In a modern recommender system, it is important to understand how products
relate to each other. For example, while a user is looking for mobile phones,
it might make sense to recommend other phones, but once they buy a phone, we
might instead want to recommend batteries, cases, or chargers. These two types
of recommendations are referred to as substitutes and complements: substitutes
are products that can be purchased instead of each other, while complements are
products that can be purchased in addition to each other.
Here we develop a method to infer networks of substitutable and complementary
products. We formulate this as a supervised link prediction task, where we
learn the semantics of substitutes and complements from data associated with
products. The primary source of data we use is the text of product reviews,
though our method also makes use of features such as ratings, specifications,
prices, and brands. Methodologically, we build topic models that are trained to
automatically discover topics from text that are successful at predicting and
explaining such relationships. Experimentally, we evaluate our system on the
Amazon product catalog, a large dataset consisting of 9 million products, 237
million links, and 144 million reviews.

提出了一种基于主题模型的方法，通过产品评论等多维数据，预测和发现替代和补充产品之间的关系，应用于亚马逊的大规模商品目录数据集。

推断可替代和互补产品的网络

Inferring Networks of Substitutable and Complementary Products

We consider a single buyer with a combinatorial preference that would like to
purchase related products and services from different vendors, where each
vendor supplies exactly one product. We study the general case where subsets of
products can be substitutes as well as complementary and analyze the game that
is induced on the vendors, where a vendor's strategy is the price that he asks
for his product. This model generalizes both Bertrand competition (where
vendors are perfect substitutes) and Nash bargaining (where they are perfect
complements), and captures a wide variety of scenarios that can appear in
complex crowd sourcing or in automatic pricing of related products.
We study the equilibria of such games and show that a pure efficient
equilibrium always exists. In the case of submodular buyer preferences we fully
characterize the set of pure Nash equilibria, essentially showing uniqueness.
For the even more restricted "substitutes" buyer preferences we also prove
uniqueness over {\em mixed} equilibria. Finally we begin the exploration of
natural generalizations of our setting such as when services have costs, when
there are multiple buyers or uncertainty about the the buyer's valuation, and
when a single vendor supplies multiple products.

考虑了一个单一的买家想要从不同供应商购买相关产品和服务的组合偏好问题，其中每个供应商只提供一个产品，模型广泛适用于复杂的众包或自动定价等情况，研究了供应商游戏和纳什均衡相关问题。

网上组合市场的价格竞争

Price Competition in Online Combinatorial Markets

Complements between goods - where one good takes on added value in the
presence of another - have been a thorn in the side of algorithmic mechanism
designers. On the one hand, complements are common in the standard motivating
applications for combinatorial auctions, like spectrum license auctions. On the
other, welfare maximization in the presence of complements is notoriously
difficult, and this intractability has stymied theoretical progress in the
area. For example, there are no known positive results for combinatorial
auctions in which bidder valuations are multi-parameter and
non-complement-free, other than the relatively weak results known for general
valuations.
To make inroads on the problem of combinatorial auction design in the
presence of complements, we propose a model for valuations with complements
that is parameterized by the "size" of the complements. A valuation in our
model is represented succinctly by a weighted hypergraph, where the size of the
hyper-edges corresponds to degree of complementarity. Our model permits a
variety of computationally efficient queries, and non-trivial
welfare-maximization algorithms and mechanisms.
We design the following polynomial-time approximation algorithms and truthful
mechanisms for welfare maximization with bidders with hypergraph valuations.
1- For bidders whose valuations correspond to subgraphs of a known graph that
is planar (or more generally, excludes a fixed minor), we give a truthful and
(1+epsilon)-approximate mechanism.
2- We give a polynomial-time, r-approximation algorithm for welfare
maximization with hypergraph-r valuations. Our algorithm randomly rounds a
compact linear programming relaxation of the problem.
3- We design a different approximation algorithm and use it to give a
polynomial-time, truthful-in-expectation mechanism that has an approximation
factor of O(log^r m).

研究中提出了一种评估具有互补性的商品的模型，该模型的参数化方法取决于互补性的 “大小”，并为各种计算机查询、效用最大化算法和机制提供了一种选择。