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.

Note

Running the following cell will install tutorial dependencies on Google Colab only. It will have no effect on environments other than Google Colab.

!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 seaborn as sns
import torch

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

Last run with scvi-tools version: 1.4.2

Note

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

sc.set_figure_params(figsize=(6, 6), frameon=False)
sns.set_theme()
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()

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	0.000067	0.000083	0.791881	0.000249	0.028401	0.178944	0.000124	0.000127	0.000042	0.000081
AAACCCACATCGGTTA-1	0.000355	0.000080	0.994418	0.000145	0.004022	0.000783	0.000044	0.000082	0.000036	0.000033
AAACCCAGTACCGCGT-1	0.001367	0.000709	0.535644	0.000629	0.026290	0.431260	0.001948	0.000592	0.001299	0.000263
AAACCCAGTATCGAAA-1	0.002804	0.001986	0.001903	0.004099	0.001806	0.002473	0.003381	0.762394	0.010886	0.208269
AAACCCAGTCGTCATA-1	0.008132	0.000645	0.000678	0.000477	0.000866	0.001077	0.000553	0.719184	0.004398	0.263991

# 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	0.000004	0.000021	2.584630e-06	0.000004	0.000002	0.000001	0.000032	0.000003	0.000001	0.000005
HES4	0.000005	0.000025	7.775395e-06	0.000013	0.000010	0.000006	0.000674	0.000009	0.000007	0.000006
ISG15	0.001438	0.000041	2.638122e-04	0.000432	0.000380	0.000474	0.000736	0.001791	0.001141	0.000192
TNFRSF18	0.000474	0.000098	7.196131e-07	0.000028	0.000002	0.000001	0.000003	0.000061	0.000306	0.000131
TNFRSF4	0.000700	0.000040	1.322569e-06	0.000007	0.000003	0.000001	0.000003	0.000051	0.000676	0.000012

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	ACTB	0.191605	CD74	0.061852	S100A9	0.142184	CD74	0.109387	HLA-DRA	0.078017	FTH1	0.063310	FTL	0.113057	TMSB4X	0.109844	TMSB4X	0.124022	IGKC	0.134810
1	TMSB4X	0.134309	ACTB	0.043040	S100A8	0.098740	IGKC	0.063001	CD74	0.072705	FTL	0.059216	ACTB	0.069695	ACTB	0.108426	TMSB10	0.083133	IGLC2	0.084782
2	TMSB10	0.087340	TMSB4X	0.032689	LYZ	0.057181	HLA-DRA	0.060019	ACTB	0.066977	LYZ	0.057700	TMSB4X	0.059973	GNLY	0.102056	ACTB	0.078424	IGHA1	0.073240
3	ACTG1	0.061597	FTH1	0.027223	FTL	0.042574	TMSB4X	0.044334	TMSB4X	0.048515	TMSB4X	0.033342	FTH1	0.059017	NKG7	0.076737	JUNB	0.036529	CCL5	0.069848
4	S100A4	0.042297	HLA-DRA	0.021627	ACTB	0.040240	IGHM	0.041840	HLA-DRB1	0.046785	ACTB	0.030895	S100A4	0.029738	TMSB10	0.044803	FTL	0.028967	GZMA	0.044131