Global Baseline EstimatesProblem statement: Most recommender systems use personalized algorithms like “content management” and “item-item collaborative filtering.” Sometimes non-personalized recommenders are also useful or necessary. One of the best non-personalized recommender system algorithms is the “Global Baseline Estimate.
The job here is to use the survey data collected and write the R code that makes a movie recommendation using the Global Baseline Estimate algorithm
Step 1. Create Movie Dataframe
# Create the movie_ratings dataframe
movie_ratings <- data.frame(
Critic = c("Vivien", "Carrie", "Julie", "Drew"),
Gone_with_the_Wind = c(NA, 4, 2, 5),
Star_Wars = c(NA, 5, 5, 4),
Sound_of_Music = c(5, 4, 2, NA),
ET = c(4, 3, NA, NA),
stringsAsFactors = FALSE
)
# View the dataframe
print(movie_ratings)## Critic Gone_with_the_Wind Star_Wars Sound_of_Music ET
## 1 Vivien NA NA 5 4
## 2 Carrie 4 5 4 3
## 3 Julie 2 5 2 NA
## 4 Drew 5 4 NA NAStep 2. Convert to long format data
ratings_long <- movie_ratings %>%
pivot_longer(
cols = -Critic,
names_to = "Movie",
values_to = "Rating"
) %>%
filter(!is.na(Rating)) %>% # Remove missing ratings
rename(userId = Critic, movieId = Movie, rating = Rating)
# View the long format data
print(ratings_long)## # A tibble: 11 × 3
## userId movieId rating
## <chr> <chr> <dbl>
## 1 Vivien Sound_of_Music 5
## 2 Vivien ET 4
## 3 Carrie Gone_with_the_Wind 4
## 4 Carrie Star_Wars 5
## 5 Carrie Sound_of_Music 4
## 6 Carrie ET 3
## 7 Julie Gone_with_the_Wind 2
## 8 Julie Star_Wars 5
## 9 Julie Sound_of_Music 2
## 10 Drew Gone_with_the_Wind 5
## 11 Drew Star_Wars 4Step 3: Calculate the Global Average Rating (μ)
# Calculate the global average rating
mu <- mean(ratings_long$rating, na.rm = TRUE)
print(paste("Global average rating (μ):", round(mu, 3)))## [1] "Global average rating (μ): 3.909"Step 4: Calculate User Biases (bᵤ)
user_biases <- ratings_long %>%
group_by(userId) %>%
summarize(b_u = mean(rating - mu, na.rm = TRUE))
# View user biases
print(user_biases)## # A tibble: 4 × 2
## userId b_u
## <chr> <dbl>
## 1 Carrie 0.0909
## 2 Drew 0.591
## 3 Julie -0.909
## 4 Vivien 0.591Step 5: Calculate Movie Biases (bᵢ)
movie_biases <- ratings_long %>%
group_by(movieId) %>%
summarize(b_i = mean(rating - mu, na.rm = TRUE))
# View movie biases
print(movie_biases)## # A tibble: 4 × 2
## movieId b_i
## <chr> <dbl>
## 1 ET -0.409
## 2 Gone_with_the_Wind -0.242
## 3 Sound_of_Music -0.242
## 4 Star_Wars 0.758Step 6: Create All Possible User-Movie Combinations
all_combinations <- expand.grid(
userId = unique(ratings_long$userId),
movieId = unique(ratings_long$movieId)
)
# View all combinations
print(all_combinations)## userId movieId
## 1 Vivien Sound_of_Music
## 2 Carrie Sound_of_Music
## 3 Julie Sound_of_Music
## 4 Drew Sound_of_Music
## 5 Vivien ET
## 6 Carrie ET
## 7 Julie ET
## 8 Drew ET
## 9 Vivien Gone_with_the_Wind
## 10 Carrie Gone_with_the_Wind
## 11 Julie Gone_with_the_Wind
## 12 Drew Gone_with_the_Wind
## 13 Vivien Star_Wars
## 14 Carrie Star_Wars
## 15 Julie Star_Wars
## 16 Drew Star_WarsStep 7: Generate Predictions for All Combinations Generated predictions for all possible critic-movie combinations using the formula: r̂ᵤᵢ = μ + bᵤ + bᵢ
predictions <- all_combinations %>%
left_join(user_biases, by = "userId") %>%
left_join(movie_biases, by = "movieId") %>%
mutate(
# Handle cases where we don't have bias information
b_u = ifelse(is.na(b_u), 0, b_u),
b_i = ifelse(is.na(b_i), 0, b_i),
# Calculate predicted rating
predicted_rating = mu + b_u + b_i,
# Apply caps to ensure ratings are between 0 and 5
predicted_rating = pmax(0, pmin(5, predicted_rating)),
#round off to 2 numeric value after decimal
predicted_rating = round(predicted_rating,2)
) %>%
select(userId, movieId, predicted_rating)
# View predictions
print(predictions)## userId movieId predicted_rating
## 1 Vivien Sound_of_Music 4.26
## 2 Carrie Sound_of_Music 3.76
## 3 Julie Sound_of_Music 2.76
## 4 Drew Sound_of_Music 4.26
## 5 Vivien ET 4.09
## 6 Carrie ET 3.59
## 7 Julie ET 2.59
## 8 Drew ET 4.09
## 9 Vivien Gone_with_the_Wind 4.26
## 10 Carrie Gone_with_the_Wind 3.76
## 11 Julie Gone_with_the_Wind 2.76
## 12 Drew Gone_with_the_Wind 4.26
## 13 Vivien Star_Wars 5.00
## 14 Carrie Star_Wars 4.76
## 15 Julie Star_Wars 3.76
## 16 Drew Star_Wars 5.00Step 8: Get Recommendations for Specific Users
# Function to get top N recommendations for a user
get_recommendations <- function(user_id, n = 2) {
user_predictions <- predictions %>%
filter(userId == user_id) %>%
arrange(desc(predicted_rating)) %>%
head(n)
return(user_predictions)
}
# Get recommendations for each user
users <- unique(ratings_long$userId)
for(user in users) {
cat("\nTop recommendations for", user, ":\n")
print(get_recommendations(user))
}##
## Top recommendations for Vivien :
## userId movieId predicted_rating
## 1 Vivien Star_Wars 5.00
## 2 Vivien Sound_of_Music 4.26
##
## Top recommendations for Carrie :
## userId movieId predicted_rating
## 1 Carrie Star_Wars 4.76
## 2 Carrie Sound_of_Music 3.76
##
## Top recommendations for Julie :
## userId movieId predicted_rating
## 1 Julie Star_Wars 3.76
## 2 Julie Sound_of_Music 2.76
##
## Top recommendations for Drew :
## userId movieId predicted_rating
## 1 Drew Star_Wars 5.00
## 2 Drew Sound_of_Music 4.26Step 9: Compare Predictions with Actual Ratings
comparison <- ratings_long %>%
full_join(predictions, by = c("userId", "movieId")) %>%
rename(actual_rating = rating)
# View comparison
print(comparison)## # A tibble: 16 × 4
## userId movieId actual_rating predicted_rating
## <chr> <chr> <dbl> <dbl>
## 1 Vivien Sound_of_Music 5 4.26
## 2 Vivien ET 4 4.09
## 3 Carrie Gone_with_the_Wind 4 3.76
## 4 Carrie Star_Wars 5 4.76
## 5 Carrie Sound_of_Music 4 3.76
## 6 Carrie ET 3 3.59
## 7 Julie Gone_with_the_Wind 2 2.76
## 8 Julie Star_Wars 5 3.76
## 9 Julie Sound_of_Music 2 2.76
## 10 Drew Gone_with_the_Wind 5 4.26
## 11 Drew Star_Wars 4 5
## 12 Drew Sound_of_Music NA 4.26
## 13 Julie ET NA 2.59
## 14 Drew ET NA 4.09
## 15 Vivien Gone_with_the_Wind NA 4.26
## 16 Vivien Star_Wars NA 5Conclusion: This implementation demonstrated that even a simple non-personalized approach can provide meaningful recommendations by leveraging aggregate patterns in rating behavior. The global baseline model serves as an important benchmark in recommendation system evaluation - any more complex personalized algorithm should outperform this basic approach to be considered effective.
The assignment successfully illustrated how to transform raw rating data into actionable recommendations using fundamental statistical concepts, providing a solid foundation for understanding more sophisticated recommendation techniques.