User and product embeddings

User and product embeddings¶

We calculate user and product embeddings based on the training set, and evaluate the results on the unseen test set. We will evaluate the results by plotting the user and product similarity versus the review score. The dataset is created in the Obtain_dataset Notebook.

1. Calculate user and product embeddings¶

We calculate these embeddings simply by averaging all the reviews about the same product or written by the same user within the training set.

In [2]:

import pandas as pd
import numpy as np
from sklearn.model_selection import train_test_split

df = pd.read_csv('output/embedded_babbage_similarity_50k.csv', index_col=0)  # note that you will need to generate this file to run the code below
df['babbage_similarity'] = df.babbage_similarity.apply(eval).apply(np.array)
X_train, X_test, y_train, y_test = train_test_split(df, df.Score, test_size = 0.2, random_state=42)

user_embeddings = X_train.groupby('UserId').babbage_similarity.apply(np.mean)
prod_embeddings = X_train.groupby('ProductId').babbage_similarity.apply(np.mean)
len(user_embeddings), len(prod_embeddings)

import pandas as pd import numpy as np from sklearn.model_selection import train_test_split df = pd.read_csv('output/embedded_babbage_similarity_50k.csv', index_col=0) # note that you will need to generate this file to run the code below df['babbage_similarity'] = df.babbage_similarity.apply(eval).apply(np.array) X_train, X_test, y_train, y_test = train_test_split(df, df.Score, test_size = 0.2, random_state=42) user_embeddings = X_train.groupby('UserId').babbage_similarity.apply(np.mean) prod_embeddings = X_train.groupby('ProductId').babbage_similarity.apply(np.mean) len(user_embeddings), len(prod_embeddings)

Out[2]:

(24502, 19035)

We can see that most of the users and products appear within the 50k examples only once.

2. Evaluate the embeddings¶

To evaluate the recommendations, we look at the similarity of the user and product embeddings amongst the reviews in the unseen test set. We calculate the cosine distance between the user and product embeddings, which gives us a similarity score between 0 and 1. We then normalize the scores to be evenly split between 0 and 1, by calculating the percentile of the similarity score amongst all predicted scores.

In [3]:

from openai.embeddings_utils import cosine_similarity

# evaluate embeddings as recommendations on X_test
def evaluate_single_match(row):
    user_id = row.UserId
    product_id = row.ProductId
    try:
        user_embedding = user_embeddings[user_id]
        product_embedding = prod_embeddings[product_id]
        similarity = cosine_similarity(user_embedding, product_embedding)
        return similarity
    except Exception as e:
        return np.nan

X_test['cosine_similarity'] = X_test.apply(evaluate_single_match, axis=1)
X_test['percentile_cosine_similarity'] = X_test.cosine_similarity.rank(pct=True)

from openai.embeddings_utils import cosine_similarity # evaluate embeddings as recommendations on X_test def evaluate_single_match(row): user_id = row.UserId product_id = row.ProductId try: user_embedding = user_embeddings[user_id] product_embedding = prod_embeddings[product_id] similarity = cosine_similarity(user_embedding, product_embedding) return similarity except Exception as e: return np.nan X_test['cosine_similarity'] = X_test.apply(evaluate_single_match, axis=1) X_test['percentile_cosine_similarity'] = X_test.cosine_similarity.rank(pct=True)

2.1 Visualize cosine similarity by review score¶

We group the cosine similarity scores by the review score, and plot the distribution of cosine similarity scores for each review score.

In [18]:

import matplotlib.pyplot as plt
import statsmodels.api as sm


correlation = X_test[['percentile_cosine_similarity', 'Score']].corr().values[0,1]
print('Correlation between user & vector similarity percentile metric and review number of stars (score): %.2f%%' % (100*correlation))

# boxplot of cosine similarity for each score
X_test.boxplot(column='percentile_cosine_similarity', by='Score')
plt.title('')
plt.show()
plt.close()

import matplotlib.pyplot as plt import statsmodels.api as sm correlation = X_test[['percentile_cosine_similarity', 'Score']].corr().values[0,1] print('Correlation between user & vector similarity percentile metric and review number of stars (score): %.2f%%' % (100*correlation)) # boxplot of cosine similarity for each score X_test.boxplot(column='percentile_cosine_similarity', by='Score') plt.title('') plt.show() plt.close()

Correlation between user&vector similarity percentile metric and review number of stars (score): 22.11%

We can observe a weak trend, showing that the higher the similarity score between the user and the product embedding, the higher the review score. Therefore, the user and product embeddings can weakly predict the review score - even before the user receives the product!

Because this signal works in a different way than the more commonly used collaborative filtering, it can act as an additional feature to slightly improve the performance on existing problems.