NeuralProcesses 0.1.8

A framework for composing Neural Processes in Python

Neural Processes

The package and manual are still under construction. If something is not working or unclear, please feel free to open an issue.

A framework for composing Neural Processes in Python. See also NeuralProcesses.jl.

Contents:

• Installation
• Examples of Predefined Models
  • PyTorch
    • GNP
    • ConvGNP
  • TensorFlow
    • GNP
    • ConvGNP
    • ConvGNP With Auxiliary Variables
• Masking
  • Masking Particular Inputs
  • Using Masks to Batch Contexts of Different Sizes
• Build Your Own Model
  • ConvGNP
  • ConvGNP With Auxiliary Variables

Installation

See the instructions here. Then simply

pip install neuralprocesses

Manual

Inputs and outputs are always tensors with shape (b, d, n) where b is the batch size, d is the dimensionality of the inputs/outputs, and n is the number of data points.

Examples of Predefined Models

PyTorch

GNP

import lab as B
import torch

import neuralprocesses.torch as nps

cnp = nps.construct_gnp(dim_x=2, dim_y=3, likelihood="lowrank")
dist = cnp(
    B.randn(torch.float32, 16, 2, 10),  # Context inputs
    B.randn(torch.float32, 16, 3, 10),  # Context outputs
    B.randn(torch.float32, 16, 2, 15),  # Target inputs
)
mean, var = dist.mean, dist.var  # Prediction for target outputs

print(dist.logpdf(B.randn(torch.float32, 16, 3, 15)))
print(dist.sample())
print(dist.kl(dist))
print(dist.entropy())

ConvGNP

import lab as B
import torch

import neuralprocesses.torch as nps

cnp = nps.construct_convgnp(dim_x=2, dim_y=3, likelihood="lowrank")
dist = cnp(
    B.randn(torch.float32, 16, 2, 10),  # Context inputs
    B.randn(torch.float32, 16, 3, 10),  # Context outputs
    B.randn(torch.float32, 16, 2, 15),  # Target inputs
)
mean, var = dist.mean, dist.var  # Prediction for target outputs

print(dist.logpdf(B.randn(torch.float32, 16, 3, 15)))
print(dist.sample())
print(dist.kl(dist))
print(dist.entropy())

TensorFlow

GNP

import lab as B
import tensorflow as tf

import neuralprocesses.tensorflow as nps

cnp = nps.construct_gnp(dim_x=2, dim_y=3, likelihood="lowrank")
dist = cnp(
    B.randn(tf.float32, 16, 2, 10),  # Context inputs
    B.randn(tf.float32, 16, 3, 10),  # Context outputs
    B.randn(tf.float32, 16, 2, 15),  # Target inputs
)
mean, var = dist.mean, dist.var  # Prediction for target outputs

print(dist.logpdf(B.randn(tf.float32, 16, 3, 15)))
print(dist.sample())
print(dist.kl(dist))
print(dist.entropy())

ConvGNP

import lab as B
import tensorflow as tf

import neuralprocesses.tensorflow as nps

cnp = nps.construct_convgnp(dim_x=2, dim_y=3, likelihood="lowrank")
dist = cnp(
    B.randn(tf.float32, 16, 2, 10),  # Context inputs
    B.randn(tf.float32, 16, 3, 10),  # Context outputs
    B.randn(tf.float32, 16, 2, 15),  # Target inputs
)
mean, var = dist.mean, dist.var  # Prediction for target outputs

print(dist.logpdf(B.randn(tf.float32, 16, 3, 15)))
print(dist.sample())
print(dist.kl(dist))
print(dist.entropy())

ConvGNP with Auxiliary Variables

import lab as B
import tensorflow as tf

import neuralprocesses.tensorflow as nps

cnp = nps.construct_convgnp(
    dim_x=2,
    dim_yc=(
        3,  # Observed data has three dimensions.
        1,  # First auxiliary variable has one dimension.
        2,  # Second auxiliary variable has two dimensions.
    ),
    # Third auxiliary variable has four dimensions and is auxiliary information specific
    # to the target inputs.
    dim_aux_t=4,
    dim_yt=3,  # Predictions have three dimensions.
    num_basis_functions=64, 
    likelihood="lowrank",
)

observed_data = (
    B.randn(tf.float32, 16, 2, 10),
    B.randn(tf.float32, 16, 3, 10),
)

# Define three auxiliary variables. The first one is specified like the observed data
# at arbitrary inputs.
aux_var1 = (
    B.randn(tf.float32, 16, 2, 12),
    B.randn(tf.float32, 16, 1, 12),  # Has one dimension.
)
# The second one is specified on a grid.
aux_var2 = (
    (B.randn(tf.float32, 16, 1, 25), B.randn(tf.float32, 16, 1, 35)),
    B.randn(tf.float32, 16, 2, 25, 35),  # Has two dimensions.
)
# The third one is specific to the target inputs. We could encode it like the first
# auxiliary variable `aux_var1`, but we illustrate how an MLP-style encoding can
# also be used. The number must match the number of target inputs!
aux_var_t = B.randn(tf.float32, 16, 4, 15)  # Has four dimensions.

dist = cnp(
    [observed_data, aux_var1, aux_var2],
    B.randn(tf.float32, 16, 2, 15),
    aux_t=aux_var_t,  # This must be given as a keyword argument.
)
mean, var = dist.mean, dist.var

print(dist.logpdf(B.randn(tf.float32, 16, 3, 15)))
print(dist.sample())
print(dist.kl(dist))
print(dist.entropy())

Masking

In this section, we'll take the following ConvGNP as a running example:

import lab as B
import torch

import neuralprocesses.torch as nps

cnp = nps.construct_convgnp(
    dim_x=2,
    dim_yc=(1, 1),  # Two context sets, both with one channel
    dim_yt=1, 
)

# Construct two sample context sets with one on a grid.
xc = B.randn(torch.float32, 1, 2, 20)
yc = B.randn(torch.float32, 1, 1, 20)
xc_grid = (B.randn(torch.float32, 1, 1, 10), B.randn(torch.float32, 1, 1, 15))
yc_grid = B.randn(torch.float32, 1, 1, 10, 15)

# Contruct sample target inputs
xt = B.randn(torch.float32, 1, 2, 50)

For example, then predictions can be made via

>>> pred = cnp([(xc, yc), (xc_grid, yc_grid)], xt)

Masking Particular Inputs

Suppose that due to a particular reason you didn't observe yc_grid[5, 5]. In the specification above, it is not possible to just omit that one element. The proposed solution is to use a mask. A mask mask is a tensor of the same size as the context outputs (yc_grid in this case) but with only one channel consisting of ones and zeros. If mask[i, 0, j, k] = 1, then that means that yc_grid[i, :, j, k] is observed. On the other hand, if mask[i, 0, j, k] = 0, then that means that yc_grid[i, :, j, k] is not observed. yc_grid[i, :, j, k] will still have values, which must be not NaNs, but those values will be ignored. To mask context outputs, use nps.Masked(yc_grid, mask).

Definition:

masked_yc = Masked(yc, mask)

Example:

>>> mask = B.ones(torch.float32, 1, 1, *B.shape(yc_grid, 2, 3))

>>> mask[:, :, 5, 5] = 0

>>> pred = cnp([(xc, yc), (xc_grid, nps.Masked(yc_grid, mask))], xt)

Masking is also possible for non-gridded contexts.

Example:

>>> mask = B.ones(torch.float32, 1, 1, B.shape(yc, 2))

>>> mask[:, :, 2:7] = 0   # Elements 3 to 7 are missing.

>>> pred = cnp([(xc, nps.Masked(yc, mask)), (xc_grid, yc_grid)], xt)

Using Masks to Batch Context Sets of Different Sizes

Suppose that we also had another context set, of a different size:

# Construct another two sample context sets with one on a grid.
xc2 = B.randn(torch.float32, 1, 2, 30)
yc2 = B.randn(torch.float32, 1, 1, 30)
xc2_grid = (B.randn(torch.float32, 1, 1, 5), B.randn(torch.float32, 1, 1, 20))
yc2_grid = B.randn(torch.float32, 1, 1, 5, 20)

Rather than running the model once for [(xc, yc), (xc_grid, yc_grid)] and once for [(xc2, yc2), (xc2_grid, yc2_grid)], we would like to concatenate the two context sets along the batch dimension and run the model only once. This, however, doesn't work, because the twe context sets have different sizes.

The proposed solution is to pad the context sets with zeros to align them, concatenate the padded contexts, and use a mask to reject the padded zeros. The function nps.merge_contexts can be used to do this automatically.

Definition:

xc_merged, yc_merged = nps.merge_contexts((xc1, yc1), (xc2, yc2), ...)

Example:

xc_merged, yc_merged = nps.merge_contexts((xc, yc), (xc2, yc2))
xc_grid_merged, yc_grid_merged = nps.merge_contexts(
    (xc_grid, yc_grid), (xc2_grid, yc2_grid)
)

>>> pred = cnp(
    [(xc_merged, yc_merged), (xc_grid_merged, yc_grid_merged)],
    B.concat(xt, xt, axis=0)
)

Build Your Own Model

ConvGNP

import lab as B
import tensorflow as tf

import neuralprocesses.tensorflow as nps

dim_x = 1
dim_y = 1

# CNN architecture:
unet = nps.UNet(
    dim=dim_x,
    in_channels=2 * dim_y,
    out_channels=(2 + 512) * dim_y,
    channels=(8, 16, 16, 32, 32, 64),
)

# Discretisation of the functional embedding:
disc = nps.Discretisation(
    points_per_unit=64,
    multiple=2**unet.num_halving_layers,
    margin=0.1,
    dim=dim_x,
)

# Create the encoder and decoder and construct the model.
encoder = nps.FunctionalCoder(
    disc,
    nps.Chain(
        nps.PrependDensityChannel(),
        nps.SetConv(scale=2 / disc.points_per_unit),
        nps.DivideByFirstChannel(),
        nps.DeterministicLikelihood(),
    ),
)
decoder = nps.Chain(
    unet,
    nps.SetConv(scale=2 / disc.points_per_unit),
    nps.LowRankGaussianLikelihood(512),
)
convgnp = nps.Model(encoder, decoder)

# Run the model on some random data.
dist = convgnp(
    B.randn(tf.float32, 16, 1, 10),
    B.randn(tf.float32, 16, 1, 10),
    B.randn(tf.float32, 16, 1, 15),
)

ConvGNP with Auxiliary Variables

import lab as B
import tensorflow as tf

import neuralprocesses.tensorflow as nps

dim_x = 2
# We will use two target sets with output dimensionalities `dim_y` and `dim_y2`.
dim_y = 1
dim_y2 = 10
# We will also use auxiliary target information of dimensionality `dim_aux_t`.
dim_aux_t = 7

# CNN architecture:
unet = nps.UNet(
    dim=dim_x,
    # The outputs are `dim_y`-dimensional, and we will use another context set
    # consisting of `dim_y2` variables. Both of these context sets will also have a
    # density channel.
    in_channels=dim_y + 1 + dim_y2 + 1,
    out_channels=8,
    channels=(8, 16, 16, 32, 32, 64),
)

# Discretisation of the functional embedding:
disc = nps.Discretisation(
    points_per_unit=32,
    multiple=2**unet.num_halving_layers,
    margin=0.1,
    dim=dim_x,
)

# Create the encoder and decoder and construct the model.
encoder = nps.FunctionalCoder(
    disc,
    nps.Chain(
        nps.PrependDensityChannel(),
        # Use a separate set conv for every context set. Here we initialise the length
        # scales of these set convs both to `2 / disc.points_per_unit`.
        nps.Parallel(
            nps.SetConv(scale=2 / disc.points_per_unit),
            nps.SetConv(scale=2 / disc.points_per_unit),
        ),
        nps.DivideByFirstChannel(),
        # Concatenate the encodings of the context sets.
        nps.Materialise(),
        nps.DeterministicLikelihood(),
    ),
)
decoder = nps.Chain(
    unet,
    nps.SetConv(scale=2 / disc.points_per_unit),
    # `nps.Augment` will concatenate any auxiliary information to the current encoding
    # before proceedings.
    nps.Augment(
        nps.Chain(
            nps.MLP(
                # Input dimensionality is equal to the number of channels coming out of
                # `unet` plus the dimensionality of the auxiliary target information.
                in_dim=8 + dim_aux_t,
                layers=(128,) * 3,
                out_dim=(2 + 512) * dim_y,
            ),
            nps.LowRankGaussianLikelihood(512),
        )
    )
)
convgnp = nps.Model(encoder, decoder)

# Run the model on some random data.
dist = convgnp(
    [
        (
            B.randn(tf.float32, 16, dim_x, 10),
            B.randn(tf.float32, 16, dim_y, 10),
        ),
        (
            # The second context set is given on a grid.
            (B.randn(tf.float32, 16, 1, 12), B.randn(tf.float32, 16, 1, 12)),
            B.randn(tf.float32, 16, dim_y2, 12, 12),
        )
    ],
    B.randn(tf.float32, 16, dim_x, 15),
    aux_t=B.randn(tf.float32, 16, dim_aux_t, 15),
)