63,782 research outputs found
Sparse Support Vector Infinite Push
In this paper, we address the problem of embedded feature selection for
ranking on top of the list problems. We pose this problem as a regularized
empirical risk minimization with -norm push loss function () and
sparsity inducing regularizers. We leverage the issues related to this
challenging optimization problem by considering an alternating direction method
of multipliers algorithm which is built upon proximal operators of the loss
function and the regularizer. Our main technical contribution is thus to
provide a numerical scheme for computing the infinite push loss function
proximal operator. Experimental results on toy, DNA microarray and BCI problems
show how our novel algorithm compares favorably to competitors for ranking on
top while using fewer variables in the scoring function.Comment: Appears in Proceedings of the 29th International Conference on
Machine Learning (ICML 2012
The P-Norm Push: A Simple Convex Ranking Algorithm that Concentrates at the Top of the List
We are interested in supervised ranking algorithms that perform especially well near the top of the
ranked list, and are only required to perform sufficiently well on the rest of the list. In this work,
we provide a general form of convex objective that gives high-scoring examples more importance.
This “push” near the top of the list can be chosen arbitrarily large or small, based on the preference
of the user. We choose ℓp-norms to provide a specific type of push; if the user sets p larger, the
objective concentrates harder on the top of the list. We derive a generalization bound based on
the p-norm objective, working around the natural asymmetry of the problem. We then derive a
boosting-style algorithm for the problem of ranking with a push at the top. The usefulness of the
algorithm is illustrated through experiments on repository data. We prove that the minimizer of the
algorithm’s objective is unique in a specific sense. Furthermore, we illustrate how our objective is
related to quality measurements for information retrieval
Bipartite Ranking: a Risk-Theoretic Perspective
We present a systematic study of the bipartite ranking problem, with the aim of explicating its connections to the class-probability estimation problem. Our study focuses on the properties of the statistical risk for bipartite ranking with general losses, which is closely related to a generalised notion of the area under the ROC
curve: we establish alternate representations of this risk, relate the Bayes-optimal risk to a class of probability divergences, and characterise the set of Bayes-optimal scorers for the risk. We further study properties of a generalised class of bipartite risks, based on the p-norm push of Rudin (2009). Our analysis is based on the rich framework of proper losses, which are the central tool in the study of class-probability estimation. We show
how this analytic tool makes transparent the generalisations of several existing results, such as the equivalence of the minimisers for four seemingly disparate risks from bipartite ranking and class-probability estimation. A novel practical implication of our analysis is the design of new families of losses for scenarios where accuracy at the head of ranked list is paramount, with comparable empirical performance to the p-norm push
A Simple and Scalable Static Analysis for Bound Analysis and Amortized Complexity Analysis
We present the first scalable bound analysis that achieves amortized
complexity analysis. In contrast to earlier work, our bound analysis is not
based on general purpose reasoners such as abstract interpreters, software
model checkers or computer algebra tools. Rather, we derive bounds directly
from abstract program models, which we obtain from programs by comparatively
simple invariant generation and symbolic execution techniques. As a result, we
obtain an analysis that is more predictable and more scalable than earlier
approaches. Our experiments demonstrate that our analysis is fast and at the
same time able to compute bounds for challenging loops in a large real-world
benchmark. Technically, our approach is based on lossy vector addition systems
(VASS). Our bound analysis first computes a lexicographic ranking function that
proves the termination of a VASS, and then derives a bound from this ranking
function. Our methodology achieves amortized analysis based on a new insight
how lexicographic ranking functions can be used for bound analysis
Fast and Accurate Random Walk with Restart on Dynamic Graphs with Guarantees
Given a time-evolving graph, how can we track similarity between nodes in a
fast and accurate way, with theoretical guarantees on the convergence and the
error? Random Walk with Restart (RWR) is a popular measure to estimate the
similarity between nodes and has been exploited in numerous applications. Many
real-world graphs are dynamic with frequent insertion/deletion of edges; thus,
tracking RWR scores on dynamic graphs in an efficient way has aroused much
interest among data mining researchers. Recently, dynamic RWR models based on
the propagation of scores across a given graph have been proposed, and have
succeeded in outperforming previous other approaches to compute RWR
dynamically. However, those models fail to guarantee exactness and convergence
time for updating RWR in a generalized form. In this paper, we propose OSP, a
fast and accurate algorithm for computing dynamic RWR with insertion/deletion
of nodes/edges in a directed/undirected graph. When the graph is updated, OSP
first calculates offset scores around the modified edges, propagates the offset
scores across the updated graph, and then merges them with the current RWR
scores to get updated RWR scores. We prove the exactness of OSP and introduce
OSP-T, a version of OSP which regulates a trade-off between accuracy and
computation time by using error tolerance {\epsilon}. Given restart probability
c, OSP-T guarantees to return RWR scores with O ({\epsilon} /c ) error in O
(log ({\epsilon}/2)/log(1-c)) iterations. Through extensive experiments, we
show that OSP tracks RWR exactly up to 4605x faster than existing static RWR
method on dynamic graphs, and OSP-T requires up to 15x less time with 730x
lower L1 norm error and 3.3x lower rank error than other state-of-the-art
dynamic RWR methods.Comment: 10 pages, 8 figure
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