NeuralProcesses 0.1.7

A framework for composing Neural Processes in Python

Neural Processes

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

This package is currently under construction. There will be more here soon. In the meantime, see NeuralProcesses.jl.

Contents:

• Installation
• Examples of Predefined Models
• Masking
  • Masking Particular Inputs
  • Using Masks to Batch Contexts of Different Sizes
• Build Your Own Model

Installation

See the instructions here. Then simply

pip install neuralprocesses

Examples of Predefined Models

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),
    B.randn(tf.float32, 16, 3, 10),
    B.randn(tf.float32, 16, 2, 15),
)
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())

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),
    B.randn(tf.float32, 16, 3, 10),
    B.randn(tf.float32, 16, 2, 15),
)
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())

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())

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),
    B.randn(torch.float32, 16, 3, 10),
    B.randn(torch.float32, 16, 2, 15),
)
mean, var = dist.mean, dist.var

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),
    B.randn(torch.float32, 16, 3, 10),
    B.randn(torch.float32, 16, 2, 15),
)
mean, var = dist.mean, dist.var

print(dist.logpdf(B.randn(torch.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

TensorFlow

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(),
    ),
)
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),
)