80 research outputs found
Individualized Rank Aggregation using Nuclear Norm Regularization
In recent years rank aggregation has received significant attention from the
machine learning community. The goal of such a problem is to combine the
(partially revealed) preferences over objects of a large population into a
single, relatively consistent ordering of those objects. However, in many
cases, we might not want a single ranking and instead opt for individual
rankings. We study a version of the problem known as collaborative ranking. In
this problem we assume that individual users provide us with pairwise
preferences (for example purchasing one item over another). From those
preferences we wish to obtain rankings on items that the users have not had an
opportunity to explore. The results here have a very interesting connection to
the standard matrix completion problem. We provide a theoretical justification
for a nuclear norm regularized optimization procedure, and provide
high-dimensional scaling results that show how the error in estimating user
preferences behaves as the number of observations increase
Analysis of Crowdsourced Sampling Strategies for HodgeRank with Sparse Random Graphs
Crowdsourcing platforms are now extensively used for conducting subjective
pairwise comparison studies. In this setting, a pairwise comparison dataset is
typically gathered via random sampling, either \emph{with} or \emph{without}
replacement. In this paper, we use tools from random graph theory to analyze
these two random sampling methods for the HodgeRank estimator. Using the
Fiedler value of the graph as a measurement for estimator stability
(informativeness), we provide a new estimate of the Fiedler value for these two
random graph models. In the asymptotic limit as the number of vertices tends to
infinity, we prove the validity of the estimate. Based on our findings, for a
small number of items to be compared, we recommend a two-stage sampling
strategy where a greedy sampling method is used initially and random sampling
\emph{without} replacement is used in the second stage. When a large number of
items is to be compared, we recommend random sampling with replacement as this
is computationally inexpensive and trivially parallelizable. Experiments on
synthetic and real-world datasets support our analysis
ChoiceRank: Identifying Preferences from Node Traffic in Networks
Understanding how users navigate in a network is of high interest in many
applications. We consider a setting where only aggregate node-level traffic is
observed and tackle the task of learning edge transition probabilities. We cast
it as a preference learning problem, and we study a model where choices follow
Luce's axiom. In this case, the marginal counts of node visits are a
sufficient statistic for the transition probabilities. We show how to
make the inference problem well-posed regardless of the network's structure,
and we present ChoiceRank, an iterative algorithm that scales to networks that
contains billions of nodes and edges. We apply the model to two clickstream
datasets and show that it successfully recovers the transition probabilities
using only the network structure and marginal (node-level) traffic data.
Finally, we also consider an application to mobility networks and apply the
model to one year of rides on New York City's bicycle-sharing system.Comment: Accepted at ICML 201
Just Sort It! A Simple and Effective Approach to Active Preference Learning
We address the problem of learning a ranking by using adaptively chosen
pairwise comparisons. Our goal is to recover the ranking accurately but to
sample the comparisons sparingly. If all comparison outcomes are consistent
with the ranking, the optimal solution is to use an efficient sorting
algorithm, such as Quicksort. But how do sorting algorithms behave if some
comparison outcomes are inconsistent with the ranking? We give favorable
guarantees for Quicksort for the popular Bradley-Terry model, under natural
assumptions on the parameters. Furthermore, we empirically demonstrate that
sorting algorithms lead to a very simple and effective active learning
strategy: repeatedly sort the items. This strategy performs as well as
state-of-the-art methods (and much better than random sampling) at a minuscule
fraction of the computational cost.Comment: Accepted at ICML 201
- …