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()

WARNING: Running pip as the 'root' user can result in broken permissions and conflicting behaviour with the system package manager, possibly rendering your system unusable.It is recommended to use a virtual environment instead: https://pip.pypa.io/warnings/venv. Use the --root-user-action option if you know what you are doing and want to suppress this warning.

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: 1.1.6

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	0.000442	0.000388	0.184993	0.002144	0.752604	0.055904	0.003084	0.000102	0.000109	0.000229
AAACCCACATCGGTTA-1	0.001727	0.000209	0.001586	0.001331	0.969433	0.025163	0.000204	0.000115	0.000183	0.000048
AAACCCAGTACCGCGT-1	0.002755	0.002519	0.427630	0.001193	0.493127	0.040972	0.027584	0.000575	0.002702	0.000943
AAACCCAGTATCGAAA-1	0.000939	0.002033	0.001625	0.001936	0.001200	0.001432	0.001604	0.001056	0.009517	0.978658
AAACCCAGTCGTCATA-1	0.000770	0.000189	0.000200	0.000244	0.000176	0.000162	0.000243	0.000100	0.000598	0.997318

# 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	0.000006	0.000055	0.000002	0.000003	2.650438e-06	0.000002	0.000003	0.000006	0.000001	0.000002
HES4	0.000008	0.001070	0.000007	0.000013	7.052645e-06	0.000010	0.000030	0.000009	0.000006	0.000006
ISG15	0.001506	0.000278	0.000014	0.000570	2.733733e-04	0.000084	0.001458	0.000200	0.001160	0.001372
TNFRSF18	0.000066	0.000006	0.000002	0.000010	8.475461e-07	0.000002	0.000002	0.000041	0.000387	0.000132
TNFRSF4	0.000045	0.000005	0.000002	0.000005	1.578560e-06	0.000004	0.000003	0.000009	0.000809	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	ACTB	0.250761	FTL	0.099662	LYZ	0.071014	CD74	0.148474	S100A9	0.145165	ACTB	0.068644	FTL	0.102359	IGKC	0.251105	TMSB4X	0.126876	ACTB	0.087591
1	TMSB4X	0.132250	ACTB	0.074163	FTH1	0.049132	HLA-DRA	0.082345	S100A8	0.101481	HLA-DRA	0.066628	FTH1	0.080575	IGLC2	0.136026	TMSB10	0.085798	TMSB4X	0.087425
2	TMSB10	0.088221	TMSB4X	0.059276	FTL	0.040657	TMSB4X	0.057995	LYZ	0.056132	LYZ	0.057734	TMSB4X	0.052844	IGHA1	0.088759	ACTB	0.082420	GNLY	0.070292
3	ACTG1	0.084450	FTH1	0.051802	NEAT1	0.029303	HLA-DRB1	0.047452	FTL	0.044074	CD74	0.049384	ACTB	0.040321	IGHM	0.059784	JUNB	0.033901	NKG7	0.053497
4	S100A4	0.037430	S100A4	0.031290	ACTB	0.028314	TMSB10	0.044340	ACTB	0.038659	CST3	0.042179	TMSB10	0.027831	IGLC3	0.041155	FTH1	0.027448	CCL5	0.040805