,
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bottom=-tail_bound,
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top=tail_bound,
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min_bin_width=min_bin_width,
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min_bin_height=min_bin_height,
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min_derivative=min_derivative,
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)
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return outputs, logabsdet
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def rational_quadratic_spline(
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inputs,
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unnormalized_widths,
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unnormalized_heights,
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unnormalized_derivatives,
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inverse=False,
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left=0.0,
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right=1.0,
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bottom=0.0,
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top=1.0,
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min_bin_width=DEFAULT_MIN_BIN_WIDTH,
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min_bin_height=DEFAULT_MIN_BIN_HEIGHT,
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min_derivative=DEFAULT_MIN_DERIVATIVE,
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):
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if torch.min(inputs) < left or torch.max(inputs) > right:
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raise ValueError("Input to a transform is not within its domain")
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num_bins = unnormalized_widths.shape[-1]
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if min_bin_width * num_bins > 1.0:
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raise ValueError("Minimal bin width too large for the number of bins")
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if min_bin_height * num_bins > 1.0:
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raise ValueError("Minimal bin height too large for the number of bins")
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widths = F.softmax(unnormalized_widths, dim=-1)
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widths = min_bin_width + (1 - min_bin_width * num_bins) * widths
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cumwidths = torch.cumsum(widths, dim=-1)
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cumwidths = F.pad(cumwidths, pad=(1, 0), mode="constant", value=0.0)
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cumwidths = (right - left) * cumwidths + left
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cumwidths[..., 0] = left
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cumwidths[..., -1] = right
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widths = cumwidths[..., 1:] - cumwidths[..., :-1]
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derivatives = min_derivative + F.softplus(unnormalized_derivatives)
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heights = F.softmax(unnormalized_heights, dim=-1)
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heights = min_bin_height + (1 - min_bin_height * num_bins) * heights
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cumheights = torch.cumsum(heights, dim=-1)
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cumheights = F.pad(cumheights, pad=(1, 0), mode="constant", value=0.0)
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cumheights = (top - bottom) * cumheights + bottom
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cumheights[..., 0] = bottom
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cumheights[..., -1] = top
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heights = cumheights[..., 1:] - cumheights[..., :-1]
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if inverse:
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bin_idx = searchsorted(cumheights, inputs)[..., None]
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else:
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bin_idx = searchsorted(cumwidths, inputs)[..., None]
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input_cumwidths = cumwidths.gather(-1, bin_idx)[..., 0]
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input_bin_widths = widths.gather(-1, bin_idx)[..., 0]
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input_cumheights = cumheights.gather(-1, bin_idx)[..., 0]
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delta = heights / widths
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input_delta = delta.gather(-1, bin_idx)[..., 0]
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input_derivatives = derivatives.gather(-1, bin_idx)[..., 0]
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input_derivatives_plus_one = derivatives[..., 1:].gather(-1, bin_idx)[..., 0]
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input_heights = heights.gather(-1, bin_idx)[..., 0]
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if inverse:
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a = (inputs - input_cumheights) * (
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input_derivatives + input_derivatives_plus_one - 2 * input_delta
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) + input_heights * (input_delta - input_derivatives)
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b = input_heights * input_derivatives - (inputs - input_cumheights) * (
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input_derivatives + input_derivatives_plus_one - 2 * input_delta
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)
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c = -input_delta * (inputs - input_cumheights)
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discriminant = b.pow(2) - 4 * a * c
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assert (discriminant >= 0).all()
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root = (2 * c) / (-b - torch.sqrt(discriminant))
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outputs = root * input_bin_widths + input_cumwidths
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theta_one_minus_theta = root * (1 - root)
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denominator = input_delta + (
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(input_derivatives + input_derivatives_plus_one - 2 * input_delta) * theta_one_minus_theta
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)
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derivative_numerator = input_delta.pow(2) * (
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input_derivatives_plus_one * root.pow(2)
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+ 2 * input_delta * theta_one_minus_theta
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+ input_derivatives * (1 - root).pow(2)
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)
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logabsdet = torch.log(derivative_numerator) - 2 * torch.log(denominator)
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return outputs, -logabsdet
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else:
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theta = (inputs - input_cumwidths) / input_bin_widths
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theta_one_minus_theta = theta * (1 - theta)
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numerator = input_heights * (input_delta * theta.pow(2) + input_derivatives * theta_one_minus_theta)
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denominator = input_delta + (
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(input_derivatives + input_derivatives_plus_one - 2 * input_delta) * theta_one_minus_theta
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)
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outputs = input_cumheights + numerator / denominator
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derivative_numerator = input_delta.pow(2) * (
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input_derivatives_plus_one * theta.pow(2)
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+ 2 * input_delta * theta_one_minus_theta
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+ input_derivatives * (1 - theta).pow(2)
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)
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logabsdet = torch.log(derivative_numerator) - 2 * torch.log(denominator)
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return outputs, logabsdet
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