Getting started with astir

Table of Contents:

• 0 Loading necessary libraries

• 1 Load data

• 2 Fitting cell type

• 3 Fitting cell state

• 4 Saving results

• 5 Accessing internal functions and data

• 6 Saving models

• 7 Plot clustermap of expression data

• 8 Hierarchical model specification

0. Load necessary libraries

# !pip install -e ../../..
import os
import sys
module_path = os.path.abspath(os.path.join('../../..'))
if module_path not in sys.path:
    sys.path.append(module_path)

from astir.data import from_csv_yaml

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

%load_ext autoreload
%autoreload 2
%matplotlib inline

The autoreload extension is already loaded. To reload it, use:
  %reload_ext autoreload

1. Load data

We start by reading expression data in the form of a csv file and marker gene information in the form of a yaml file:

expression_mat_path = "../../../astir/tests/test-data/sce.csv"
# expression_mat_path = "data/sample_data.csv"
yaml_marker_path = "../../../astir/tests/test-data/jackson-2020-markers.yml"

Note

Expression data should already be cleaned and normalized. In our workflow, we perform this by a log-transformation of the data with a pseudocount of 1 (i.e. log(x+1)), followed by winsorization at the (1%,99%) percentiles.

We can view both the expression data and marker data:

!head -n 20 ../../../astir/tests/test-data/jackson-2020-markers.yml

cell_states:
  RTK_signalling:
    - Her2
    - EGFR
  cell_growth:
    - Ki-67
    - phospho mTOR
  mTOR_signalling:
    - phospho mTOR
    - phospho S6
  apoptosis:
    - cleaved PARP
    - Cleaved Caspase3

cell_types:
  stromal:
    - Vimentin
    - Fibronectin
  B cells:
    - CD45

pd.read_csv(expression_mat_path, index_col=0)[['EGFR','E-Cadherin', 'CD45', 'Cytokeratin 5']].head()

	EGFR	E-Cadherin	CD45	Cytokeratin 5
BaselTMA_SP41_186_X5Y4_3679	0.346787	0.938354	0.227730	0.095283
BaselTMA_SP41_153_X7Y5_246	0.833752	1.364884	0.068526	0.124031
BaselTMA_SP41_20_X12Y5_197	0.110006	0.177361	0.301222	0.052750
BaselTMA_SP41_14_X1Y8_84	0.282666	1.122174	0.606941	0.093352
BaselTMA_SP41_166_X15Y4_266	0.209066	0.402554	0.588273	0.064545

Then we can create an astir object using the from_csv_yaml function. For more data loading options, see the data loading tutorial.

ast = from_csv_yaml(expression_mat_path, marker_yaml=yaml_marker_path)
print(ast)

Astir object with 6 cell types, 4 cell states, and 4931 cells.

2. Fitting cell types

To fit cell types, simply call

ast.fit_type(max_epochs=10, n_init=3, n_init_epochs=2)

training restart 1/5: 100%|██████████| 5/5 [ 3.76s/epochs, current loss: -1693.0]
training restart 2/5: 100%|██████████| 5/5 [ 4.03s/epochs, current loss: 1273.4]
training restart 3/5: 100%|██████████| 5/5 [ 3.54s/epochs, current loss: -640.5]
training restart 4/5: 100%|██████████| 5/5 [ 3.41s/epochs, current loss: 198.5]
training restart 5/5: 100%|██████████| 5/5 [ 3.44s/epochs, current loss: -415.8]
training restart (final):  94%|█████████▍| 47/50 [ 3.51s/epochs, current loss: -17252.6]

Note

Controlling inference There are many different options for controlling inference in the fit_type function, including max_epochs (maximum number of epochs to train), learning_rate (ADAM optimizer learning rate), batch_size (minibatch size), delta_loss (stops iteration once the change in loss falls below this value), n_inits (number of restarts using random initializations). For full details, see the function documentation.

We should always plot the losses to assess convergence:

plt.figure(figsize=(5,4))
plt.plot(np.arange(len(ast.get_type_losses())), ast.get_type_losses())
plt.ylabel("Loss")
plt.xlabel("Epoch")

Text(0.5, 0, 'Epoch')

We can then get cell type assignment probabilities by calling

assignments = ast.get_celltype_probabilities()
assignments

	stromal	B cells	T cells	macrophage	epithelial(basal)	epithelial(luminal)	Other
BaselTMA_SP43_115_X4Y8_1	5.981264e-05	4.351427e-01	4.413378e-06	4.778704e-05	0.005910	0.000002	5.588340e-01
BaselTMA_SP43_115_X4Y8_2	7.080264e-05	3.849646e-01	5.889273e-06	4.314298e-05	0.044710	0.000007	5.701980e-01
BaselTMA_SP43_115_X4Y8_3	2.086748e-04	1.871444e-01	9.592506e-04	4.061270e-04	0.290781	0.039960	4.805403e-01
BaselTMA_SP43_115_X4Y8_4	2.980559e-04	4.438626e-01	6.048962e-06	1.707915e-04	0.011950	0.000006	5.437063e-01
BaselTMA_SP43_115_X4Y8_5	1.121071e-04	4.681895e-01	2.136392e-05	3.064268e-05	0.017083	0.000002	5.145617e-01
...	...	...	...	...	...	...	...
BaselTMA_SP43_115_X4Y8_4927	4.338320e-07	1.912927e-03	2.400906e-07	1.376804e-06	0.993716	0.000003	4.365914e-03
BaselTMA_SP43_115_X4Y8_4928	2.193680e-04	3.908094e-01	3.504072e-04	2.164537e-04	0.009062	0.000018	5.993251e-01
BaselTMA_SP43_115_X4Y8_4929	1.189970e-08	7.369497e-07	5.310283e-09	8.920690e-09	0.999534	0.000464	8.322494e-07
BaselTMA_SP43_115_X4Y8_4930	5.812946e-08	6.018526e-09	2.364501e-08	5.991192e-09	0.000590	0.999410	6.340690e-08
BaselTMA_SP43_115_X4Y8_4931	1.341373e-05	1.754594e-06	2.443332e-06	8.300306e-07	0.060859	0.939114	8.438225e-06

4931 rows × 7 columns

We can also visualize the assignment probabilities using a heatmap:

sns.heatmap(assignments)

<matplotlib.axes._subplots.AxesSubplot at 0x7f8d611c72d0>

where each row corresponds to a cell, and each column to a cell type, with the entry being the probability of that cell belonging to a particular cell type.

To fetch an array corresponding to the most likely cell type assignments, call

ast.get_celltypes()

	cell_type
BaselTMA_SP43_115_X4Y8_1	Unknown
BaselTMA_SP43_115_X4Y8_2	Unknown
BaselTMA_SP43_115_X4Y8_3	Unknown
BaselTMA_SP43_115_X4Y8_4	Unknown
BaselTMA_SP43_115_X4Y8_5	Unknown
...	...
BaselTMA_SP43_115_X4Y8_4927	epithelial(basal)
BaselTMA_SP43_115_X4Y8_4928	Unknown
BaselTMA_SP43_115_X4Y8_4929	epithelial(basal)
BaselTMA_SP43_115_X4Y8_4930	epithelial(luminal)
BaselTMA_SP43_115_X4Y8_4931	epithelial(luminal)

4931 rows × 1 columns

Cell type diagnostics

It is important to run diagnostics to ensure that cell types express their markers at higher levels than other cell types. To do this, run the diagnostics_celltype() function, which will alert to any issues if a cell type doesn’t express its marker signficantly higher than an alternative cell type (for which that protein isn’t a marker):

ast.diagnostics_celltype().head(n=10)

	feature	should be expressed higher in	than	mean cell type 1	mean cell type 2	p-value	note
0	Fibronectin	stromal	B cells	2.045195	1.565420	inf	Only 1 cell in a type: comparison not possible
1	Vimentin	stromal	B cells	2.994335	1.095477	inf	Only 1 cell in a type: comparison not possible
2	CD20	B cells	stromal	0.403677	0.081944	inf	Only 1 cell in a type: comparison not possible
3	CD20	B cells	T cells	0.403677	0.123195	inf	Only 1 cell in a type: comparison not possible
4	CD20	B cells	macrophage	0.403677	0.212008	inf	Only 1 cell in a type: comparison not possible
5	CD20	B cells	epithelial(basal)	0.403677	0.118228	inf	Only 1 cell in a type: comparison not possible
6	CD20	B cells	epithelial(luminal)	0.403677	0.131991	inf	Only 1 cell in a type: comparison not possible
7	CD20	B cells	Other	0.403677	0.017356	inf	Only 1 cell in a type: comparison not possible
8	CD45	B cells	stromal	0.077596	0.227257	inf	Only 1 cell in a type: comparison not possible
9	CD45	B cells	epithelial(basal)	0.077596	0.182078	inf	Only 1 cell in a type: comparison not possible

Note

In this tutorial, we end up with many “Only 1 cell in a type: comparison not possible” notes - this is simply because the small dataset size results in only a single cell assigned to many types, making statistical testing infeasible.

Calling ast.diagnostics_celltype() returns a pd.DataFrame, where each column corresponds to a particular protein and two cell types, with a warning if the protein is not expressed at higher levels in the cell type for which it is a marker than the cell type for which it is not.

The diagnostics:

1. Iterates through every cell type and every marker for that cell type

2. Given a cell type c and marker g, find the set of cell types D that don’t have g as a marker

3. For each cell type d in D, perform a t-test between the expression of marker g in c vs d

4. If g is not expressed significantly higher (at significance alpha), output a diagnostic explaining this for further investigation.

If multiple issues are found, the markers and cell types may need refined.

3. Fitting cell state

Similarly as before, to fit cell state, call

ast.fit_state(batch_size = 1024, learning_rate=1e-3, max_epochs=10)

/Users/jinelles.h/Documents/Camlab/astir-top-level/astir/astir/models/cellstate.py:176: UserWarning: Delta loss batch size is greater than the number of epochs
  warnings.warn("Delta loss batch size is greater than the number of epochs")
training restart 1/5: 100%|██████████| 5/5 [ 3.41s/epochs, current loss: 59.8]
training restart 2/5: 100%|██████████| 5/5 [ 3.40s/epochs, current loss: 98.0]
training restart 3/5: 100%|██████████| 5/5 [ 3.51s/epochs, current loss: 78.2]
training restart 4/5: 100%|██████████| 5/5 [ 3.48s/epochs, current loss: 88.0]
training restart 5/5: 100%|██████████| 5/5 [ 3.37s/epochs, current loss: 60.0]
training restart (final): 100%|██████████| 50/50 [ 3.60s/epochs, current loss: 14.5]
/Users/jinelles.h/Documents/Camlab/astir-top-level/astir/astir/astir.py:268: UserWarning: Maximum epochs reached. More iteration may be needed to complete the training.
  warnings.warn(msg)

and similary plot the losses via

plt.figure(figsize=(5,4))
plt.plot(np.arange(len(ast.get_state_losses())), ast.get_state_losses())
plt.ylabel("Loss")
plt.xlabel("Epoch")

Text(0.5, 0, 'Epoch')

and cell state assignments can be inferred via

states = ast.get_cellstates()
states

	RTK_signalling	cell_growth	mTOR_signalling	apoptosis
BaselTMA_SP43_115_X4Y8_1	0.219178	0.178849	0.133436	0.144105
BaselTMA_SP43_115_X4Y8_2	0.296468	0.119678	0.200147	0.157937
BaselTMA_SP43_115_X4Y8_3	0.181820	0.185739	0.117271	0.117391
BaselTMA_SP43_115_X4Y8_4	0.271369	0.091272	0.145709	0.170535
BaselTMA_SP43_115_X4Y8_5	0.238632	0.219416	0.147383	0.165110
...	...	...	...	...
BaselTMA_SP43_115_X4Y8_4927	0.377885	0.229766	0.257093	0.232393
BaselTMA_SP43_115_X4Y8_4928	0.144620	0.335371	0.105722	0.134628
BaselTMA_SP43_115_X4Y8_4929	0.494012	0.387052	0.286395	0.357899
BaselTMA_SP43_115_X4Y8_4930	0.624909	0.492357	0.315533	0.519452
BaselTMA_SP43_115_X4Y8_4931	0.631358	0.453455	0.292822	0.536574

4931 rows × 4 columns

plt.scatter(
    states['RTK_signalling'],
    ast.get_state_dataset().get_exprs_df()['Her2']
)

<matplotlib.collections.PathCollection at 0x7f8d60937b90>

Cell state diagnostics

It is important to run diagnostics on cell states model for the same reasons stated for the cell type model. Astir.diagnostics_cellstate() spots any non marker protein and pathway pairs whose expressions are higher than those of the marker proteins of the pathway.

ast.diagnostics_cellstate().head(n=10)

	pathway	protein A	correlation of protein A	protein B	correlation of protein B	note
0	RTK_signalling	EGFR	0.823298	Cleaved Caspase3	0.831128	EGFR is marker for RTK_signalling but Cleaved ...
1	RTK_signalling	EGFR	0.823298	cleaved PARP	0.831128	EGFR is marker for RTK_signalling but cleaved ...
2	cell_growth	Ki-67	0.058879	Cleaved Caspase3	0.862459	Ki-67 is marker for cell_growth but Cleaved Ca...
3	cell_growth	Ki-67	0.058879	EGFR	0.897650	Ki-67 is marker for cell_growth but EGFR isn't
4	cell_growth	Ki-67	0.058879	Her2	0.750985	Ki-67 is marker for cell_growth but Her2 isn't
5	cell_growth	Ki-67	0.058879	cleaved PARP	0.862459	Ki-67 is marker for cell_growth but cleaved PA...
6	cell_growth	Ki-67	0.058879	phospho S6	0.272989	Ki-67 is marker for cell_growth but phospho S6...
7	mTOR_signalling	phospho S6	0.699387	EGFR	0.720013	phospho S6 is marker for mTOR_signalling but E...
8	mTOR_signalling	phospho S6	0.699387	Her2	0.757867	phospho S6 is marker for mTOR_signalling but H...

Calling ast.diagnostics_cellstate() returns a pd.DataFrame, where each column corresponds to a particular protein and two cell types, with a warning if the protein is not expressed at higher levels in the cell state for which it is a marker than the cell state for which it is not.

The diagnostics:

1. Get correlations between all cell states and proteins

2. For each cell state c, get the smallest correlation with marker g

3. For each cell state c and its non marker g, find any correlation that is bigger than those smallest correlation for c.

4. Any c and g pairs found in step 3 will be included in the output of Astir.diagnostics_cellstate(), including an explanation.

If multiple issues are found, the markers and cell states may need refined.

4. Saving results

Both cell type and cell state information can easily be saved to disk via

ast.type_to_csv("data/cell-types.csv")
ast.state_to_csv("data/cell-states.csv")

!head -n 3 data/cell-types.csv

,stromal,B cells,T cells,macrophage,epithelial(basal),epithelial(luminal),Other
BaselTMA_SP43_115_X4Y8_1,5.9812641356773485e-05,0.43514272442399615,4.4133780759206555e-06,4.778704083811438e-05,0.00590960852651017,1.6351770806453748e-06,0.5588340188121422
BaselTMA_SP43_115_X4Y8_2,7.080264289768121e-05,0.38496458175145926,5.889272783675721e-06,4.3142984449199766e-05,0.04471036731616506,7.2442437475747445e-06,0.5701979717884975

!head -n 3 data/cell-states.csv

,RTK_signalling,cell_growth,mTOR_signalling,apoptosis
BaselTMA_SP43_115_X4Y8_1,0.2191776340692214,0.17884886731101723,0.13343558969907734,0.1441052515306596
BaselTMA_SP43_115_X4Y8_2,0.29646752007327026,0.11967817733248733,0.20014708539822942,0.1579368118796618

where the first (unnamed) column always corresponds to the cell name/ID.

5. Accessing internal functions and data

Data stored in astir objects is in the form of an SCDataSet. These can be retrieved via

celltype_data = ast.get_type_dataset()
celltype_data

<astir.data.scdataset.SCDataset at 0x7f8d60bd6ed0>

and similarly for cell state via ast.get_state_dataset().

These have several helper functions to retrieve relevant information to the dataset:

celltype_data.get_cell_names()[0:4] # cell names

['BaselTMA_SP43_115_X4Y8_1',
 'BaselTMA_SP43_115_X4Y8_2',
 'BaselTMA_SP43_115_X4Y8_3',
 'BaselTMA_SP43_115_X4Y8_4']

celltype_data.get_classes() # cell type names

['stromal',
 'B cells',
 'T cells',
 'macrophage',
 'epithelial(basal)',
 'epithelial(luminal)']

print(celltype_data.get_n_classes()) # number of cell types
print(celltype_data.get_n_features()) # number of features / proteins

6
14

celltype_data.get_exprs() # Return a torch tensor corresponding to the expression data used

tensor([[4.2121e-02, 5.2044e-02, 1.7348e-03,  ..., 6.1314e-01, 4.4827e-02,
         3.8841e-01],
        [0.0000e+00, 3.4770e-02, 0.0000e+00,  ..., 9.4025e-01, 1.9424e-02,
         5.6716e-01],
        [1.8200e-02, 7.8596e-02, 0.0000e+00,  ..., 6.2852e-01, 4.0905e-02,
         8.4946e-01],
        ...,
        [1.4403e-01, 7.0877e-02, 2.0325e-01,  ..., 1.7303e+00, 2.1434e-01,
         9.4889e-01],
        [3.6400e-02, 9.9307e-02, 1.1815e-01,  ..., 1.6467e+00, 1.3463e-01,
         1.9238e+00],
        [5.4069e-02, 1.1861e-01, 5.3894e-02,  ..., 1.4265e+00, 4.9443e-01,
         1.6126e+00]], dtype=torch.float64)

celltype_data.get_exprs_df() # Return a pandas DataFrame corresponding to the expression data used

	CD20	CD3	CD45	CD68	Cytokeratin 14	Cytokeratin 19	Cytokeratin 5	Cytokeratin 7	Cytokeratin 8/18	E-Cadherin	Fibronectin	Her2	Vimentin	pan Cytokeratin
BaselTMA_SP43_115_X4Y8_1	0.042121	0.052044	0.001735	0.042628	0.046076	0.076746	0.113790	0.073571	0.110530	0.800019	0.324533	0.613138	0.044827	0.388409
BaselTMA_SP43_115_X4Y8_2	0.000000	0.034770	0.000000	0.084581	0.059064	0.056487	0.098873	0.019242	0.152825	0.972369	0.384034	0.940250	0.019424	0.567159
BaselTMA_SP43_115_X4Y8_3	0.018200	0.078596	0.000000	0.042628	0.026254	0.126815	0.165966	0.310404	0.253835	1.108996	0.256832	0.628524	0.040905	0.849462
BaselTMA_SP43_115_X4Y8_4	0.000000	0.018701	0.015682	0.108294	0.071382	0.052757	0.022484	0.093607	0.062275	1.204820	0.661950	0.530076	0.093848	0.418222
BaselTMA_SP43_115_X4Y8_5	0.099789	0.073795	0.093230	0.122463	0.000000	0.238924	0.193627	0.000000	0.125397	1.225161	0.623664	0.493992	0.000000	0.296923
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
BaselTMA_SP43_115_X4Y8_4927	0.000000	0.036476	0.142845	0.384770	0.046530	0.000362	0.139654	0.000000	0.000000	1.730274	0.233316	1.276169	0.171234	0.396967
BaselTMA_SP43_115_X4Y8_4928	0.000000	0.100622	0.089643	0.091315	0.000000	0.098437	0.000000	0.000000	0.155443	0.908461	0.411734	0.365833	0.110548	0.789458
BaselTMA_SP43_115_X4Y8_4929	0.144029	0.070877	0.203246	0.503439	0.051248	0.200929	0.138156	0.045556	0.057138	2.136403	0.841147	1.730263	0.214340	0.948885
BaselTMA_SP43_115_X4Y8_4930	0.036400	0.099307	0.118155	0.447235	0.285294	0.270529	0.107387	0.423265	0.234452	1.884903	0.767309	1.646707	0.134634	1.923792
BaselTMA_SP43_115_X4Y8_4931	0.054069	0.118611	0.053894	0.484753	0.340787	0.133814	0.150674	0.365944	0.163528	1.843372	1.161388	1.426493	0.494433	1.612622

4931 rows × 14 columns

ast.normalize()

ast.get_type_dataset().get_exprs_df()

	CD20	CD3	CD45	CD68	Cytokeratin 14	Cytokeratin 19	Cytokeratin 5	Cytokeratin 7	Cytokeratin 8/18	E-Cadherin	Fibronectin	Her2	Vimentin	pan Cytokeratin
BaselTMA_SP43_115_X4Y8_1	0.008424	0.010409	0.000347	0.008586	0.009215	0.015349	0.022756	0.014714	0.022104	0.159329	0.064861	0.122322	0.008965	0.077604
BaselTMA_SP43_115_X4Y8_2	0.000000	0.006954	0.000000	0.016915	0.011813	0.011297	0.019773	0.003848	0.030560	0.193268	0.076731	0.186959	0.003885	0.113190
BaselTMA_SP43_115_X4Y8_3	0.003640	0.015719	0.000000	0.008586	0.005251	0.025360	0.033187	0.062041	0.050745	0.220020	0.051344	0.125376	0.008181	0.169086
BaselTMA_SP43_115_X4Y8_4	0.000000	0.003740	0.003136	0.021657	0.014276	0.010551	0.004497	0.018720	0.012455	0.238691	0.132006	0.105818	0.018769	0.083547
BaselTMA_SP43_115_X4Y8_5	0.019956	0.014758	0.018645	0.024490	0.000000	0.047767	0.038716	0.000000	0.025077	0.242644	0.124412	0.098638	0.000000	0.059350
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
BaselTMA_SP43_115_X4Y8_4927	0.000000	0.007295	0.028565	0.076878	0.009306	0.000123	0.027927	0.000000	0.000000	0.339496	0.046690	0.252541	0.034240	0.079310
BaselTMA_SP43_115_X4Y8_4928	0.000000	0.020123	0.017928	0.018262	0.000000	0.019686	0.000000	0.000000	0.031084	0.180707	0.082254	0.073101	0.022108	0.157243
BaselTMA_SP43_115_X4Y8_4929	0.028802	0.014175	0.040638	0.100518	0.010249	0.040175	0.027628	0.009111	0.011427	0.415244	0.167446	0.339493	0.042855	0.188656
BaselTMA_SP43_115_X4Y8_4930	0.007280	0.019860	0.023629	0.089328	0.057028	0.054079	0.021476	0.084552	0.046873	0.368578	0.152866	0.323661	0.026924	0.375847
BaselTMA_SP43_115_X4Y8_4931	0.010813	0.023720	0.010779	0.096799	0.068105	0.026760	0.030130	0.073124	0.032700	0.360796	0.230238	0.281564	0.098726	0.317179

4931 rows × 14 columns

6. Saving models

After fixing the models, we can save the cell type/state assignment, the losses, the parameters (e.g. mu, rho, log_sigma, etc) and the run informations (e.g. batch_size, learning_rate, delta_loss, etc) to an hdf5 file.

ast.save_models("data/astir_summary.hdf5")

The hierarchy of the hdf5 file would be:

Only the model that is trained will be saved (CellTypeModel or CellStateModel or both). If the functioned is called before any model is trained, exception will be raised. Data saved in the file is either int or np.array.

7. Plot clustermap of expression data

After fixing the cell type model, we can also plot a heatmap of protein expression of cells clustered by type. The heatmap will be saved at the location plot_name, which is default to "./celltype_protein_cluster.png"

ast.type_clustermap(plot_name="./img/celltype_protein_cluster.png", threshold = 0.7, figsize=(7, 5))

Note: threshold is the probability threshold above which a cell is assigned to a cell type, default to 0.7.

8. Hierarchical model specification

In the marker yaml file, the user can also add a section called hierarchy, which specifies the hierarchical structure of cell types. Here’s an example:

hierarchy:
  immune:
    - B cells
    - T cells
    - macrophage
  epithelial:
    - epithelial(basal)
    - epithelial(luminal)

Some notes: 1. The section would be accessed by key hierarchy. 2. In the section, the higher-levelled cell type names should be the keys. 3. The values in the section should also exist as the cell type names in the cell_types section. (e.g. if we have "B cells" in marker["hierarchy"]["immune"], we should also be able to get marker["cell_types"]["B cells"])

This section could be used to summarize the cell types assignment at a higher hierarchical level. (e.g. a cell is predicted as “immune” instead of “B cells” or “T cells”)

hierarchy_probs = ast.assign_celltype_hierarchy()
hierarchy_probs.head()

	immune	epithelial
BaselTMA_SP43_115_X4Y8_1	0.435195	0.005911
BaselTMA_SP43_115_X4Y8_2	0.385014	0.044718
BaselTMA_SP43_115_X4Y8_3	0.188510	0.330741
BaselTMA_SP43_115_X4Y8_4	0.444039	0.011956
BaselTMA_SP43_115_X4Y8_5	0.468241	0.017085

To make it more clear, here’s a heatmap for the cell assignment in a higher hierarchy:

The way it is calculated is simply summing up the probabilities of the cell type assignments under the same hierarchy.