Movie Recommendation with Bayesian

In this article, a movie recommender system is going to be designed under Bayesian framework. This problem appeared as a project in the course MITx: 6.008.1x Computational Probability and Inference, where Bayesian inference is used to determine which movie to watch next.

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The below table shows the input for the recommender system, we have 470 movies and each movie is rated by 1000 different users, the user ratings for the first 5 movies are shown below.

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The following shows the MAP estimates for the movie ratings for the first 5 movies.

MAP_Ratings Movies
0 2 Toy Story (1995)
1 5 Jumanji (1995)
2 6 Grumpier Old Men (1995)
3 6 Father of the Bride Part II (1995)
4 8 Heat (1995)
Movies with the highest MAP ratings
12 Monkeys (Twelve Monkeys) (1995)
Babe (1995)
Seven (a.k.a. Se7en) (1995)
From Dusk Till Dawn (1996)
Braveheart (1995)
Apollo 13 (1995)
Batman Forever (1995)
Crimson Tide (1995)
Die Hard: With a Vengeance (1995)
Net, The (1995)
Don Juan DeMarco (1995)
Dumb & Dumber (1994)
Hoop Dreams (1994)
Star Wars: Episode IV - A New Hope (a.k.a. Star Wars) (1977)
Like Water for Chocolate (Como agua para chocolate) (1992)
Legends of the Fall (1994)
Outbreak (1995)
Stargate (1994)
Santa Clause, The (1994)
Star Trek: Generations (1994)
Forrest Gump (1994)
Lion King, The (1994)
Naked Gun 33 1/3: The Final Insult (1994)
Speed (1994)
Addams Family Values (1993)
Beverly Hills Cop III (1994)
Fugitive, The (1993)
Hot Shots! Part Deux (1993)
Jurassic Park (1993)
Much Ado About Nothing (1993)
Mrs. Doubtfire (1993)
Robin Hood: Men in Tights (1993)
Schindler's List (1993)
Sleepless in Seattle (1993)
Blade Runner (1982)
Tombstone (1993)
Home Alone (1990)
Ghost (1990)
Aladdin (1992)
Terminator 2: Judgment Day (1991)
Dances with Wolves (1990)
Batman (1989)
Snow White and the Seven Dwarfs (1937)
Beauty and the Beast (1991)
Fargo (1996)
Wallace & Gromit: A Close Shave (1995)
Singin' in the Rain (1952)
Rear Window (1954)
North by Northwest (1959)
Some Like It Hot (1959)
Maltese Falcon, The (1941)
Wizard of Oz, The (1939)
Gone with the Wind (1939)
Citizen Kane (1941)
2001: A Space Odyssey (1968)
Mary Poppins (1964)
English Patient, The (1996)
One Flew Over the Cuckoo's Nest (1975)
Star Wars: Episode V - The Empire Strikes Back (1980)
Princess Bride, The (1987)
Brazil (1985)
Aliens (1986)
Army of Darkness (1993)
Psycho (1960)
Amadeus (1984)
Annie Hall (1977)
Boat, The (Das Boot) (1981)
Fantasia (1940)
Butch Cassidy and the Sundance Kid (1969)
Alien³ (1992)
Star Trek IV: The Voyage Home (1986)
Jaws (1975)
Contact (1997)
Hunt for Red October, The (1990)
Game, The (1997)
Gattaca (1997)
Starship Troopers (1997)
As Good As It Gets (1997)
Blade (1998)
Enemy of the State (1998)
Rushmore (1998)
Shakespeare in Love (1998)
You've Got Mail (1998)
Office Space (1999)
Matrix, The (1999)
Notting Hill (1999)
Run Lola Run (Lola rennt) (1998)
Ghostbusters (a.k.a. Ghost Busters) (1984)
Sixth Sense, The (1999)
Airplane! (1980)
American Beauty (1999)
Gladiator (2000)
Unbreakable (2000)
Crouching Tiger, Hidden Dragon (Wu hu zang long) (2000)
Memento (2000)
Moulin Rouge (2001)
Donnie Darko (2001)
Amelie (Fabuleux destin d'Amélie Poulain, Le) (2001)
Catch Me If You Can (2002)
Pirates of the Caribbean: The Curse of the Black Pearl (2003
Eternal Sunshine of the Spotless Mind (2004)

 Average Posterior Entropy of the Movie Ratings = 0.0366234427451

The following figures show how the posterior entropy of the movie-ratings changes as we have more and more data available.

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