Hi, everyone I am Yitong Meng, we are researchers from
the Chinese University of Hong Kong and JD.com. Today we are going to talk about our
paper Wasserstein collaborative filtering for cold-start item recommendation
our motivation is a very simple problem and very important.
We talked about how to recommend new items for existing users.
This problem is important because, for example, on the news website, people are usually
interested in the latest news which have no interaction data at all.
For e-commerce websites such as Amazon, they recommend new products to users to make more profits.
This is our problem definition.
Given the users preference distribution p_u and the distance among the items,
we are going to infer users preference distribution on cold-start items.
The user preference distribution (on warm items) can be estimated by normalizing a user's ratings on his rated items,
and distance among items can be derived from side information
such as tags and texts on items.
our contributions are threefold. We are the first to apply the Wasserstein distance to this problem.
we found that Wasserstein distance is a very good fit for the cold-start problem and
we proved that our model preserves the consistency of user tastes.
we formulated a complete solution for this problem
and incorporated an entropy regularizer and collaborative filtering technique to further boost the performance.
We conducted extensive experiments to compare with the state-of-the-art.
we use the Waterston distance to model the disparity between a user's preferences
on his rated items and cold-start items. p_u is the preference distribution on the warm items.
and q_u is the preference distribution on cold-start items.
Their distance is defined as a weighted sum of the item distances.
W is the weighting matrix. D(i,j) is distance between item i and item j.
the constraint here means the marginal distribution of W
should be equal to p_u and q_u respectively.
We take least value among all the possible values. For details about how to
use this distance in recommender systems, please also refer to our another paper on ECIR.
We assume users preference is consistent on warm and cold-start items.
and thus a users preference on cold-start items can be solved by
minimizing the Wasserstein distance. this constraint means q should be a probabilistic distribution.
We derive a theorem about the Wasserstein filtering.
it basically means Wasserstein filtering
preserves the consistency of user tastes on warm and cold-start items
for the proof of this theorem, please refer to our paper.
However, Wasserstein filtering has some drawbacks. According to the definition of the Wasserstein distance,
the number of nonzero values in q_u is definitely less than p_u,
and p_u is usually very small because users usually only interact with
a small portion of the items on a recommender system.
But the number of cold-start items should be large. Therefore, most entries in q_u is zero.
The problem is that we may not even have enough nonzero entries to make up a top-K recommendation.
To solve this problem,
we need to incorporate a entropy regularizer to smooth q_u. The resulting problem is called
"entropy regularized Wasserstein filtering (EWF)". EWF can be solved in closed form, according to the work of Cuturi and Payre.
Inspired by the success of collaborative filtering, we can learn the q_u of all users jointly with the assumption
that all users' preference on cold-start items are generated from a
common latent space so we factorize the users preference on cold-start items as
a product of two low-dimensional matrices. This is very like the probabilistic matrix factorization work.
Then we formulate the Wasserstein collaborative filtering
problem as follows. We minimize the distance for all users and the
preference of a user on cold-start items is represented by a summation of latent vectors.
The constraint means that each row of U Lambda should be a
probabilistic distribution. This problem can be solved using a block coordinate descent algorithm,
proposed by Rolet et al. in 2016.
We conduct the experiments on two well known datasets. First is the MovieLens
and the second is Epinions. For the item distance D(i,j) we can derive the distance
from side information. For MovieLens, we use tag-genomes and
and for epinions, we use doc2vec on the user comments.
Here is experimental results. These are our proposed methods and former ones are existing state-of-the-arts.
We can see that or my method outperforms the state-of-the-arts on both datasets.
The entropy regularizer can improve performance of Wasserstein filtering by a large extent.
The collaborative filtering technique
can improve EWF slightly on some metrics. This is our paper.
Thank you very much!