Jill-Jênn Vie

Researcher at Inria

% Using Ratings & Posters\newline for Anime & Manga Recommendations % Jill-Jênn Vie % RIKEN Center for Advanced Intelligence Project (Tokyo)\newline Mangaki (Paris) — header-includes: - \usepackage{tikz} - \usepackage{array} - \usepackage{icomma} - \usepackage{multicol,booktabs} - \def\R{\mathcal{R}} handout: true —

Jill-Jênn Vie

RIKEN Center for Advanced Intelligence Project

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Recommendation System

Problem

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Every supervised machine learning algorithm

fit($X$, $y$)

\centering \begin{tabular}{ccc} \toprule \multicolumn{2}{c}{$X$} & $y$\ \cmidrule{1-2} \texttt{user_id} & \texttt{work_id} & \texttt{rating}\ \midrule 24 & 823 & like
12 & 823 & dislike
12 & 25 & favorite
\ldots & \ldots & \ldots\ \bottomrule \end{tabular}

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$\hat{y}$ = predict($X$)

\centering \begin{tabular}{ccc} \toprule \multicolumn{2}{c}{$X$} & $\hat{y}$\ \cmidrule{1-2} \texttt{user_id} & \texttt{work_id} & \texttt{rating}\ \midrule 24 & 25 & \only<2>{?}\only<3>{\alert{disliked}}
12 & 42 & \only<2>{?}\only<3>{\alert{liked}}\ \bottomrule \end{tabular}

Evaluation: Root Mean Squared Error (RMSE)

If I predict $\hat{y_i}$ for each user-work pair to test among $n$,
while truth is $y^*_i$:

\[RMSE(\hat{y}, y^*) = \sqrt{\frac1n \sum_i (\hat{y}_i - y^*_i)^2}.\]

Dataset: Mangaki

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Recommendation algorithms

Content-based

(features for movies: directors, genre, etc.)

Collaborative filtering

(solely based on ratings)

Hybrid recommender systems

(combine those two)

KNN $\rightarrow$ measure similarity between users (or items)

$K$-nearest neighbors

Hint

If $R’$ the $N \times M$ matrix of rows $\frac{\R_u}{   \R_u   }$, we can get the $N \times N$ score matrix by computing $R’ R’^T$.

Matrix factorization $\rightarrow$ reduce dimension to generalize

\vspace{-7mm}

\(R = \left(\begin{array}{c} \R_1\\ \R_2\\ \vdots\\ \R_n \end{array}\right) = \raisebox{-1cm}{\begin{tikzpicture} \draw (0,0) rectangle (2.5,2); \end{tikzpicture}} = \raisebox{-1cm}{\begin{tikzpicture} \draw (0,0) rectangle ++(1,2); \draw node at (0.5,1) {$C$}; \draw (1.1,1) rectangle ++(2.5,1); \draw node at (2.35,1.5) {$P$}; \end{tikzpicture}}\) \(\text{$R$: 2k users $\times$ 15k works} \iff \left\{\begin{array}{l} \text{$C$: 2k users $\times$ \alert{20 profiles}}\\ \text{$P$: \alert{20 profiles} $\times$ 15k works}\\ \end{array}\right.\) $\R_\text{Bob}$ is a linear combination of profiles $P_1$, $P_2$, etc..

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Interpreting Key Profiles

\begin{tabular}{@{}lccc@{}} If $P$ & $P_1$: adventure & $P_2$: romance & $P_3$: plot twist
And $C_u$ & $0,2$ & $-0,5$ & $0,6$ \end{tabular}

$\Rightarrow$ $u$ \alert{likes a bit} adventure, \alert{hates} romance, \alert{loves} plot twists.

\vspace{2mm}

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Ex. Singular Value Decomposition (SVD)

$R = (U \cdot \Sigma)V^T$ where $U : N \times r$ et $V : M \times r$ are orthogonal and $\Sigma : r \times r$ is diagonal, with singular values in decreasing order.

Visualizing first two columns of $V_j$ in SVD

\alert{Closer} points mean similar taste

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Find your taste by plotting first two columns of $U_i$

You will \alert{like} movies that are \alert{in your direction}

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Variants of Matrix Factorization for Recommendation

$R$ ratings, $C$ coefficients, $P$ profiles ($F$ features).

$R = CP = CF^T \Rightarrow r_{ij} \simeq \hat{r}_{ij} \triangleq C_i \cdot F_j$.

Objective functions (reconstruction error) to minimize

SVD : $\sum_{i, j}~(r_{ij} - C_i \cdot F_j)^2$ (deterministic)

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ALS : $\sum_{i, j \textnormal{\alert{ known}}}~(r_{ij} - C_i \cdot F_j)^2$

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\alert<6>{ALS-WR} : $\sum_{i, j \textnormal{\alert{ known}}}~(r_{ij} - C_i \cdot F_j)^2 + \lambda (\sum_i \alert<6>{N_i} ||C_i||^2 + \sum_j \alert<6>{M_j} ||F_j||^2)$
where $N_i$ ($M_j$): how many times user $i$ rated (item $j$ was rated)

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WALS by Tensorflow™ : \(\sum_{i, j} w_{ij} \cdot (r_{ij} - C_i \cdot F_j)^2 + \lambda (\sum_i ||C_i||^2 + \sum_j ||F_j||^2)\)
where $w_{ij}$: how much can you trust rating $r_{ij}$.

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Who do you think wins?

ALS for feature extraction

$R = CP$

Issue: Item Cold-Start

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But we have posters!

Illustration2Vec (Saito and Matsui, 2015)

\centering

{width=40%}\ {width=40%}\

LASSO for explanation of user preferences

$T$ matrix of 15000 works $\times$ 502 tags ($t_{jk}$: tag $k$ appears in item $j$)

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Interpretation and explanation

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Least Absolute Shrinkage and Selection Operator (LASSO)

\[\frac1{2 N_i} {\lVert \R_i - P_i T^T \rVert}_2^2 + \alpha \alert{ {\lVert P_i \rVert}_1}.\]

\noindent where $N_i$ is the number of items rated by user $i$.

Blending

We would like to do:

\[\hat{r}_{ij}^{BALSE} = \begin{cases} \hat{r}_{ij}^{ALS} & \text{if item $j$ was rated at least $\gamma$ times}\\ \hat{r}_{ij}^{LASSO} & \text{otherwise} \end{cases}\]

But we can’t. Why? \pause \alert{Not differentiable!}

\[\hat{r}_{ij}^{BALSE} = \alert{\sigma(\beta(R_j - \gamma))} \hat{r}_{ij}^{ALS} + \left(1 - \alert{\sigma(\beta(R_j - \gamma))}\right) \hat{r}_{ij}^{LASSO}\]

\noindent where $R_j$ denotes how many times item $j$ was rated
$\beta$ and $\gamma$ are learned by stochastic gradient descent.

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\centering

We call this gate the \alert{Steins;Gate}.

Blended Alternate Least Squares with Explanation

\centering

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We call this model \alert{BALSE}.

Results

\centering

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Thank you!

\centering {width=50%}\

\raggedright

Read the article

\small Using Posters to Recommend Anime and Mangas in a Cold-Start Scenario

\normalsize \alert{github.com/mangaki/balse} (PDF on arXiv, front page of HNews)

Compete to Mangaki Data Challenge: \alert{research.mangaki.fr}

Try it: \alert{https://mangaki.fr} \newline Twitter: \alert{@MangakiFR}