Note

This page was generated from AutoZI_tutorial.ipynb. Interactive online version: Colab badge.

Identification of zero-inflated genes

AutoZI is a deep generative model adapted from scVI allowing a gene-specific treatment of zero-inflation. For each gene \(g\), AutoZI notably learns the distribution of a random variable \(\delta_g\) which denotes the probability that gene \(g\) is not zero-inflated. In this notebook, we present the use of the model on a PBMC dataset.

More details about AutoZI can be found in : https://www.biorxiv.org/content/10.1101/794875v2

[1]:

import sys

#if branch is stable, will install via pypi, else will install from source
branch = "stable"
IN_COLAB = "google.colab" in sys.modules

if IN_COLAB and branch == "stable":
    !pip install --quiet scvi-tools[tutorials]
elif IN_COLAB and branch != "stable":
    !pip install --quiet --upgrade jsonschema
    !pip install --quiet git+https://github.com/yoseflab/scvi-tools@$branch#egg=scvi-tools[tutorials]

Imports, data loading and preparation

[2]:

import numpy as np
import pandas as pd
import anndata

import scanpy as sc
import scvi

[3]:

pbmc = scvi.data.pbmc_dataset(run_setup_anndata=False)
pbmc.layers["counts"] = pbmc.X.copy()
sc.pp.normalize_total(pbmc, target_sum=10e4)
sc.pp.log1p(pbmc)
pbmc.raw = pbmc
scvi.data.poisson_gene_selection(
    pbmc,
    n_top_genes=1000,
    batch_key="batch",
    subset=True,
    layer="counts",
)
scvi.data.setup_anndata(
    pbmc,
    labels_key="str_labels",
    batch_key="batch",
    layer="counts",
)

INFO     File data/gene_info_pbmc.csv already downloaded
INFO     File data/pbmc_metadata.pickle already downloaded
INFO     File data/pbmc8k/filtered_gene_bc_matrices.tar.gz already downloaded
INFO     Extracting tar file
INFO     Removing extracted data at data/pbmc8k/filtered_gene_bc_matrices
INFO     File data/pbmc4k/filtered_gene_bc_matrices.tar.gz already downloaded
INFO     Extracting tar file
INFO     Removing extracted data at data/pbmc4k/filtered_gene_bc_matrices

/home/galen/.pyenv/versions/3.8.3/envs/scvi-dev/lib/python3.8/site-packages/pandas/core/arrays/categorical.py:2487: FutureWarning: The `inplace` parameter in pandas.Categorical.remove_unused_categories is deprecated and will be removed in a future version.
  res = method(*args, **kwargs)

Sampling from binomial...: 100%|██████████| 10000/10000 [00:00<00:00, 11465.69it/s]
Sampling from binomial...: 100%|██████████| 10000/10000 [00:00<00:00, 11546.41it/s]
INFO     Using batches from adata.obs["batch"]
INFO     Using labels from adata.obs["str_labels"]
INFO     Using data from adata.layers["counts"]
INFO     Computing library size prior per batch
INFO     Successfully registered anndata object containing 11990 cells, 1000 vars, 2 batches,
         9 labels, and 0 proteins. Also registered 0 extra categorical covariates and 0 extra
         continuous covariates.
INFO     Please do not further modify adata until model is trained.

Analyze gene-specific ZI

In AutoZI, all \(\delta_g\)’s follow a common \(\text{Beta}(\alpha,\beta)\) prior distribution where \(\alpha,\beta \in (0,1)\) and the zero-inflation probability in the ZINB component is bounded below by \(\tau_{\text{dropout}} \in (0,1)\). AutoZI is encoded by the AutoZIVAE class whose inputs, besides the size of the dataset, are \(\alpha\) (alpha_prior), \(\beta\) (beta_prior), \(\tau_{\text{dropout}}\) (minimal_dropout). By default, we set \(\alpha = 0.5, \beta = 0.5, \tau_{\text{dropout}} = 0.01\).

Note : we can learn \(\alpha,\beta\) in an Empirical Bayes fashion, which is possible by setting alpha_prior = None and beta_prior = None

[4]:

vae = scvi.model.AUTOZI(pbmc)

We fit, for each gene \(g\), an approximate posterior distribution \(q(\delta_g) = \text{Beta}(\alpha^g,\beta^g)\) (with \(\alpha^g,\beta^g \in (0,1)\)) on which we rely. We retrieve \(\alpha^g,\beta^g\) for all genes \(g\) (and \(\alpha,\beta\), if learned) as numpy arrays using the method get_alphas_betas of AutoZIVAE.

[5]:

vae.train(max_epochs=200, plan_kwargs = {'lr':1e-2})

GPU available: True, used: True
TPU available: None, using: 0 TPU cores

Epoch 200/200: 100%|██████████| 200/200 [07:38<00:00,  2.29s/it, loss=726, v_num=1]

[6]:

outputs = vae.get_alphas_betas()
alpha_posterior = outputs['alpha_posterior']
beta_posterior = outputs['beta_posterior']

Now that we obtained fitted \(\alpha^g,\beta^g\), different metrics are possible. Bayesian decision theory suggests us the posterior probability of the zero-inflation hypothesis \(q(\delta_g < 0.5)\), but also other metrics such as the mean wrt \(q\) of \(\delta_g\) are possible. We focus on the former. We decide that gene \(g\) is ZI if and only if \(q(\delta_g < 0.5)\) is greater than a given threshold, say \(0.5\). We may note that it is equivalent to \(\alpha^g < \beta^g\). From this we can deduce the fraction of predicted ZI genes in the dataset.

[7]:

from scipy.stats import beta

# Threshold (or Kzinb/Knb+Kzinb in paper)
threshold = 0.5

# q(delta_g < 0.5) probabilities
zi_probs = beta.cdf(0.5, alpha_posterior, beta_posterior)

# ZI genes
is_zi_pred = (zi_probs > threshold)

print('Fraction of predicted ZI genes :', is_zi_pred.mean())

Fraction of predicted ZI genes : 0.455

We noted that predictions were less accurate for genes \(g\) whose average expressions - or predicted NB means, equivalently - were low. Indeed, genes assumed not to be ZI were more often predicted as ZI for such low average expressions. A threshold of 1 proved reasonable to separate genes predicted with more or less accuracy. Hence we may want to focus on predictions for genes with average expression above 1.

[8]:

mask_sufficient_expression = (np.array(pbmc.X.mean(axis=0)) > 1.).reshape(-1)
print('Fraction of genes with avg expression > 1 :', mask_sufficient_expression.mean())
print('Fraction of predicted ZI genes with avg expression > 1 :', is_zi_pred[mask_sufficient_expression].mean())

Fraction of genes with avg expression > 1 : 0.499
Fraction of predicted ZI genes with avg expression > 1 : 0.43887775551102204

Analyze gene-cell-type-specific ZI

One may argue that zero-inflation should also be treated on the cell-type (or ‘label’) level, in addition to the gene level. AutoZI can be extended by assuming a random variable \(\delta_{gc}\) for each gene \(g\) and cell type \(c\) which denotes the probability that gene \(g\) is not zero-inflated in cell-type \(c\). The analysis above can be extended to this new scale.

[9]:

# Model definition
vae_genelabel = scvi.model.AUTOZI(
    pbmc,
    dispersion='gene-label',
    zero_inflation='gene-label'
)

# Training
vae_genelabel.train(max_epochs=200, plan_kwargs = {'lr':1e-2})

# Retrieve posterior distribution parameters
outputs_genelabel = vae_genelabel.get_alphas_betas()
alpha_posterior_genelabel = outputs_genelabel['alpha_posterior']
beta_posterior_genelabel = outputs_genelabel['beta_posterior']

GPU available: True, used: True
TPU available: None, using: 0 TPU cores

Epoch 200/200: 100%|██████████| 200/200 [06:35<00:00,  1.98s/it, loss=732, v_num=1]

[10]:

# q(delta_g < 0.5) probabilities
zi_probs_genelabel = beta.cdf(0.5,alpha_posterior_genelabel, beta_posterior_genelabel)

# ZI gene-cell-types
is_zi_pred_genelabel = (zi_probs_genelabel > threshold)

ct = pbmc.obs.str_labels.astype("category")
codes = np.unique(ct.cat.codes)
cats = ct.cat.categories
for ind_cell_type, cell_type in zip(codes, cats):
    is_zi_pred_genelabel_here = is_zi_pred_genelabel[:,ind_cell_type]
    print('Fraction of predicted ZI genes for cell type {} :'.format(cell_type),
          is_zi_pred_genelabel_here.mean(),'\n')

Fraction of predicted ZI genes for cell type B cells : 0.476

Fraction of predicted ZI genes for cell type CD14+ Monocytes : 0.486

Fraction of predicted ZI genes for cell type CD4 T cells : 0.462

Fraction of predicted ZI genes for cell type CD8 T cells : 0.448

Fraction of predicted ZI genes for cell type Dendritic Cells : 0.414

Fraction of predicted ZI genes for cell type FCGR3A+ Monocytes : 0.492

Fraction of predicted ZI genes for cell type Megakaryocytes : 0.451

Fraction of predicted ZI genes for cell type NK cells : 0.495

Fraction of predicted ZI genes for cell type Other : 0.462


[11]:

# With avg expressions > 1
for ind_cell_type, cell_type in zip(codes, cats):
    mask_sufficient_expression = (np.array(pbmc.X[pbmc.obs.str_labels.values.reshape(-1) == cell_type,:].mean(axis=0)) > 1.).reshape(-1)
    print('Fraction of genes with avg expression > 1 for cell type {} :'.format(cell_type),
          mask_sufficient_expression.mean())
    is_zi_pred_genelabel_here = is_zi_pred_genelabel[mask_sufficient_expression,ind_cell_type]
    print('Fraction of predicted ZI genes with avg expression > 1 for cell type {} :'.format(cell_type),
          is_zi_pred_genelabel_here.mean(), '\n')

Fraction of genes with avg expression > 1 for cell type B cells : 0.39
Fraction of predicted ZI genes with avg expression > 1 for cell type B cells : 0.43846153846153846

Fraction of genes with avg expression > 1 for cell type CD14+ Monocytes : 0.491
Fraction of predicted ZI genes with avg expression > 1 for cell type CD14+ Monocytes : 0.46028513238289204

Fraction of genes with avg expression > 1 for cell type CD4 T cells : 0.433
Fraction of predicted ZI genes with avg expression > 1 for cell type CD4 T cells : 0.4503464203233256

Fraction of genes with avg expression > 1 for cell type CD8 T cells : 0.499
Fraction of predicted ZI genes with avg expression > 1 for cell type CD8 T cells : 0.43687374749499

Fraction of genes with avg expression > 1 for cell type Dendritic Cells : 0.861
Fraction of predicted ZI genes with avg expression > 1 for cell type Dendritic Cells : 0.4065040650406504

Fraction of genes with avg expression > 1 for cell type FCGR3A+ Monocytes : 0.74
Fraction of predicted ZI genes with avg expression > 1 for cell type FCGR3A+ Monocytes : 0.4648648648648649

Fraction of genes with avg expression > 1 for cell type Megakaryocytes : 0.749
Fraction of predicted ZI genes with avg expression > 1 for cell type Megakaryocytes : 0.4152202937249666

Fraction of genes with avg expression > 1 for cell type NK cells : 0.575
Fraction of predicted ZI genes with avg expression > 1 for cell type NK cells : 0.4504347826086956

Fraction of genes with avg expression > 1 for cell type Other : 0.787
Fraction of predicted ZI genes with avg expression > 1 for cell type Other : 0.45870393900889456


[ ]:
Introduction to gimVI Annotation with CellAssign