This tutorial shows how to apply a model interpretability library, Captum, to a deep learning recommender model (DLRM).
More about the DLRM achitecture and usage can be found here: https://github.com/facebookresearch/dlrm.
For our experiments we used Criteo's traffic over a period of seven days. The dataset is also available on kaggle for download: https://www.kaggle.com/c/criteo-display-ad-challenge. We pre-trained a DLRM model using 39M Ads from the Criteo dataset. From a feature importance calculation perspective, we used a small fraction of preprocessed data.
In this tutorial we aim to answer the following questions:
The first, sceond and third questions are also visualized in the diagram below.
Note: Please run this tutorial in a GPU environment. It is most probably going to fail in a CPU environment.
import IPython
IPython.display.Image(filename='img/dlrm_arch.png')
import sys
import numpy as np
import torch
# Replace this path with the repo of DLRM project <PATH-TO-DLRM-REPO>
sys.path.insert(0, '<PATH-TO-DLRM-REPO>')
from dlrm_s_pytorch import DLRM_Net
from captum.attr import IntegratedGradients, LayerConductance, NeuronConductance
import matplotlib.pyplot as plt
torch.__version__
Defining the device used to store the model and the tensors.
device = torch.device("cuda:1" if torch.cuda.is_available() else "cpu")
Initializing an instance of DLRM_Net model and defining parameters necessary to load pretrained DLRM model.
m_spa=16
ln_emb=np.array([1460,583,10131227,2202608,305,24,12517,633,3,93145,5683,8351593,3194,27,14992,5461306,10,5652,2173,4,7046547,18,15,286181,105,142572])
ln_bot=np.array([13,512,256,64,16])
ln_top=np.array([367,512,256,1])
dlrm = DLRM_Net(
m_spa,
ln_emb,
ln_bot,
ln_top,
arch_interaction_op="dot",
arch_interaction_itself=False,
sigmoid_bot=-1,
sigmoid_top=ln_top.size - 2,
sync_dense_params=True,
loss_threshold=0.0,
ndevices=-1,
qr_flag=False,
qr_operation=None,
qr_collisions=None,
qr_threshold=None,
md_flag=False,
md_threshold=None,
)
Let's download a pre-trained DLRM model from an AWS S3 bucket.
!wget https://pytorch-tutorial-assets.s3.amazonaws.com/kg.pt -O models/kg.pt
Loading pre-trained DLRM model and moving it to predefined device.
model_path = 'models/kg.pt'
ld_model = torch.load(model_path)
dlrm.load_state_dict(ld_model["state_dict"])
dlrm = dlrm.to(device)
Since the actual test dataset is pretty large and requires preprocessing, we preprocessed a small portion of it and stored as batches in two 'pt' files so that it is easier for us to work with. The first 'pt' file, X_S_T_test_above_0999, contains 497 samples that are predicted as Clicked Ads with a high prediction score, larger than 0.999. The second 'pt' file, X_S_T_test, contains 1100 samples, Ads that aren't conditioned on the prediction scores.
The reason why we separated the samples in two groups is that in our analysis we often want to understand most salient features for the Ads that are predicted as Clicked with a high prediction score, close to 1.0, versus to the Ads that have mixed prediction scores (some are high and some low).
Below, we load both files, so that we can perform model interpretabily for those preprocessed subsets of data.
S_T_Z_test_above_0999 = torch.load('data/dlrm/X_S_T_test_above_0999')
S_T_Z_test = torch.load('data/dlrm/X_S_T_test')
Redefining forward pass for the DLRM model so that it accepts sparse embeddings instead of feature indices and offsets. This is done this way because apply_emb cannot be easily replaced by model hooks. https://github.com/facebookresearch/dlrm/blob/52b77f80a24303294a02c86b574529cdc420aac5/dlrm_s_pytorch.py#L276.
def sequential_forward(dense_x, *sparse_y):
x = dlrm.apply_mlp(dense_x, dlrm.bot_l)
ly = list(sparse_y)
# interact features (dense and sparse)
z = dlrm.interact_features(x, ly)
# obtain probability of a click (using top mlp)
p = dlrm.apply_mlp(z, dlrm.top_l)
# clamp output if needed
if 0.0 < dlrm.loss_threshold and dlrm.loss_threshold < 1.0:
z = torch.clamp(p, min=dlrm.loss_threshold, max=(1.0 - dlrm.loss_threshold))
else:
z = p
return z
Let's extract individual features for each sample from both batches of data. Each sample is represented through dense and sparse features. In this example X_test represents dense features. lS_o_test and lS_i_test represent sparse features. lS_o_test represents the offset of each sparse feature group and lS_i_test the index. More details about it can be found here: https://github.com/facebookresearch/dlrm/blob/52b77f80a24303294a02c86b574529cdc420aac5/dlrm_s_pytorch.py#L276.
X_test_above_0999 = S_T_Z_test_above_0999['X_test'].to(device)
lS_o_test_above_0999 = S_T_Z_test_above_0999['lS_o_test'].to(device)
lS_i_test_above_0999 = S_T_Z_test_above_0999['lS_i_test'].to(device)
probs_above_0999 = S_T_Z_test_above_0999['probs'].to(device)
X_test = S_T_Z_test['X_test'].to(device)
lS_o_test = S_T_Z_test['lS_o_test'].to(device)
lS_i_test = S_T_Z_test['lS_i_test'].to(device)
probs = S_T_Z_test['probs'].to(device)
We used one of the sample-based feature importance algorithms, namely Integrated Gradients, in order to understand which features are important in predicting Ads as Clicked with high prediction scores.
ig = IntegratedGradients(sequential_forward)
Below we compute feature importances both for dense and sparse features. We performed the computations both for the batch that contains Ads that are predicted as Clicked with high prediction score and the batch that doesn't set any conditions on the prediction score.
embeddings = dlrm.apply_emb(lS_o_test, lS_i_test, dlrm.emb_l, dlrm.v_W_l)
attributions, delta = ig.attribute((X_test, *embeddings), n_steps=10, return_convergence_delta=True)
attr_dense = attributions[0]
attr_sparse = torch.stack(attributions[1:], dim=1)
# ...... the batch that contains Ads that are predicted as Clicked with high prediction score ......
embeddings_above_0999 = dlrm.apply_emb(lS_o_test_above_0999, lS_i_test_above_0999, dlrm.emb_l, dlrm.v_W_l)
attributions_above_0999, delta_above_0999 = ig.attribute((X_test_above_0999, *embeddings_above_0999), \
n_steps=10, return_convergence_delta=True)
attr_dense_above_0999 = attributions_above_0999[0]
attr_sparse_above_0999 = torch.stack(attributions_above_0999[1:], dim=1)
Defining labels / names for dense and sparse features.
dense_names = ['d{}'.format(i) for i in range(attr_dense.shape[1])]
sparse_names = ['s{}'.format(i) for i in range(attr_sparse.shape[1])]
names = dense_names + sparse_names
Below we visualize feature importance scores for five different Ads, color-coded in five different colors that were predicted as Clicked with 0.999 prediction score. X-axis corresponds to the input features and y-axis to the attribution scores. The first 13 features correspond to dense and the last 26 to sparse features. As we can see, the sparse features primarily contribute to Clicked predictions whereas dense, contribute to both Clicked and Non-Clicked predictions.
import matplotlib.pyplot as plt
import pandas as pd
parameters = {'figure.figsize': (20, 6),
'axes.labelsize': 25,
'axes.titlesize': 25,
'xtick.labelsize': 14,
'ytick.labelsize': 14}
plt.rcParams.update(parameters)
# Sample-based interpretability
def sample_features(idx):
return torch.cat([attr_dense_above_0999[idx, :], \
attr_sparse_above_0999[idx, :, :].sum(axis=1)], axis=0).cpu().detach().numpy()
f0 = sample_features(0)
f1 = sample_features(1)
f2 = sample_features(2)
f3 = sample_features(3)
f4 = sample_features(4)
samples_df = pd.DataFrame(index=dense_names + sparse_names,
data={'Sample1': f0,
'Sample2': f1,
'Sample3': f2,
'Sample4': f3,
'Sample5': f4,
})
ax = samples_df.plot(kind="bar", stacked=True)
plt.xlabel('Input Features', fontsize=20)
plt.ylabel('Attributions', fontsize=20)
plt.title('Feature importances for 5 samples with prediction score > 0.999', pad=20)
plt.show()
A helper function to plot aggregated feature importance.
def plot_fi(fi_scores, title, x_axis='Input Features', \
x_axis_labels=dense_names + sparse_names, y_axis='Attribution'):
plt.rcParams["figure.figsize"] = (22,4)
plt.bar(x_axis_labels, fi_scores.detach().cpu().numpy())
plt.xlabel(x_axis, fontsize=20, labelpad=20)
plt.ylabel(y_axis, fontsize=20, labelpad=20)
plt.title(title, pad=20)
plt.show()
Below we plot aggregated feature importance scores across all 497 samples that have a prediction score close to 1.0.
We can see that the primary and consistent high predictive signal is coming from the sparse features. Dense features contribute to both Clicked and Non-Clicked predictions.
all_features_above_0999 = torch.cat([attr_dense_above_0999.sum(dim=0), attr_sparse_above_0999.sum(dim=(0,2))])
plot_fi(all_features_above_0999, 'Feature Importances cross {} Examples that were predicted as Ads with a ' \
'prediction score > 0.999'.format(len(probs_above_0999)))
In the next example, instead of taking samples with the high prediction score let's consider all samples in S_T_Z_test batch. We can clearly see that the relative contribution score for the sparse features reduces and the dense features became significantly prominent which speaks to the fact that the primary signal for Non-Clicked is coming from the dense features. This observation, however, is made by using all-zero baseline for the Integrated Gradients algorithm.
When we compute prediction score for all-zero input tensor we observe that the prediction score is 0.2, Non-Clicked. Ideally we would like the prediction score for baseline to be more neutral, somewhere close to 0.
To dig deeper into whether sparse or dense features are more important for Clicked and Non-Clicked predictions we set those features to 0, one at a time and observe prediction score changes.
If we zero out all sparse features we notice that all samples get classified as Non-Clicked.
embeddings_above_0999_zeros = [torch.zeros_like(embedding) for embedding in embeddings_above_0999]
zero_emb_perc = 100 * sum(sequential_forward(X_test_above_0999, *embeddings_above_0999_zeros) > 0.5).item() \
/ X_test_above_0999.size(0)
print("The percentage of samples that are classified as `Clicked` after "
"zeroing out sparse features: {}%".format(zero_emb_perc))
If we zero out dense features, we notice that almost all Ads still classified as Clicked. If we look closer into the scores we will noticed that for some samples the scores have even increased.
zero_dense_perc = 100 * sum(sequential_forward(torch.zeros_like(X_test_above_0999), \
*embeddings_above_0999) > 0.5).item() / X_test_above_0999.size(0)
print("The percentage of samples that are classified as `Clicked` "
"after zero-ing out dense features: {}%".format(int(zero_dense_perc)))
all_features = torch.cat([attr_dense.sum(dim=0), attr_sparse.sum(dim=(0,2))])
plot_fi(all_features, 'Feature Importances cross {} Examples that were predicted as Ads'.format(len(probs)))
Now let’s look deeper into the interaction layer. More specifically, let’s examine the importance of pairwise feature interactions in the output of the interaction layer. In the interaction layer we consider interactions between 27 16-dimensional feature representations, 26 corresponding to sparse and 1 to dense features. The last 16-dimensional dense representation is emerged after transforming 13 dense features into one 16-dimensional embedding vector. In the interaction layer we consider pairwise interactions of 27 features using dot products. This results to 27 x 26 x 0.5 = 351 pairwise interactions excluding self interactions. In the very end, 16-dimensional dense feature representation is being prepended to resulting interactions leading to 16 + 351 = 367 neurons in the output of second concatenation layer.
We use the Layer Conductance algorithm to estimate the importance of all 367 neurons.
lc = LayerConductance(sequential_forward, dlrm.top_l)
layer_attribution = lc.attribute(inputs=(X_test_above_0999, *embeddings_above_0999),
n_steps=10,
attribute_to_layer_input=True)
The figure below demonstrates the importance scores of each neuron in the output of interaction layer. The first 16 neurons have mixed contributions both to Clicked and Non-Clicked predictions. The following 351 interaction neurons either primarily contribute to Clicked or have no effect on the prediction. In fact we can see that many of those interactions have no effect on the prediction. This observations, however, are supported by 497 samples that are predicted as Clicked with a prediction score larger than 0.999. One might think that the samples might not be representative enough, however, even if we increase the sample size we still observe similar patterns. As an extension of this work one might think of performing statistical significance testing for random subsamples that are predicted as Clicked with high prediction score to make more convincing arguments.
layer_attrs_all_sum = layer_attribution.sum(axis=0)
plot_fi(layer_attrs_all_sum, \
title='Feature Interaction Importances for {} samples that are predicted ' \
'as clicks with pred score > 0.999'.format(len(layer_attribution)),
x_axis='Interaction Indices',
x_axis_labels=list(range(len(layer_attrs_all_sum)))
)
Please note that in the example above we sum the attributions across all examples for each neuron. This means that if the attributions are positive and negative they can cancel out each other. For deeper analysis we also recommend to look into attribution scores assigned by each example for a given neuron. For the neurons indexed with 5 and 6 we observe that zero score is assigned consistently across all samples.
print("The percentage of samples that have zero attribution for neuron "
"index 5: {}% in `X_test_above_0999` dataset.".format(100 * sum(layer_attribution[:, 5] == 0.0).item() \
/ layer_attribution.size(0)))
print("The percentage of samples that have zero attribution for neuron "
"index 6: {}% in `X_test_above_0999` dataset.".format(100 * sum(layer_attribution[:, 6] == 0.0).item() / layer_attribution.size(0)))
In this last section we look into the aggregated attribution scores stacked for 82 Ads that were predicted as Clicked with prediction score > 0.6 for all 256 neurons in the last fully connected layer.
For our experiments we used LayerConductance algorithm for top_l layer.
ncl = LayerConductance(sequential_forward, dlrm.top_l[3])
On figure below we visualize stacked attribution scores per neuron, considering that the attribution scores can be both positive and negative. When we analyze resulting neuron importances, we conclude that 45 out of 256 neurons always assigned a negative and another 24 always assigned zero attribution scores according to all 82 Ads samples with prediction score > 0.6. The remaining neurons are assigned either positive or mixed (positive, zero or negative) attribution scores.
indices = (probs.squeeze() > 0.6).nonzero().view(-1)
neuron_attributions = ncl.attribute(inputs=(X_test, *embeddings), n_steps=10)
neuron_attributions_select = torch.index_select(neuron_attributions, 0, indices).transpose(1,0)
neuron_attributions_select = neuron_attributions_select.cpu().detach().numpy()
Below we can see the attributions for 10 samples stacked on each other for all 256 neurons in the last fully connected layer. We chose 10 samples only because it is visually easier to perceive.
all_neurons = pd.DataFrame(neuron_attributions_select[:, :10])
all_neurons.plot(kind="barh", stacked=True, mark_right=True, legend=False)
plt.rcParams["figure.figsize"] = (200,200)
plt.xlabel('Accumulated Attributions', fontsize=40)
plt.ylabel('Neuron Indices', fontsize=40)
The number of neurons that have zero contribution in predicting that an Ad is Clicked out of all 82 samples.
zero_contributions = sum((neuron_attributions_select != 0.0).sum(axis=1) == 0.0)
zero_contributions
The number of neurons that have negative contributions in predicting that an Ad is Clicked out of all 82 samples.
negative_contributions = sum((neuron_attributions_select > 0.0).sum(axis=1) == 0.0) - zero_contributions
negative_contributions
We can extend our analysis further and ablate the neurons that have zero contribution to the prediction or are negatively correlated with the ads prediction across all samples. According to the specific examples demonstrated above we can see that based on our sample size of 82 (prediction score > 0.6), 24 neurons out of 256 always demonstrate zero contribution to the prediction. If we ablate these neurons we can see that the False Negatives are reducing and overall Recall and F1 score of the model are increasing. Since this is a tutorial and measuring the accuracy and F1 scores on test data can be time consuming we do not demonstrate it here but the users are welcome to ablate those neurons based on the neuron importance scores and examine the difference in the Accuracy and F1 scores.
Similar thinking can also be applied to the neurons that are always negatively correlated with the Clicked prediction.