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.

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

install()

import os

import pandas as pd
import scanpy as sc
import scvi

sc.set_figure_params(figsize=(4, 4))

%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.

save_path = "data"
adata = sc.read(
    os.path.join(save_path, "pbmc_10k_protein_v3.h5ad"),
    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 [06:01<00:00,  2.85it/s, v_num=1, elbo_train=1.84e+7]Epoch 1000/1000: 100%|██████████| 1000/1000 [06:01<00:00,  2.76it/s, v_num=1, elbo_train=1.84e+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	0.000140	0.000091	0.000370	0.004209	0.000192	0.757920	0.236237	0.000104	0.000217	0.000519
AAACCCACATCGGTTA-1	0.000160	0.000183	0.000105	0.005576	0.000126	0.957939	0.017213	0.000168	0.000186	0.018343
AAACCCAGTACCGCGT-1	0.000474	0.002273	0.006529	0.001293	0.001002	0.550447	0.431790	0.000396	0.000861	0.004936
AAACCCAGTATCGAAA-1	0.984710	0.004950	0.001520	0.001724	0.001361	0.000984	0.001483	0.000960	0.001237	0.001071
AAACCCAGTCGTCATA-1	0.995573	0.000500	0.000265	0.000235	0.000245	0.000262	0.000278	0.000118	0.000163	0.002360

# 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	0.000002	0.000001	0.000014	0.000002	0.000140	4.226326e-06	0.000001	0.000005	0.000018	0.000004
HES4	0.000007	0.000005	0.000153	0.000010	0.004792	6.340905e-06	0.000005	0.000007	0.000026	0.000007
ISG15	0.001345	0.001193	0.001350	0.000300	0.000057	2.926238e-04	0.000223	0.000307	0.000039	0.001298
TNFRSF18	0.000133	0.000423	0.000003	0.000005	0.000035	8.482926e-07	0.000001	0.000064	0.000089	0.000019
TNFRSF4	0.000059	0.000831	0.000003	0.000004	0.000031	1.750126e-06	0.000002	0.000007	0.000037	0.000022

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	TMSB4X	0.087940	TMSB4X	0.128904	FTL	0.121524	CD74	0.151225	TMSB4X	0.099046	S100A9	0.144305	LYZ	0.074579	IGKC	0.222961	CD74	0.075236	ACTB	0.277791
1	ACTB	0.085636	TMSB10	0.086715	FTH1	0.070623	HLA-DRA	0.118559	ACTB	0.088994	S100A8	0.099209	FTH1	0.052626	IGLC2	0.122605	ACTB	0.040889	TMSB4X	0.114209
2	GNLY	0.070562	ACTB	0.077280	ACTB	0.058146	HLA-DRB1	0.069039	FTH1	0.032347	LYZ	0.052620	FTL	0.042102	IGHA1	0.078818	HLA-DRA	0.029397	ACTG1	0.089032
3	NKG7	0.054295	JUNB	0.034678	TMSB4X	0.055765	TMSB4X	0.061284	H3F3A	0.031736	FTL	0.045681	ACTB	0.032262	IGHM	0.055276	TMSB4X	0.026814	TMSB10	0.077840
4	CCL5	0.041439	FTH1	0.028662	S100A4	0.030253	ACTB	0.048254	CDKN1C	0.029134	ACTB	0.036801	TMSB4X	0.029318	IGLC3	0.037869	FTH1	0.025850	S100A4	0.051337