Topic Modeling with Amortized LDA

In this tutorial, we will explore how to run the amortized Latent Dirichlet Allocation (LDA) model implementation in scvi-tools. LDA is a topic modelling method first introduced in the natural language processing field. By treating each cell as a document and each gene expression count as a word, we can carry over the method to the single-cell biology field.

Below, we will train the model over a dataset, plot the topics over a UMAP of the reference set, and inspect the topics for characteristic gene sets.

As an example, we use the PBMC 10K dataset from 10x Genomics.

Uncomment the following lines in Google Colab in order to install scvi-tools:

# !pip install --quiet scvi-colab
# from scvi_colab import install

# install()

import os
import tempfile

import pandas as pd
import scanpy as sc
import scvi
import torch

scvi.settings.seed = 0
print("Last run with scvi-tools version:", scvi.__version__)

Last run with scvi-tools version: 1.0.3

You can modify save_dir below to change where the data files for this tutorial are saved.

sc.set_figure_params(figsize=(4, 4))
torch.set_float32_matmul_precision("high")
save_dir = tempfile.TemporaryDirectory()

%config InlineBackend.print_figure_kwargs={'facecolor' : "w"}
%config InlineBackend.figure_format='retina'

Load and process data

Load the 10x genomics PBMC dataset. Generally, it is good practice for LDA to remove ubiquitous genes, to prevent the model from modeling these genes as a separate topic. Here, we first filter out all mitochrondrial genes, then select the top 1000 variable genes with seurat_v3 method from the remaining genes.

adata_path = os.path.join(save_dir.name, "pbmc_10k_protein_v3.h5ad")
adata = sc.read(
    adata_path,
    backup_url="https://github.com/YosefLab/scVI-data/raw/master/pbmc_10k_protein_v3.h5ad?raw=true",
)

adata.layers["counts"] = adata.X.copy()  # preserve counts
sc.pp.normalize_total(adata, target_sum=10e4)
sc.pp.log1p(adata)
adata.raw = adata  # freeze the state in `.raw`

adata = adata[:, ~adata.var_names.str.startswith("MT-")]
sc.pp.highly_variable_genes(
    adata, flavor="seurat_v3", layer="counts", n_top_genes=1000, subset=True
)

Create and fit AmortizedLDA model

Here, we initialize and fit an AmortizedLDA model on the dataset. We pick 10 topics to model in this case.

n_topics = 10

scvi.model.AmortizedLDA.setup_anndata(adata, layer="counts")
model = scvi.model.AmortizedLDA(adata, n_topics=n_topics)

Note

By default we train with KL annealing which means the effective loss will generally not decrease steadily in the beginning. Our Pyro implementations present this train loss term as the elbo_train in the progress bar which is misleading. We plan on correcting this in the future.

model.train()

Epoch 1000/1000: 100%|██████████| 1000/1000 [05:40<00:00,  2.88it/s, v_num=1, elbo_train=1.86e+7]Epoch 1000/1000: 100%|██████████| 1000/1000 [05:40<00:00,  2.93it/s, v_num=1, elbo_train=1.86e+7]

Visualizing learned topics

By calling model.get_latent_representation(), the model will compute a Monte Carlo estimate of the topic proportions for each cell. Since we use a logistic-Normal distribution to approximate the Dirichlet distribution, the model cannot compute the analytic mean. The number of samples used to compute the latent representation can be configured with the optional argument n_samples.

topic_prop = model.get_latent_representation()
topic_prop.head()

	topic_0	topic_1	topic_2	topic_3	topic_4	topic_5	topic_6	topic_7	topic_8	topic_9
index
AAACCCAAGATTGTGA-1	0.000188	0.037885	0.148025	0.000161	0.808256	0.004403	0.000129	0.000486	0.000289	0.000177
AAACCCACATCGGTTA-1	0.000206	0.000244	0.042489	0.000188	0.949140	0.004010	0.000092	0.000338	0.003173	0.000121
AAACCCAGTACCGCGT-1	0.000887	0.232126	0.195196	0.000731	0.560573	0.001700	0.002559	0.003135	0.002484	0.000607
AAACCCAGTATCGAAA-1	0.001437	0.001861	0.000900	0.000966	0.001105	0.001951	0.005143	0.001816	0.000643	0.984177
AAACCCAGTCGTCATA-1	0.000173	0.000321	0.000169	0.000107	0.000227	0.000313	0.000402	0.000174	0.000925	0.997188

# Save topic proportions in obsm and obs columns.
adata.obsm["X_LDA"] = topic_prop
for i in range(n_topics):
    adata.obs[f"LDA_topic_{i}"] = topic_prop[[f"topic_{i}"]]

Plot UMAP

sc.tl.pca(adata, svd_solver="arpack")
sc.pp.neighbors(adata, n_pcs=30, n_neighbors=20)
sc.tl.umap(adata)
sc.tl.leiden(adata, key_added="leiden_scVI", resolution=0.8)

# Save UMAP to custom .obsm field.
adata.obsm["raw_counts_umap"] = adata.obsm["X_umap"].copy()

sc.pl.embedding(adata, "raw_counts_umap", color=["leiden_scVI"], frameon=False)

Color UMAP by topic proportions

By coloring by UMAP by topic proportions, we find that the learned topics are generally dominant in cells close together in the UMAP space. In some cases, a topic is dominant in multiple clusters in the UMAP, which indicates similarilty between these clusters despite being far apart in the plot. This is not surprising considering that UMAP does not preserve local relationships beyond a certain threshold.

sc.pl.embedding(
    adata,
    "raw_counts_umap",
    color=[f"LDA_topic_{i}" for i in range(n_topics)],
    frameon=False,
)

Plot UMAP in topic space

sc.pp.neighbors(adata, use_rep="X_LDA", n_neighbors=20, metric="hellinger")
sc.tl.umap(adata)

# Save UMAP to custom .obsm field.
adata.obsm["topic_space_umap"] = adata.obsm["X_umap"].copy()

sc.pl.embedding(
    adata,
    "topic_space_umap",
    color=[f"LDA_topic_{i}" for i in range(n_topics)],
    frameon=False,
)

Find top genes per topic

Similar to the topic proportions, model.get_feature_by_topic() returns a Monte Carlo estimate of the gene by topic matrix, which contains the proportion that a gene is weighted in each topic. This is also due to another approximation of the Dirichlet with a logistic-Normal distribution. We can inspect each topic in this matrix and sort by proportion allocated to each gene to determine top genes characterizing each topic.

feature_by_topic = model.get_feature_by_topic()
feature_by_topic.head()

	topic_0	topic_1	topic_2	topic_3	topic_4	topic_5	topic_6	topic_7	topic_8	topic_9
index
AL645608.8	0.000018	0.000003	0.000002	0.000005	2.360189e-06	0.000003	0.000001	0.000033	0.000005	0.000002
HES4	0.000024	0.000006	0.000006	0.000010	8.129477e-06	0.000011	0.000007	0.000696	0.000008	0.000006
ISG15	0.000031	0.000879	0.000018	0.000197	2.258939e-04	0.000624	0.001139	0.000623	0.001597	0.001388
TNFRSF18	0.000147	0.000002	0.000001	0.000032	7.911760e-07	0.000006	0.000396	0.000003	0.000038	0.000131
TNFRSF4	0.000040	0.000002	0.000003	0.000007	1.579124e-06	0.000005	0.000834	0.000004	0.000048	0.000057

rank_by_topic = pd.DataFrame()
for i in range(n_topics):
    topic_name = f"topic_{i}"
    topic = feature_by_topic[topic_name].sort_values(ascending=False)
    rank_by_topic[topic_name] = topic.index
    rank_by_topic[f"{topic_name}_prop"] = topic.values

rank_by_topic.head()

	topic_0	topic_0_prop	topic_1	topic_1_prop	topic_2	topic_2_prop	topic_3	topic_3_prop	topic_4	topic_4_prop	topic_5	topic_5_prop	topic_6	topic_6_prop	topic_7	topic_7_prop	topic_8	topic_8_prop	topic_9	topic_9_prop
0	CD74	0.059290	FTH1	0.086838	LYZ	0.083449	IGKC	0.233030	S100A9	0.143519	CD74	0.156806	TMSB4X	0.126411	FTL	0.112751	ACTB	0.264263	TMSB4X	0.087633
1	ACTB	0.040588	FTL	0.073924	ACTB	0.057350	IGLC2	0.125259	S100A8	0.098891	HLA-DRA	0.113971	TMSB10	0.085176	ACTB	0.069703	TMSB4X	0.135907	ACTB	0.086186
2	TMSB4X	0.029750	TMSB4X	0.041812	CST3	0.035908	IGHA1	0.083673	LYZ	0.057798	TMSB4X	0.067430	ACTB	0.077509	TMSB4X	0.058746	TMSB10	0.094544	GNLY	0.070738
3	FTH1	0.025553	LYZ	0.037145	S100A4	0.027521	IGHM	0.056419	FTL	0.043597	HLA-DRB1	0.066456	JUNB	0.034766	FTH1	0.056941	ACTG1	0.087103	NKG7	0.054089
4	HLA-DRA	0.019603	NEAT1	0.029798	VIM	0.027337	IGLC3	0.039387	ACTB	0.038481	ACTB	0.046950	FTL	0.028121	S100A4	0.030024	S100A4	0.036098	CCL5	0.041511

Clean up

Uncomment the following line to remove all data files created in this tutorial:

# save_dir.cleanup()