ABaCo demo: Mgnify study MGYS00001135#

In this demo we will implement ABaCo for batch correction on Mgnify study MGYS00001135 and ENA Bioproject PRJEB13832, a proof-of-concept study for surveilling infections diseases and AMR via metagenomics analysis of local sewage samples in Copenhagen.


Data Description:

  • The metagenomics dataset collected by the Technical University of Denmark (DTU) and analysed via Mgnify pipeline version 2.0 is a dataset composed of 54 samples with 749 identified taxa at the genus level.

  • The samples were collected from 3 different wastewater treatment plant (WWTP) locations, accounting for the biological source of variation.

  • Samples were analyzed on 2 different dates accounting for the technical source of variation (i.e., batch effect).

  • The sample data and metadata were retrieved from the Mgnify API using the following mgnifyapi repo and stored as an Annotated Dataset AnnData.

Goal:

With ABaCo the aim is to remove the technical variation (batch effect) while maintaining any biological variation (wastewater treatment plant location).


To start we read in the annotated dataset.

import anndata as ad
import pandas as pd 
import numpy as np

# read in annotated dataset
adata = ad.read_h5ad("data/mgnify_MGYS00001135.h5ad")
# print details
adata
AnnData object with n_obs × n_vars = 54 × 749
    obs: 'analysis_id', 'sample_id', 'assembly_run_id', 'experiment_type', 'pipeline_version', 'study_id', 'instrument_platform', 'sample_name', 'biosample', 'sample_description', 'latitude', 'longitude', 'geolocation', 'biome_feature', 'biome_material', 'id', 'collection_date', 'collection_date_year', 'collection_date_month', 'collection_date_day', 'analysis_completed_date', 'analysis_completed_date_year', 'analysis_completed_date_month', 'analysis_completed_date_day', 'fname_run_id', 'erp_id', 'study_name', 'n_samples', 'biomes', 'ww_plant', 'X_numtaxa', 'X_chao1', 'X_shannon', 'X_pielou', 'X_simpson', 'X_inv_simpson'
    var: 'sk', 'k', 'p', 'c', 'o', 'f', 'g'
    layers: 'abaco', 'clr_X', 'clr_abaco', 'normalized_X', 'normalized_abaco'

The columns (variables, vars) are the different taxa annotated with taxonomic ranks (sk = super kingdom, k = kingdom, p = phylum, c = class, o = order, f = family, g = genus).

The rows (observations, obs) are the metadata for the different samples in the study MGYS00001135.

The ones of interest for this demo are:

  • The analysis_completed_date which accounts for batch effect for our purposes, and

  • ww_plant which are the different sampling locations and we will use as our biological variance that we wish to retain after batch correction.


We can easily extract a df from anndata so that we meet the data format required for abaco.

batch_col = 'analysis_completed_date'
bio_col = 'ww_plant'
id_col = 'index'

# the raw counts as df
df_taxa = adata.to_df()

# appending on the categorical data of interest
df_all = pd.concat([df_taxa, adata.obs[[batch_col, bio_col]]], axis=1).reset_index()
df_all.info()
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 54 entries, 0 to 53
Columns: 752 entries, index to ww_plant
dtypes: category(2), float64(749), object(1)
memory usage: 316.9+ KB

pd.DataFrame Requirements for ABaCo:

The dataset contains the following making it compatible with the ABaCo framework:

id_col

batch_col

bio_col

count1

count2

A

24/07/2025

RA

#

#

B

15/06/2024

RD

#

#

C

24/07/2025

RL

#

#

  • The data has categorical columns:

    1. unique ids to identify the observations/samples e.g. sample id col

    2. ids for the batch/factor groupings to be corrected by abaco. e.g. dates of sample analysis batch_col

    3. biological/experimental factor variation for abaco to retain when correcting batch effect e.g., sampling location bio_col

  • And taxa counts to be trained on.

We can use abaco.plots.plotPCoA() to visualize any batch and biological effects based on the given categories.

from abaco.plots import plotPCoA
import plotly.io as pio
pio.renderers.default = "notebook_connected"

plotPCoA(
    data=df_all, 
    sample_label=id_col, 
    batch_label=batch_col,  
    experiment_label=bio_col,
)
  • Batch effect (colours):

    • Analysis of the samples were completed on 2 different dates which could result in a technical source of variation captured by the slight clustering of batches along PCo1

  • Biological effect (shapes):

    • The samples were collected from 3 different wwtps which we use as the biological source of variation for abaco to retain during batch correction.

    • There isn’t a clear clustering of shapes in the PCoA plot, but we can take a look at other metrics such as alpha diversity indices between wwtp locations that should be retained after abaco reconstruction.

Alpha diversity of original samples#

For each sample we will calculate the below richess, evenness and diversity indices and store them as additional sample (obs) metadata in the anndata set.

Richness

  • number of unique species per sample

  • Chao1 estimate - correction to above which is likely an underestimation

Diversity

  • Shannon diversity index - if a sample is more diverse then there is more entropy (predicting the next taxa is more difficult) and thus the Shannon diversity index is higher.

  • Simpson index (and inverse) - probability of 2 microbes being the same taxa (Simpson index closer to 0 is more diverse, while a higher inverse Simpson index means a sample is more diverse)

Evenness

  • Pielou’s evenness index - when abundances are more homogenous in a sample then more even so higher Pielou

The formulas are included with the below code. The metrics name will be prefixed with ‘X_’ so that we can later compare them to ‘abaco_’ metrics.

Preprocessing the count tables#

The raw counts require preprocessing because samples will have different total read counts due to technical differences during sequencing. We can normalize the samples to get relative abundances of the taxa summing to 1 (composition data).

# normalize original data and store as additional anndata layer
adata.layers['normalized_X'] = (adata.X/adata.X.sum(axis=1).reshape(-1,1))
# sanity check 
adata.layers['normalized_X'].sum(axis=1)
array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1.])

Our normalized, compositional data (CoDa) is bound to a simplex. To move forward with any statistical tests or ML we can choose to map the coda to unconstrained vectors by log-ratio transforming (e.g., centred log-ratio via skbio.stats.composition.clr()) the data.

from skbio.stats.composition import clr 

# CLR transform normalized data, replacing zeros with smallll val to avoid log(0)
adata.layers['clr_X'] = clr(np.where(adata.layers['normalized_X'] > 0, adata.layers['normalized_X'], 1e-10))

# save anndata with new layers
adata.write_h5ad("data/mgnify_MGYS00001135.h5ad")

Alpha diversity as sample metadata#

# Diversity: Number of unique taxa per sample as new metadata
adata.obs['X_numtaxa'] = (adata.X > 0).sum(axis=1) 

# Diversity with correction: Chao1 estimator
# Chao1 = num observed taxa + (num singletons / (2 x num doubletons))
num_singletons = (adata.X == 1).sum(axis=1)
num_doubletons = (adata.X == 2).sum(axis=1)
adata.obs['X_chao1'] = (adata.X > 0).sum(axis=1) + (num_singletons / (2 * num_doubletons))

# Diversity: Shannon index H = -sum(p_i * log(p_i)), entropy
from scipy.stats import entropy
adata.obs['X_shannon'] = entropy(adata.layers['normalized_X'], nan_policy='omit', axis=1)

# Evenness: Pielou evenness index P = H/H_max, H_max = ln(num species)
adata.obs['X_pielou'] = adata.obs['X_shannon'] / np.log(adata.obs['X_numtaxa'])

# Diversity: simpson index lambda = sum(p_i ^2)
adata.obs['X_simpson'] = (adata.layers['normalized_X'] ** 2).sum(axis=1)

# Diversity: inverse simpson index D = 1/lambda
adata.obs['X_inv_simpson'] = 1 / adata.obs['X_simpson']

We can quickly visualize the distribution and relationships between the metrics by batch and biological groups using seaborn.pairplot()

import seaborn as sns
import matplotlib.pyplot as plt

# preparing the df for vis
df_alphas = adata.obs[[
    'X_numtaxa', 'X_chao1', 'X_shannon', 
    'X_pielou', 'X_simpson', 'X_inv_simpson',
    batch_col, bio_col
]].copy()

# plotting by bio groups
g1 = sns.pairplot(df_alphas, hue=bio_col, corner=True, height=1.8)
g1.figure.suptitle('Alpha Diversity by Biological Groups', fontsize=22)
plt.setp(g1._legend.get_texts(), fontsize=18)
plt.setp(g1._legend.get_title(), fontsize=20)

g2 = sns.pairplot(df_alphas, hue=batch_col, corner=True, height=1.8)
g2.figure.suptitle('Alpha Diversity by Batch Groups', fontsize=22)
plt.setp(g2._legend.get_texts(), fontsize=18)
plt.setp(g2._legend.get_title(), fontsize=20)
[None]
../_images/92430c102caf777711ec990abc4a2b9afb1cf0a7f2353393685cccb8cae14853.png ../_images/585b6a61d9da91c538ebae3e246fd4cfd7acc97af679627ef4ad00eaaf6e54f1.png

The pairplots suggest that the batch effect could be influencing the alpha diversity of the samples.


The goal#

Here the aim of ABaCo is to:

  1. correct the batch effect (e.g., the points should no longer cluster by colour in the PCoA and pairplot) while

  2. maintaining biological variance (e.g., the pairplot coloured by bio group should be not change).

Ideally, after using AbaCo to transform the data, the resulting PCoA and pairplot coloured by batches will look like a colourful mixture of points and the pairplot coloured by wwtp location should not change.


Using ABaCo#

Setting up ABaCo#

We instantiate the abaco.metaABaCo() class and pass the required parameters shown in the cell below. Thus, running abaco with the default optional parameters.

Usually, setup of the parameters is required, which are explained in brief in the documentation e.g. help(metaABaCo)

from abaco.ABaCo import metaABaCo
import torch

device = torch.device("cuda" if torch.cuda.is_available() else "cpu")

# Instaantiate the ABaCo model
model = metaABaCo(
    data=df_all, # Pre-processed dataframe
    n_bios=df_all[bio_col].nunique(), # Number of biological groups in the data
    bio_label=bio_col, # Column where biological groups are labeled in the dataframe
    n_batches=df_all[batch_col].nunique(), # Number of batch groups in the data
    batch_label=batch_col, # Column where batch groups are labeled in the dataframe
    n_features=df_taxa.shape[1], # Number of features (taxonomic groups)
    prior="MoG", # Prior distribution 
    device=device, # Device
)
help(metaABaCo)

Hide code cell output

Help on class metaABaCo in module abaco.ABaCo:

class metaABaCo(torch.nn.modules.module.Module)
 |  metaABaCo(data, n_bios, bio_label, n_batches, batch_label, n_features, device, prior='MoG', pdist='ZINB', d_z=16, epochs=[1000, 2000, 2000], encoder_net=[512, 256, 128], decoder_net=[128, 256, 512], vae_act_fun=ReLU(), disc_net=[128, 64], disc_act_fun=ReLU())
 |  
 |  Method resolution order:
 |      metaABaCo
 |      torch.nn.modules.module.Module
 |      builtins.object
 |  
 |  Methods defined here:
 |  
 |  __init__(self, data, n_bios, bio_label, n_batches, batch_label, n_features, device, prior='MoG', pdist='ZINB', d_z=16, epochs=[1000, 2000, 2000], encoder_net=[512, 256, 128], decoder_net=[128, 256, 512], vae_act_fun=ReLU(), disc_net=[128, 64], disc_act_fun=ReLU())
 |      Function to create the metaABaCo model.
 |      
 |      Parameters
 |      ----------
 |      data: pd.DataFrame
 |          Pre-processed DataFrame to correct. Only feature columns to correct should be of numerical data type.
 |      n_bios: int
 |          Number of labels or (potential) clusters based on biological variance. For example, if 2 experimental
 |          conditions (e.g., control and treatment) then n_bios = 2.
 |      bio_label: char
 |          Column label where biological labels are contained in data.
 |      n_batches: int
 |          Number of batches in the dataset. For example, if samples were sequenced in
 |          5 batches (e.g., 5 different dates) then batches = 5.
 |      batch_label: char
 |          Column label where batch labels are contained in data.
 |      n_features: int
 |          Number of features in the input data, columns. For example, if the input is a gene expression matrix with 1000 genes,
 |          then input_size = 1000.
 |      device: torch.device
 |          Device to run the model on, e.g., "cuda" or "cpu".
 |      prior: str
 |          Prior distribution used. Baseline is "VMM" (VampPrior Mixture Model). Options are "VMM" and
 |          "MoG" (Mixture of Gaussians).
 |      pdist: str
 |          Output distribution used. Baseline is "ZINB" (Zero-inflated Negative Binomial).
 |      d_z: int
 |          Dimensionality of the latent space. For example, if d_z = 16, then the latent space will have 16 dimensions.
 |      epochs: list
 |          Number of epochs for first, second and third phase of ABaCo. Default is [1000, 2000, 2000]
 |      encoder_net: list
 |          List of integers defining the architecture of the encoder. Each integer is a layer size.
 |          For example, [1024, 512, 256] means the encoder will have three layers with 1024, 512, and 256 neurons respectively.
 |      decoder_net: list
 |          List of integers defining the architecture of the decoder. Each integer is a layer size.
 |          For example, [256, 512, 1024] means the decoder will have three layers with 256, 512, and 1024 neurons respectively.
 |      vae_act_func: nn.Module
 |          Activation function for the VAE encoder and decoder. Default is nn.ReLU().
 |      disc_net: list
 |          List of integers defining the architecture of the discriminator. Each integer is a layer size.
 |          For example, [256, 128, 64] means the discriminator will have three layers with 256, 128, and 64 neurons respectively.
 |      disc_act_fun: nn.Module
 |          Activation function for the discriminator. Default is nn.ReLU().
 |  
 |  batch_correct(self, train_loader, vae_optimizer, disc_optimizer, adv_optimizer, w_disc=1.0, w_adv=1.0, w_elbo_nll=1.0, w_elbo_kl=1.0, w_bio_penalty=1.0, w_cluster_penalty=1.0)
 |      Train the conditional VAE model for batch correction. This is trained after VAE prior parameters are defined,
 |  
 |  batch_mask(self, train_loader, decoder_optimizer, smooth_annealing=True, cycle_reg=None, w_elbo_nll=1.0, w_cycle=0.001)
 |      Pre-trained VAE will now have frozen encoder and batch labels masked at the encoder.
 |  
 |  correct(self, seed=None, mask=True)
 |  
 |  fit(self, smooth_annealing=True, cycle_reg=None, seed=None, w_elbo_nll=1.0, w_elbo_kl=1.0, w_bio_penalty=1.0, w_cluster_penalty=1.0, w_cycle=0.001, w_disc=1.0, w_adv=1.0, phase_1_vae_lr=0.001, phase_2_vae_lr=0.001, phase_3_vae_lr=1e-06, disc_lr=0.001, adv_lr=0.001)
 |  
 |  plot_pca_posterior(self, figsize=(14, 6), palette='tab10')
 |      Get the plot of the first 2 principal components of the posterior distribution.
 |  
 |  train_vae(self, train_loader, optimizer, w_elbo_nll=1.0, w_elbo_kl=1.0, w_bio_penalty=1.0, w_cluster_penalty=1.0)
 |      Train the conditional VAE model. If clustering prior is used, penalization term is applied to increase sparsity of the clusters.
 |      
 |      Parameters:
 |          vae: [VAE]
 |              Variational Autoencoder model
 |          train_loader: [torch.utils.data.DataLoader]
 |              DataLoader for the training data
 |          optimizer: [torch.optim.Optimizer]
 |              Optimizer for training
 |          epochs: [int]
 |              Number of training epochs
 |          device: [str]
 |              Device to use for computations
 |  
 |  ----------------------------------------------------------------------
 |  Data and other attributes defined here:
 |  
 |  __annotations__ = {}
 |  
 |  ----------------------------------------------------------------------
 |  Methods inherited from torch.nn.modules.module.Module:
 |  
 |  __call__ = _wrapped_call_impl(self, *args, **kwargs)
 |  
 |  __delattr__(self, name)
 |      Implement delattr(self, name).
 |  
 |  __dir__(self)
 |      Default dir() implementation.
 |  
 |  __getattr__(self, name: str) -> Union[torch.Tensor, ForwardRef('Module')]
 |      # It is crucial that the return type is not annotated as `Any`, otherwise type checking
 |      # on `torch.nn.Module` and all its subclasses is largely disabled as a result. See:
 |      # https://github.com/pytorch/pytorch/pull/115074
 |  
 |  __getstate__(self)
 |      Helper for pickle.
 |  
 |  __repr__(self)
 |      Return repr(self).
 |  
 |  __setattr__(self, name: str, value: Union[torch.Tensor, ForwardRef('Module')]) -> None
 |      Implement setattr(self, name, value).
 |  
 |  __setstate__(self, state)
 |  
 |  add_module(self, name: str, module: Optional[ForwardRef('Module')]) -> None
 |      Add a child module to the current module.
 |      
 |      The module can be accessed as an attribute using the given name.
 |      
 |      Args:
 |          name (str): name of the child module. The child module can be
 |              accessed from this module using the given name
 |          module (Module): child module to be added to the module.
 |  
 |  apply(self: ~T, fn: Callable[[ForwardRef('Module')], NoneType]) -> ~T
 |      Apply ``fn`` recursively to every submodule (as returned by ``.children()``) as well as self.
 |      
 |      Typical use includes initializing the parameters of a model
 |      (see also :ref:`nn-init-doc`).
 |      
 |      Args:
 |          fn (:class:`Module` -> None): function to be applied to each submodule
 |      
 |      Returns:
 |          Module: self
 |      
 |      Example::
 |      
 |          >>> @torch.no_grad()
 |          >>> def init_weights(m):
 |          >>>     print(m)
 |          >>>     if type(m) == nn.Linear:
 |          >>>         m.weight.fill_(1.0)
 |          >>>         print(m.weight)
 |          >>> net = nn.Sequential(nn.Linear(2, 2), nn.Linear(2, 2))
 |          >>> net.apply(init_weights)
 |          Linear(in_features=2, out_features=2, bias=True)
 |          Parameter containing:
 |          tensor([[1., 1.],
 |                  [1., 1.]], requires_grad=True)
 |          Linear(in_features=2, out_features=2, bias=True)
 |          Parameter containing:
 |          tensor([[1., 1.],
 |                  [1., 1.]], requires_grad=True)
 |          Sequential(
 |            (0): Linear(in_features=2, out_features=2, bias=True)
 |            (1): Linear(in_features=2, out_features=2, bias=True)
 |          )
 |  
 |  bfloat16(self: ~T) -> ~T
 |      Casts all floating point parameters and buffers to ``bfloat16`` datatype.
 |      
 |      .. note::
 |          This method modifies the module in-place.
 |      
 |      Returns:
 |          Module: self
 |  
 |  buffers(self, recurse: bool = True) -> collections.abc.Iterator[torch.Tensor]
 |      Return an iterator over module buffers.
 |      
 |      Args:
 |          recurse (bool): if True, then yields buffers of this module
 |              and all submodules. Otherwise, yields only buffers that
 |              are direct members of this module.
 |      
 |      Yields:
 |          torch.Tensor: module buffer
 |      
 |      Example::
 |      
 |          >>> # xdoctest: +SKIP("undefined vars")
 |          >>> for buf in model.buffers():
 |          >>>     print(type(buf), buf.size())
 |          <class 'torch.Tensor'> (20L,)
 |          <class 'torch.Tensor'> (20L, 1L, 5L, 5L)
 |  
 |  children(self) -> collections.abc.Iterator['Module']
 |      Return an iterator over immediate children modules.
 |      
 |      Yields:
 |          Module: a child module
 |  
 |  compile(self, *args, **kwargs)
 |      Compile this Module's forward using :func:`torch.compile`.
 |      
 |      This Module's `__call__` method is compiled and all arguments are passed as-is
 |      to :func:`torch.compile`.
 |      
 |      See :func:`torch.compile` for details on the arguments for this function.
 |  
 |  cpu(self: ~T) -> ~T
 |      Move all model parameters and buffers to the CPU.
 |      
 |      .. note::
 |          This method modifies the module in-place.
 |      
 |      Returns:
 |          Module: self
 |  
 |  cuda(self: ~T, device: Union[int, torch.device, NoneType] = None) -> ~T
 |      Move all model parameters and buffers to the GPU.
 |      
 |      This also makes associated parameters and buffers different objects. So
 |      it should be called before constructing the optimizer if the module will
 |      live on GPU while being optimized.
 |      
 |      .. note::
 |          This method modifies the module in-place.
 |      
 |      Args:
 |          device (int, optional): if specified, all parameters will be
 |              copied to that device
 |      
 |      Returns:
 |          Module: self
 |  
 |  double(self: ~T) -> ~T
 |      Casts all floating point parameters and buffers to ``double`` datatype.
 |      
 |      .. note::
 |          This method modifies the module in-place.
 |      
 |      Returns:
 |          Module: self
 |  
 |  eval(self: ~T) -> ~T
 |      Set the module in evaluation mode.
 |      
 |      This has an effect only on certain modules. See the documentation of
 |      particular modules for details of their behaviors in training/evaluation
 |      mode, i.e. whether they are affected, e.g. :class:`Dropout`, :class:`BatchNorm`,
 |      etc.
 |      
 |      This is equivalent with :meth:`self.train(False) <torch.nn.Module.train>`.
 |      
 |      See :ref:`locally-disable-grad-doc` for a comparison between
 |      `.eval()` and several similar mechanisms that may be confused with it.
 |      
 |      Returns:
 |          Module: self
 |  
 |  extra_repr(self) -> str
 |      Return the extra representation of the module.
 |      
 |      To print customized extra information, you should re-implement
 |      this method in your own modules. Both single-line and multi-line
 |      strings are acceptable.
 |  
 |  float(self: ~T) -> ~T
 |      Casts all floating point parameters and buffers to ``float`` datatype.
 |      
 |      .. note::
 |          This method modifies the module in-place.
 |      
 |      Returns:
 |          Module: self
 |  
 |  forward = _forward_unimplemented(self, *input: Any) -> None
 |      Define the computation performed at every call.
 |      
 |      Should be overridden by all subclasses.
 |      
 |      .. note::
 |          Although the recipe for forward pass needs to be defined within
 |          this function, one should call the :class:`Module` instance afterwards
 |          instead of this since the former takes care of running the
 |          registered hooks while the latter silently ignores them.
 |  
 |  get_buffer(self, target: str) -> 'Tensor'
 |      Return the buffer given by ``target`` if it exists, otherwise throw an error.
 |      
 |      See the docstring for ``get_submodule`` for a more detailed
 |      explanation of this method's functionality as well as how to
 |      correctly specify ``target``.
 |      
 |      Args:
 |          target: The fully-qualified string name of the buffer
 |              to look for. (See ``get_submodule`` for how to specify a
 |              fully-qualified string.)
 |      
 |      Returns:
 |          torch.Tensor: The buffer referenced by ``target``
 |      
 |      Raises:
 |          AttributeError: If the target string references an invalid
 |              path or resolves to something that is not a
 |              buffer
 |  
 |  get_extra_state(self) -> Any
 |      Return any extra state to include in the module's state_dict.
 |      
 |      Implement this and a corresponding :func:`set_extra_state` for your module
 |      if you need to store extra state. This function is called when building the
 |      module's `state_dict()`.
 |      
 |      Note that extra state should be picklable to ensure working serialization
 |      of the state_dict. We only provide backwards compatibility guarantees
 |      for serializing Tensors; other objects may break backwards compatibility if
 |      their serialized pickled form changes.
 |      
 |      Returns:
 |          object: Any extra state to store in the module's state_dict
 |  
 |  get_parameter(self, target: str) -> 'Parameter'
 |      Return the parameter given by ``target`` if it exists, otherwise throw an error.
 |      
 |      See the docstring for ``get_submodule`` for a more detailed
 |      explanation of this method's functionality as well as how to
 |      correctly specify ``target``.
 |      
 |      Args:
 |          target: The fully-qualified string name of the Parameter
 |              to look for. (See ``get_submodule`` for how to specify a
 |              fully-qualified string.)
 |      
 |      Returns:
 |          torch.nn.Parameter: The Parameter referenced by ``target``
 |      
 |      Raises:
 |          AttributeError: If the target string references an invalid
 |              path or resolves to something that is not an
 |              ``nn.Parameter``
 |  
 |  get_submodule(self, target: str) -> 'Module'
 |      Return the submodule given by ``target`` if it exists, otherwise throw an error.
 |      
 |      For example, let's say you have an ``nn.Module`` ``A`` that
 |      looks like this:
 |      
 |      .. code-block:: text
 |      
 |          A(
 |              (net_b): Module(
 |                  (net_c): Module(
 |                      (conv): Conv2d(16, 33, kernel_size=(3, 3), stride=(2, 2))
 |                  )
 |                  (linear): Linear(in_features=100, out_features=200, bias=True)
 |              )
 |          )
 |      
 |      (The diagram shows an ``nn.Module`` ``A``. ``A`` which has a nested
 |      submodule ``net_b``, which itself has two submodules ``net_c``
 |      and ``linear``. ``net_c`` then has a submodule ``conv``.)
 |      
 |      To check whether or not we have the ``linear`` submodule, we
 |      would call ``get_submodule("net_b.linear")``. To check whether
 |      we have the ``conv`` submodule, we would call
 |      ``get_submodule("net_b.net_c.conv")``.
 |      
 |      The runtime of ``get_submodule`` is bounded by the degree
 |      of module nesting in ``target``. A query against
 |      ``named_modules`` achieves the same result, but it is O(N) in
 |      the number of transitive modules. So, for a simple check to see
 |      if some submodule exists, ``get_submodule`` should always be
 |      used.
 |      
 |      Args:
 |          target: The fully-qualified string name of the submodule
 |              to look for. (See above example for how to specify a
 |              fully-qualified string.)
 |      
 |      Returns:
 |          torch.nn.Module: The submodule referenced by ``target``
 |      
 |      Raises:
 |          AttributeError: If at any point along the path resulting from
 |              the target string the (sub)path resolves to a non-existent
 |              attribute name or an object that is not an instance of ``nn.Module``.
 |  
 |  half(self: ~T) -> ~T
 |      Casts all floating point parameters and buffers to ``half`` datatype.
 |      
 |      .. note::
 |          This method modifies the module in-place.
 |      
 |      Returns:
 |          Module: self
 |  
 |  ipu(self: ~T, device: Union[int, torch.device, NoneType] = None) -> ~T
 |      Move all model parameters and buffers to the IPU.
 |      
 |      This also makes associated parameters and buffers different objects. So
 |      it should be called before constructing the optimizer if the module will
 |      live on IPU while being optimized.
 |      
 |      .. note::
 |          This method modifies the module in-place.
 |      
 |      Arguments:
 |          device (int, optional): if specified, all parameters will be
 |              copied to that device
 |      
 |      Returns:
 |          Module: self
 |  
 |  load_state_dict(self, state_dict: collections.abc.Mapping[str, typing.Any], strict: bool = True, assign: bool = False)
 |      Copy parameters and buffers from :attr:`state_dict` into this module and its descendants.
 |      
 |      If :attr:`strict` is ``True``, then
 |      the keys of :attr:`state_dict` must exactly match the keys returned
 |      by this module's :meth:`~torch.nn.Module.state_dict` function.
 |      
 |      .. warning::
 |          If :attr:`assign` is ``True`` the optimizer must be created after
 |          the call to :attr:`load_state_dict` unless
 |          :func:`~torch.__future__.get_swap_module_params_on_conversion` is ``True``.
 |      
 |      Args:
 |          state_dict (dict): a dict containing parameters and
 |              persistent buffers.
 |          strict (bool, optional): whether to strictly enforce that the keys
 |              in :attr:`state_dict` match the keys returned by this module's
 |              :meth:`~torch.nn.Module.state_dict` function. Default: ``True``
 |          assign (bool, optional): When set to ``False``, the properties of the tensors
 |              in the current module are preserved whereas setting it to ``True`` preserves
 |              properties of the Tensors in the state dict. The only
 |              exception is the ``requires_grad`` field of :class:`~torch.nn.Parameter`s
 |              for which the value from the module is preserved.
 |              Default: ``False``
 |      
 |      Returns:
 |          ``NamedTuple`` with ``missing_keys`` and ``unexpected_keys`` fields:
 |              * **missing_keys** is a list of str containing any keys that are expected
 |                  by this module but missing from the provided ``state_dict``.
 |              * **unexpected_keys** is a list of str containing the keys that are not
 |                  expected by this module but present in the provided ``state_dict``.
 |      
 |      Note:
 |          If a parameter or buffer is registered as ``None`` and its corresponding key
 |          exists in :attr:`state_dict`, :meth:`load_state_dict` will raise a
 |          ``RuntimeError``.
 |  
 |  modules(self) -> collections.abc.Iterator['Module']
 |      Return an iterator over all modules in the network.
 |      
 |      Yields:
 |          Module: a module in the network
 |      
 |      Note:
 |          Duplicate modules are returned only once. In the following
 |          example, ``l`` will be returned only once.
 |      
 |      Example::
 |      
 |          >>> l = nn.Linear(2, 2)
 |          >>> net = nn.Sequential(l, l)
 |          >>> for idx, m in enumerate(net.modules()):
 |          ...     print(idx, '->', m)
 |      
 |          0 -> Sequential(
 |            (0): Linear(in_features=2, out_features=2, bias=True)
 |            (1): Linear(in_features=2, out_features=2, bias=True)
 |          )
 |          1 -> Linear(in_features=2, out_features=2, bias=True)
 |  
 |  mtia(self: ~T, device: Union[int, torch.device, NoneType] = None) -> ~T
 |      Move all model parameters and buffers to the MTIA.
 |      
 |      This also makes associated parameters and buffers different objects. So
 |      it should be called before constructing the optimizer if the module will
 |      live on MTIA while being optimized.
 |      
 |      .. note::
 |          This method modifies the module in-place.
 |      
 |      Arguments:
 |          device (int, optional): if specified, all parameters will be
 |              copied to that device
 |      
 |      Returns:
 |          Module: self
 |  
 |  named_buffers(self, prefix: str = '', recurse: bool = True, remove_duplicate: bool = True) -> collections.abc.Iterator[tuple[str, torch.Tensor]]
 |      Return an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.
 |      
 |      Args:
 |          prefix (str): prefix to prepend to all buffer names.
 |          recurse (bool, optional): if True, then yields buffers of this module
 |              and all submodules. Otherwise, yields only buffers that
 |              are direct members of this module. Defaults to True.
 |          remove_duplicate (bool, optional): whether to remove the duplicated buffers in the result. Defaults to True.
 |      
 |      Yields:
 |          (str, torch.Tensor): Tuple containing the name and buffer
 |      
 |      Example::
 |      
 |          >>> # xdoctest: +SKIP("undefined vars")
 |          >>> for name, buf in self.named_buffers():
 |          >>>     if name in ['running_var']:
 |          >>>         print(buf.size())
 |  
 |  named_children(self) -> collections.abc.Iterator[tuple[str, 'Module']]
 |      Return an iterator over immediate children modules, yielding both the name of the module as well as the module itself.
 |      
 |      Yields:
 |          (str, Module): Tuple containing a name and child module
 |      
 |      Example::
 |      
 |          >>> # xdoctest: +SKIP("undefined vars")
 |          >>> for name, module in model.named_children():
 |          >>>     if name in ['conv4', 'conv5']:
 |          >>>         print(module)
 |  
 |  named_modules(self, memo: Optional[set['Module']] = None, prefix: str = '', remove_duplicate: bool = True)
 |      Return an iterator over all modules in the network, yielding both the name of the module as well as the module itself.
 |      
 |      Args:
 |          memo: a memo to store the set of modules already added to the result
 |          prefix: a prefix that will be added to the name of the module
 |          remove_duplicate: whether to remove the duplicated module instances in the result
 |              or not
 |      
 |      Yields:
 |          (str, Module): Tuple of name and module
 |      
 |      Note:
 |          Duplicate modules are returned only once. In the following
 |          example, ``l`` will be returned only once.
 |      
 |      Example::
 |      
 |          >>> l = nn.Linear(2, 2)
 |          >>> net = nn.Sequential(l, l)
 |          >>> for idx, m in enumerate(net.named_modules()):
 |          ...     print(idx, '->', m)
 |      
 |          0 -> ('', Sequential(
 |            (0): Linear(in_features=2, out_features=2, bias=True)
 |            (1): Linear(in_features=2, out_features=2, bias=True)
 |          ))
 |          1 -> ('0', Linear(in_features=2, out_features=2, bias=True))
 |  
 |  named_parameters(self, prefix: str = '', recurse: bool = True, remove_duplicate: bool = True) -> collections.abc.Iterator[tuple[str, torch.nn.parameter.Parameter]]
 |      Return an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.
 |      
 |      Args:
 |          prefix (str): prefix to prepend to all parameter names.
 |          recurse (bool): if True, then yields parameters of this module
 |              and all submodules. Otherwise, yields only parameters that
 |              are direct members of this module.
 |          remove_duplicate (bool, optional): whether to remove the duplicated
 |              parameters in the result. Defaults to True.
 |      
 |      Yields:
 |          (str, Parameter): Tuple containing the name and parameter
 |      
 |      Example::
 |      
 |          >>> # xdoctest: +SKIP("undefined vars")
 |          >>> for name, param in self.named_parameters():
 |          >>>     if name in ['bias']:
 |          >>>         print(param.size())
 |  
 |  parameters(self, recurse: bool = True) -> collections.abc.Iterator[torch.nn.parameter.Parameter]
 |      Return an iterator over module parameters.
 |      
 |      This is typically passed to an optimizer.
 |      
 |      Args:
 |          recurse (bool): if True, then yields parameters of this module
 |              and all submodules. Otherwise, yields only parameters that
 |              are direct members of this module.
 |      
 |      Yields:
 |          Parameter: module parameter
 |      
 |      Example::
 |      
 |          >>> # xdoctest: +SKIP("undefined vars")
 |          >>> for param in model.parameters():
 |          >>>     print(type(param), param.size())
 |          <class 'torch.Tensor'> (20L,)
 |          <class 'torch.Tensor'> (20L, 1L, 5L, 5L)
 |  
 |  register_backward_hook(self, hook: Callable[[ForwardRef('Module'), Union[tuple[torch.Tensor, ...], torch.Tensor], Union[tuple[torch.Tensor, ...], torch.Tensor]], Union[NoneType, tuple[torch.Tensor, ...], torch.Tensor]]) -> torch.utils.hooks.RemovableHandle
 |      Register a backward hook on the module.
 |      
 |      This function is deprecated in favor of :meth:`~torch.nn.Module.register_full_backward_hook` and
 |      the behavior of this function will change in future versions.
 |      
 |      Returns:
 |          :class:`torch.utils.hooks.RemovableHandle`:
 |              a handle that can be used to remove the added hook by calling
 |              ``handle.remove()``
 |  
 |  register_buffer(self, name: str, tensor: Optional[torch.Tensor], persistent: bool = True) -> None
 |      Add a buffer to the module.
 |      
 |      This is typically used to register a buffer that should not to be
 |      considered a model parameter. For example, BatchNorm's ``running_mean``
 |      is not a parameter, but is part of the module's state. Buffers, by
 |      default, are persistent and will be saved alongside parameters. This
 |      behavior can be changed by setting :attr:`persistent` to ``False``. The
 |      only difference between a persistent buffer and a non-persistent buffer
 |      is that the latter will not be a part of this module's
 |      :attr:`state_dict`.
 |      
 |      Buffers can be accessed as attributes using given names.
 |      
 |      Args:
 |          name (str): name of the buffer. The buffer can be accessed
 |              from this module using the given name
 |          tensor (Tensor or None): buffer to be registered. If ``None``, then operations
 |              that run on buffers, such as :attr:`cuda`, are ignored. If ``None``,
 |              the buffer is **not** included in the module's :attr:`state_dict`.
 |          persistent (bool): whether the buffer is part of this module's
 |              :attr:`state_dict`.
 |      
 |      Example::
 |      
 |          >>> # xdoctest: +SKIP("undefined vars")
 |          >>> self.register_buffer('running_mean', torch.zeros(num_features))
 |  
 |  register_forward_hook(self, hook: Union[Callable[[~T, tuple[Any, ...], Any], Optional[Any]], Callable[[~T, tuple[Any, ...], dict[str, Any], Any], Optional[Any]]], *, prepend: bool = False, with_kwargs: bool = False, always_call: bool = False) -> torch.utils.hooks.RemovableHandle
 |      Register a forward hook on the module.
 |      
 |      The hook will be called every time after :func:`forward` has computed an output.
 |      
 |      If ``with_kwargs`` is ``False`` or not specified, the input contains only
 |      the positional arguments given to the module. Keyword arguments won't be
 |      passed to the hooks and only to the ``forward``. The hook can modify the
 |      output. It can modify the input inplace but it will not have effect on
 |      forward since this is called after :func:`forward` is called. The hook
 |      should have the following signature::
 |      
 |          hook(module, args, output) -> None or modified output
 |      
 |      If ``with_kwargs`` is ``True``, the forward hook will be passed the
 |      ``kwargs`` given to the forward function and be expected to return the
 |      output possibly modified. The hook should have the following signature::
 |      
 |          hook(module, args, kwargs, output) -> None or modified output
 |      
 |      Args:
 |          hook (Callable): The user defined hook to be registered.
 |          prepend (bool): If ``True``, the provided ``hook`` will be fired
 |              before all existing ``forward`` hooks on this
 |              :class:`torch.nn.Module`. Otherwise, the provided
 |              ``hook`` will be fired after all existing ``forward`` hooks on
 |              this :class:`torch.nn.Module`. Note that global
 |              ``forward`` hooks registered with
 |              :func:`register_module_forward_hook` will fire before all hooks
 |              registered by this method.
 |              Default: ``False``
 |          with_kwargs (bool): If ``True``, the ``hook`` will be passed the
 |              kwargs given to the forward function.
 |              Default: ``False``
 |          always_call (bool): If ``True`` the ``hook`` will be run regardless of
 |              whether an exception is raised while calling the Module.
 |              Default: ``False``
 |      
 |      Returns:
 |          :class:`torch.utils.hooks.RemovableHandle`:
 |              a handle that can be used to remove the added hook by calling
 |              ``handle.remove()``
 |  
 |  register_forward_pre_hook(self, hook: Union[Callable[[~T, tuple[Any, ...]], Optional[Any]], Callable[[~T, tuple[Any, ...], dict[str, Any]], Optional[tuple[Any, dict[str, Any]]]]], *, prepend: bool = False, with_kwargs: bool = False) -> torch.utils.hooks.RemovableHandle
 |      Register a forward pre-hook on the module.
 |      
 |      The hook will be called every time before :func:`forward` is invoked.
 |      
 |      
 |      If ``with_kwargs`` is false or not specified, the input contains only
 |      the positional arguments given to the module. Keyword arguments won't be
 |      passed to the hooks and only to the ``forward``. The hook can modify the
 |      input. User can either return a tuple or a single modified value in the
 |      hook. We will wrap the value into a tuple if a single value is returned
 |      (unless that value is already a tuple). The hook should have the
 |      following signature::
 |      
 |          hook(module, args) -> None or modified input
 |      
 |      If ``with_kwargs`` is true, the forward pre-hook will be passed the
 |      kwargs given to the forward function. And if the hook modifies the
 |      input, both the args and kwargs should be returned. The hook should have
 |      the following signature::
 |      
 |          hook(module, args, kwargs) -> None or a tuple of modified input and kwargs
 |      
 |      Args:
 |          hook (Callable): The user defined hook to be registered.
 |          prepend (bool): If true, the provided ``hook`` will be fired before
 |              all existing ``forward_pre`` hooks on this
 |              :class:`torch.nn.Module`. Otherwise, the provided
 |              ``hook`` will be fired after all existing ``forward_pre`` hooks
 |              on this :class:`torch.nn.Module`. Note that global
 |              ``forward_pre`` hooks registered with
 |              :func:`register_module_forward_pre_hook` will fire before all
 |              hooks registered by this method.
 |              Default: ``False``
 |          with_kwargs (bool): If true, the ``hook`` will be passed the kwargs
 |              given to the forward function.
 |              Default: ``False``
 |      
 |      Returns:
 |          :class:`torch.utils.hooks.RemovableHandle`:
 |              a handle that can be used to remove the added hook by calling
 |              ``handle.remove()``
 |  
 |  register_full_backward_hook(self, hook: Callable[[ForwardRef('Module'), Union[tuple[torch.Tensor, ...], torch.Tensor], Union[tuple[torch.Tensor, ...], torch.Tensor]], Union[NoneType, tuple[torch.Tensor, ...], torch.Tensor]], prepend: bool = False) -> torch.utils.hooks.RemovableHandle
 |      Register a backward hook on the module.
 |      
 |      The hook will be called every time the gradients with respect to a module
 |      are computed, i.e. the hook will execute if and only if the gradients with
 |      respect to module outputs are computed. The hook should have the following
 |      signature::
 |      
 |          hook(module, grad_input, grad_output) -> tuple(Tensor) or None
 |      
 |      The :attr:`grad_input` and :attr:`grad_output` are tuples that contain the gradients
 |      with respect to the inputs and outputs respectively. The hook should
 |      not modify its arguments, but it can optionally return a new gradient with
 |      respect to the input that will be used in place of :attr:`grad_input` in
 |      subsequent computations. :attr:`grad_input` will only correspond to the inputs given
 |      as positional arguments and all kwarg arguments are ignored. Entries
 |      in :attr:`grad_input` and :attr:`grad_output` will be ``None`` for all non-Tensor
 |      arguments.
 |      
 |      For technical reasons, when this hook is applied to a Module, its forward function will
 |      receive a view of each Tensor passed to the Module. Similarly the caller will receive a view
 |      of each Tensor returned by the Module's forward function.
 |      
 |      .. warning ::
 |          Modifying inputs or outputs inplace is not allowed when using backward hooks and
 |          will raise an error.
 |      
 |      Args:
 |          hook (Callable): The user-defined hook to be registered.
 |          prepend (bool): If true, the provided ``hook`` will be fired before
 |              all existing ``backward`` hooks on this
 |              :class:`torch.nn.Module`. Otherwise, the provided
 |              ``hook`` will be fired after all existing ``backward`` hooks on
 |              this :class:`torch.nn.Module`. Note that global
 |              ``backward`` hooks registered with
 |              :func:`register_module_full_backward_hook` will fire before
 |              all hooks registered by this method.
 |      
 |      Returns:
 |          :class:`torch.utils.hooks.RemovableHandle`:
 |              a handle that can be used to remove the added hook by calling
 |              ``handle.remove()``
 |  
 |  register_full_backward_pre_hook(self, hook: Callable[[ForwardRef('Module'), Union[tuple[torch.Tensor, ...], torch.Tensor]], Union[NoneType, tuple[torch.Tensor, ...], torch.Tensor]], prepend: bool = False) -> torch.utils.hooks.RemovableHandle
 |      Register a backward pre-hook on the module.
 |      
 |      The hook will be called every time the gradients for the module are computed.
 |      The hook should have the following signature::
 |      
 |          hook(module, grad_output) -> tuple[Tensor] or None
 |      
 |      The :attr:`grad_output` is a tuple. The hook should
 |      not modify its arguments, but it can optionally return a new gradient with
 |      respect to the output that will be used in place of :attr:`grad_output` in
 |      subsequent computations. Entries in :attr:`grad_output` will be ``None`` for
 |      all non-Tensor arguments.
 |      
 |      For technical reasons, when this hook is applied to a Module, its forward function will
 |      receive a view of each Tensor passed to the Module. Similarly the caller will receive a view
 |      of each Tensor returned by the Module's forward function.
 |      
 |      .. warning ::
 |          Modifying inputs inplace is not allowed when using backward hooks and
 |          will raise an error.
 |      
 |      Args:
 |          hook (Callable): The user-defined hook to be registered.
 |          prepend (bool): If true, the provided ``hook`` will be fired before
 |              all existing ``backward_pre`` hooks on this
 |              :class:`torch.nn.Module`. Otherwise, the provided
 |              ``hook`` will be fired after all existing ``backward_pre`` hooks
 |              on this :class:`torch.nn.Module`. Note that global
 |              ``backward_pre`` hooks registered with
 |              :func:`register_module_full_backward_pre_hook` will fire before
 |              all hooks registered by this method.
 |      
 |      Returns:
 |          :class:`torch.utils.hooks.RemovableHandle`:
 |              a handle that can be used to remove the added hook by calling
 |              ``handle.remove()``
 |  
 |  register_load_state_dict_post_hook(self, hook)
 |      Register a post-hook to be run after module's :meth:`~nn.Module.load_state_dict` is called.
 |      
 |      It should have the following signature::
 |          hook(module, incompatible_keys) -> None
 |      
 |      The ``module`` argument is the current module that this hook is registered
 |      on, and the ``incompatible_keys`` argument is a ``NamedTuple`` consisting
 |      of attributes ``missing_keys`` and ``unexpected_keys``. ``missing_keys``
 |      is a ``list`` of ``str`` containing the missing keys and
 |      ``unexpected_keys`` is a ``list`` of ``str`` containing the unexpected keys.
 |      
 |      The given incompatible_keys can be modified inplace if needed.
 |      
 |      Note that the checks performed when calling :func:`load_state_dict` with
 |      ``strict=True`` are affected by modifications the hook makes to
 |      ``missing_keys`` or ``unexpected_keys``, as expected. Additions to either
 |      set of keys will result in an error being thrown when ``strict=True``, and
 |      clearing out both missing and unexpected keys will avoid an error.
 |      
 |      Returns:
 |          :class:`torch.utils.hooks.RemovableHandle`:
 |              a handle that can be used to remove the added hook by calling
 |              ``handle.remove()``
 |  
 |  register_load_state_dict_pre_hook(self, hook)
 |      Register a pre-hook to be run before module's :meth:`~nn.Module.load_state_dict` is called.
 |      
 |      It should have the following signature::
 |          hook(module, state_dict, prefix, local_metadata, strict, missing_keys, unexpected_keys, error_msgs) -> None  # noqa: B950
 |      
 |      Arguments:
 |          hook (Callable): Callable hook that will be invoked before
 |              loading the state dict.
 |  
 |  register_module(self, name: str, module: Optional[ForwardRef('Module')]) -> None
 |      Alias for :func:`add_module`.
 |  
 |  register_parameter(self, name: str, param: Optional[torch.nn.parameter.Parameter]) -> None
 |      Add a parameter to the module.
 |      
 |      The parameter can be accessed as an attribute using given name.
 |      
 |      Args:
 |          name (str): name of the parameter. The parameter can be accessed
 |              from this module using the given name
 |          param (Parameter or None): parameter to be added to the module. If
 |              ``None``, then operations that run on parameters, such as :attr:`cuda`,
 |              are ignored. If ``None``, the parameter is **not** included in the
 |              module's :attr:`state_dict`.
 |  
 |  register_state_dict_post_hook(self, hook)
 |      Register a post-hook for the :meth:`~torch.nn.Module.state_dict` method.
 |      
 |      It should have the following signature::
 |          hook(module, state_dict, prefix, local_metadata) -> None
 |      
 |      The registered hooks can modify the ``state_dict`` inplace.
 |  
 |  register_state_dict_pre_hook(self, hook)
 |      Register a pre-hook for the :meth:`~torch.nn.Module.state_dict` method.
 |      
 |      It should have the following signature::
 |          hook(module, prefix, keep_vars) -> None
 |      
 |      The registered hooks can be used to perform pre-processing before the ``state_dict``
 |      call is made.
 |  
 |  requires_grad_(self: ~T, requires_grad: bool = True) -> ~T
 |      Change if autograd should record operations on parameters in this module.
 |      
 |      This method sets the parameters' :attr:`requires_grad` attributes
 |      in-place.
 |      
 |      This method is helpful for freezing part of the module for finetuning
 |      or training parts of a model individually (e.g., GAN training).
 |      
 |      See :ref:`locally-disable-grad-doc` for a comparison between
 |      `.requires_grad_()` and several similar mechanisms that may be confused with it.
 |      
 |      Args:
 |          requires_grad (bool): whether autograd should record operations on
 |                                parameters in this module. Default: ``True``.
 |      
 |      Returns:
 |          Module: self
 |  
 |  set_extra_state(self, state: Any) -> None
 |      Set extra state contained in the loaded `state_dict`.
 |      
 |      This function is called from :func:`load_state_dict` to handle any extra state
 |      found within the `state_dict`. Implement this function and a corresponding
 |      :func:`get_extra_state` for your module if you need to store extra state within its
 |      `state_dict`.
 |      
 |      Args:
 |          state (dict): Extra state from the `state_dict`
 |  
 |  set_submodule(self, target: str, module: 'Module', strict: bool = False) -> None
 |      Set the submodule given by ``target`` if it exists, otherwise throw an error.
 |      
 |      .. note::
 |          If ``strict`` is set to ``False`` (default), the method will replace an existing submodule
 |          or create a new submodule if the parent module exists. If ``strict`` is set to ``True``,
 |          the method will only attempt to replace an existing submodule and throw an error if
 |          the submodule does not exist.
 |      
 |      For example, let's say you have an ``nn.Module`` ``A`` that
 |      looks like this:
 |      
 |      .. code-block:: text
 |      
 |          A(
 |              (net_b): Module(
 |                  (net_c): Module(
 |                      (conv): Conv2d(3, 3, 3)
 |                  )
 |                  (linear): Linear(3, 3)
 |              )
 |          )
 |      
 |      (The diagram shows an ``nn.Module`` ``A``. ``A`` has a nested
 |      submodule ``net_b``, which itself has two submodules ``net_c``
 |      and ``linear``. ``net_c`` then has a submodule ``conv``.)
 |      
 |      To override the ``Conv2d`` with a new submodule ``Linear``, you
 |      could call ``set_submodule("net_b.net_c.conv", nn.Linear(1, 1))``
 |      where ``strict`` could be ``True`` or ``False``
 |      
 |      To add a new submodule ``Conv2d`` to the existing ``net_b`` module,
 |      you would call ``set_submodule("net_b.conv", nn.Conv2d(1, 1, 1))``.
 |      
 |      In the above if you set ``strict=True`` and call
 |      ``set_submodule("net_b.conv", nn.Conv2d(1, 1, 1), strict=True)``, an AttributeError
 |      will be raised because ``net_b`` does not have a submodule named ``conv``.
 |      
 |      Args:
 |          target: The fully-qualified string name of the submodule
 |              to look for. (See above example for how to specify a
 |              fully-qualified string.)
 |          module: The module to set the submodule to.
 |          strict: If ``False``, the method will replace an existing submodule
 |              or create a new submodule if the parent module exists. If ``True``,
 |              the method will only attempt to replace an existing submodule and throw an error
 |              if the submodule doesn't already exist.
 |      
 |      Raises:
 |          ValueError: If the ``target`` string is empty or if ``module`` is not an instance of ``nn.Module``.
 |          AttributeError: If at any point along the path resulting from
 |              the ``target`` string the (sub)path resolves to a non-existent
 |              attribute name or an object that is not an instance of ``nn.Module``.
 |  
 |  share_memory(self: ~T) -> ~T
 |      See :meth:`torch.Tensor.share_memory_`.
 |  
 |  state_dict(self, *args, destination=None, prefix='', keep_vars=False)
 |      Return a dictionary containing references to the whole state of the module.
 |      
 |      Both parameters and persistent buffers (e.g. running averages) are
 |      included. Keys are corresponding parameter and buffer names.
 |      Parameters and buffers set to ``None`` are not included.
 |      
 |      .. note::
 |          The returned object is a shallow copy. It contains references
 |          to the module's parameters and buffers.
 |      
 |      .. warning::
 |          Currently ``state_dict()`` also accepts positional arguments for
 |          ``destination``, ``prefix`` and ``keep_vars`` in order. However,
 |          this is being deprecated and keyword arguments will be enforced in
 |          future releases.
 |      
 |      .. warning::
 |          Please avoid the use of argument ``destination`` as it is not
 |          designed for end-users.
 |      
 |      Args:
 |          destination (dict, optional): If provided, the state of module will
 |              be updated into the dict and the same object is returned.
 |              Otherwise, an ``OrderedDict`` will be created and returned.
 |              Default: ``None``.
 |          prefix (str, optional): a prefix added to parameter and buffer
 |              names to compose the keys in state_dict. Default: ``''``.
 |          keep_vars (bool, optional): by default the :class:`~torch.Tensor` s
 |              returned in the state dict are detached from autograd. If it's
 |              set to ``True``, detaching will not be performed.
 |              Default: ``False``.
 |      
 |      Returns:
 |          dict:
 |              a dictionary containing a whole state of the module
 |      
 |      Example::
 |      
 |          >>> # xdoctest: +SKIP("undefined vars")
 |          >>> module.state_dict().keys()
 |          ['bias', 'weight']
 |  
 |  to(self, *args, **kwargs)
 |      Move and/or cast the parameters and buffers.
 |      
 |      This can be called as
 |      
 |      .. function:: to(device=None, dtype=None, non_blocking=False)
 |         :noindex:
 |      
 |      .. function:: to(dtype, non_blocking=False)
 |         :noindex:
 |      
 |      .. function:: to(tensor, non_blocking=False)
 |         :noindex:
 |      
 |      .. function:: to(memory_format=torch.channels_last)
 |         :noindex:
 |      
 |      Its signature is similar to :meth:`torch.Tensor.to`, but only accepts
 |      floating point or complex :attr:`dtype`\ s. In addition, this method will
 |      only cast the floating point or complex parameters and buffers to :attr:`dtype`
 |      (if given). The integral parameters and buffers will be moved
 |      :attr:`device`, if that is given, but with dtypes unchanged. When
 |      :attr:`non_blocking` is set, it tries to convert/move asynchronously
 |      with respect to the host if possible, e.g., moving CPU Tensors with
 |      pinned memory to CUDA devices.
 |      
 |      See below for examples.
 |      
 |      .. note::
 |          This method modifies the module in-place.
 |      
 |      Args:
 |          device (:class:`torch.device`): the desired device of the parameters
 |              and buffers in this module
 |          dtype (:class:`torch.dtype`): the desired floating point or complex dtype of
 |              the parameters and buffers in this module
 |          tensor (torch.Tensor): Tensor whose dtype and device are the desired
 |              dtype and device for all parameters and buffers in this module
 |          memory_format (:class:`torch.memory_format`): the desired memory
 |              format for 4D parameters and buffers in this module (keyword
 |              only argument)
 |      
 |      Returns:
 |          Module: self
 |      
 |      Examples::
 |      
 |          >>> # xdoctest: +IGNORE_WANT("non-deterministic")
 |          >>> linear = nn.Linear(2, 2)
 |          >>> linear.weight
 |          Parameter containing:
 |          tensor([[ 0.1913, -0.3420],
 |                  [-0.5113, -0.2325]])
 |          >>> linear.to(torch.double)
 |          Linear(in_features=2, out_features=2, bias=True)
 |          >>> linear.weight
 |          Parameter containing:
 |          tensor([[ 0.1913, -0.3420],
 |                  [-0.5113, -0.2325]], dtype=torch.float64)
 |          >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_CUDA1)
 |          >>> gpu1 = torch.device("cuda:1")
 |          >>> linear.to(gpu1, dtype=torch.half, non_blocking=True)
 |          Linear(in_features=2, out_features=2, bias=True)
 |          >>> linear.weight
 |          Parameter containing:
 |          tensor([[ 0.1914, -0.3420],
 |                  [-0.5112, -0.2324]], dtype=torch.float16, device='cuda:1')
 |          >>> cpu = torch.device("cpu")
 |          >>> linear.to(cpu)
 |          Linear(in_features=2, out_features=2, bias=True)
 |          >>> linear.weight
 |          Parameter containing:
 |          tensor([[ 0.1914, -0.3420],
 |                  [-0.5112, -0.2324]], dtype=torch.float16)
 |      
 |          >>> linear = nn.Linear(2, 2, bias=None).to(torch.cdouble)
 |          >>> linear.weight
 |          Parameter containing:
 |          tensor([[ 0.3741+0.j,  0.2382+0.j],
 |                  [ 0.5593+0.j, -0.4443+0.j]], dtype=torch.complex128)
 |          >>> linear(torch.ones(3, 2, dtype=torch.cdouble))
 |          tensor([[0.6122+0.j, 0.1150+0.j],
 |                  [0.6122+0.j, 0.1150+0.j],
 |                  [0.6122+0.j, 0.1150+0.j]], dtype=torch.complex128)
 |  
 |  to_empty(self: ~T, *, device: Union[int, str, torch.device, NoneType], recurse: bool = True) -> ~T
 |      Move the parameters and buffers to the specified device without copying storage.
 |      
 |      Args:
 |          device (:class:`torch.device`): The desired device of the parameters
 |              and buffers in this module.
 |          recurse (bool): Whether parameters and buffers of submodules should
 |              be recursively moved to the specified device.
 |      
 |      Returns:
 |          Module: self
 |  
 |  train(self: ~T, mode: bool = True) -> ~T
 |      Set the module in training mode.
 |      
 |      This has an effect only on certain modules. See the documentation of
 |      particular modules for details of their behaviors in training/evaluation
 |      mode, i.e., whether they are affected, e.g. :class:`Dropout`, :class:`BatchNorm`,
 |      etc.
 |      
 |      Args:
 |          mode (bool): whether to set training mode (``True``) or evaluation
 |                       mode (``False``). Default: ``True``.
 |      
 |      Returns:
 |          Module: self
 |  
 |  type(self: ~T, dst_type: Union[torch.dtype, str]) -> ~T
 |      Casts all parameters and buffers to :attr:`dst_type`.
 |      
 |      .. note::
 |          This method modifies the module in-place.
 |      
 |      Args:
 |          dst_type (type or string): the desired type
 |      
 |      Returns:
 |          Module: self
 |  
 |  xpu(self: ~T, device: Union[int, torch.device, NoneType] = None) -> ~T
 |      Move all model parameters and buffers to the XPU.
 |      
 |      This also makes associated parameters and buffers different objects. So
 |      it should be called before constructing optimizer if the module will
 |      live on XPU while being optimized.
 |      
 |      .. note::
 |          This method modifies the module in-place.
 |      
 |      Arguments:
 |          device (int, optional): if specified, all parameters will be
 |              copied to that device
 |      
 |      Returns:
 |          Module: self
 |  
 |  zero_grad(self, set_to_none: bool = True) -> None
 |      Reset gradients of all model parameters.
 |      
 |      See similar function under :class:`torch.optim.Optimizer` for more context.
 |      
 |      Args:
 |          set_to_none (bool): instead of setting to zero, set the grads to None.
 |              See :meth:`torch.optim.Optimizer.zero_grad` for details.
 |  
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from torch.nn.modules.module.Module:
 |  
 |  __dict__
 |      dictionary for instance variables (if defined)
 |  
 |  __weakref__
 |      list of weak references to the object (if defined)
 |  
 |  ----------------------------------------------------------------------
 |  Data and other attributes inherited from torch.nn.modules.module.Module:
 |  
 |  T_destination = ~T_destination
 |  
 |  call_super_init = False
 |  
 |  dump_patches = False

Training the ABaCo model#

To train ABaCo on the prepared dataset, we then use method abaco.metaABaCo.fit().

# Train the model
model.fit(seed=42)

Hide code cell output

Training: VAE for learning meaningful embeddings: 100%|██████████| 1000/1000 [00:24<00:00, 40.48it/s, bio_penalty=0.0121, clustering_loss=0.0350, elbo=385.8139, epoch=999/1001, vae_loss=385.8610]
Training: Embeddings batch effect correction using adversrial training: 100%|██████████| 2000/2000 [00:54<00:00, 36.52it/s, adv_loss=-0.7143, bio_penalty=0.6752, clustering_loss=0.0350, disc_loss=0.7143, elbo=614.0276, epoch=1999/2001, vae_loss=614.7378]
Training: VAE decoder with masked batch labels: 100%|██████████| 2000/2000 [00:37<00:00, 53.07it/s, cycle_loss=0.0000, epoch=2000/2000, vae_loss=611.9976]

Reconstructing the dataset with ABaCO#

To reconstruct the dataset we use method abaco.metaABaCo.correct() and save it as a new layer abaco in the annotated dataset.

# Reconstruct the dataset using the trained ABaCo model
corrected_dataset = model.correct(seed=42)
# save back to adata
adata.layers['abaco'] = corrected_dataset.set_index(id_col).drop(columns=[batch_col, bio_col]).values
adata.write_h5ad("data/mgnify_MGYS00001135.h5ad")

Viewing the ABaCo reconstructed dataset#

Here we again create PCoA and look at sample alpha diversities via pairplots but on the batch corrected data.

# Plot the PCoA of the reconstructed dataset
plotPCoA(
    data = corrected_dataset, 
    sample_label=id_col, 
    batch_label=batch_col, 
    experiment_label=bio_col
)

In the PCoA we see that there is more overlap of the batches based on the blue and red points being more mixed.

We can also take a look at the alpha diversity metrics:

Hide code cell source

## PREPROCESSING THE ABaCo DATA
# normalize abaco corrected data
adata.layers['normalized_abaco'] = (adata.layers['abaco']/adata.layers['abaco'].sum(axis=1).reshape(-1,1))
# CLR transform normalized ABaCo data
adata.layers['clr_abaco'] = clr(np.where(adata.layers['normalized_abaco'] > 0, adata.layers['normalized_abaco'], 1e-10))

## Alpha diversity metrics on ABaCo corrected data
# Diversity: Number of unique taxa per sample as new metadata
adata.obs['abaco_numtaxa'] = (adata.layers['abaco'] > 0).sum(axis=1) 
# Diversity with correction: Chao1 estimator
# Chao1 = num observed taxa + (num singletons / (2 x num doubletons))
num_singletons = (adata.layers['abaco'] == 1).sum(axis=1)
num_doubletons = (adata.layers['abaco'] == 2).sum(axis=1)
adata.obs['abaco_chao1'] = (adata.layers['abaco'] > 0).sum(axis=1) + (num_singletons / (2 * num_doubletons))
# Diversity: Shannon index H = -sum(p_i * log(p_i)), entropy
adata.obs['abaco_shannon'] = entropy(adata.layers['normalized_abaco'], nan_policy='omit', axis=1)
# Evenness: Pielou evenness index P = H/H_max, H_max = ln(num species)
adata.obs['abaco_pielou'] = adata.obs['abaco_shannon'] / np.log(adata.obs['abaco_numtaxa'])
# Diversity: simpson index lambda = sum(p_i ^2)
adata.obs['abaco_simpson'] = (adata.layers['normalized_abaco'] ** 2).sum(axis=1)
# Diversity: inverse simpson index D = 1/lambda
adata.obs['abaco_inv_simpson'] = 1 / adata.obs['abaco_simpson']

## PAIRPLOTS OF ALPHA DIVERSITY METRICS
# prep df for vis
df_abaco_alphas = adata.obs[[
    'abaco_numtaxa', 'abaco_chao1', 'abaco_shannon', 
    'abaco_pielou', 'abaco_simpson', 'abaco_inv_simpson',
    batch_col, bio_col
]].copy()
# plotting by bio groups
g1 = sns.pairplot(df_abaco_alphas, hue=bio_col, corner=True, height=1.8)
g1.figure.suptitle('ABaCo: Alpha Diversity by Biological Groups', fontsize=22)
plt.setp(g1._legend.get_texts(), fontsize=18)
plt.setp(g1._legend.get_title(), fontsize=20)
g2 = sns.pairplot(df_abaco_alphas, hue=batch_col, corner=True, height=1.8)
g2.figure.suptitle('ABaCo: Alpha Diversity by Batch Groups', fontsize=22)
plt.setp(g2._legend.get_texts(), fontsize=18)
plt.setp(g2._legend.get_title(), fontsize=20)
[None]
../_images/07ffa461ffee59236acab52544ca811c20c9fb31eb464113b4fe933206c7f0bd.png ../_images/4ec901d4c4e2b0d957965666a73fb19f92fa45b974fe24f61a6ed4636a8ef8cb.png

Conclusion#

The goal was to:

✅ correct the batch effect (reduce clustering of points by colour in the PCoA and pairplot coloured by batches)

✅ maintain biological variance (maintain pattern of shapes in PCoA and maintain pairplot coloured by wwtp location)

A brief visual inspection of the PCoA and alpha diversity of the reconstructed data suggests that ABaCo reduced the batch effect associated with analyzing the samples on different dates, while still retaining any variance due to the condition of wwtp location.