26,902 research outputs found
A Bandit Approach to Maximum Inner Product Search
There has been substantial research on sub-linear time approximate algorithms
for Maximum Inner Product Search (MIPS). To achieve fast query time,
state-of-the-art techniques require significant preprocessing, which can be a
burden when the number of subsequent queries is not sufficiently large to
amortize the cost. Furthermore, existing methods do not have the ability to
directly control the suboptimality of their approximate results with
theoretical guarantees. In this paper, we propose the first approximate
algorithm for MIPS that does not require any preprocessing, and allows users to
control and bound the suboptimality of the results. We cast MIPS as a Best Arm
Identification problem, and introduce a new bandit setting that can fully
exploit the special structure of MIPS. Our approach outperforms
state-of-the-art methods on both synthetic and real-world datasets.Comment: AAAI 201
Let's Make Block Coordinate Descent Go Fast: Faster Greedy Rules, Message-Passing, Active-Set Complexity, and Superlinear Convergence
Block coordinate descent (BCD) methods are widely-used for large-scale
numerical optimization because of their cheap iteration costs, low memory
requirements, amenability to parallelization, and ability to exploit problem
structure. Three main algorithmic choices influence the performance of BCD
methods: the block partitioning strategy, the block selection rule, and the
block update rule. In this paper we explore all three of these building blocks
and propose variations for each that can lead to significantly faster BCD
methods. We (i) propose new greedy block-selection strategies that guarantee
more progress per iteration than the Gauss-Southwell rule; (ii) explore
practical issues like how to implement the new rules when using "variable"
blocks; (iii) explore the use of message-passing to compute matrix or Newton
updates efficiently on huge blocks for problems with a sparse dependency
between variables; and (iv) consider optimal active manifold identification,
which leads to bounds on the "active set complexity" of BCD methods and leads
to superlinear convergence for certain problems with sparse solutions (and in
some cases finite termination at an optimal solution). We support all of our
findings with numerical results for the classic machine learning problems of
least squares, logistic regression, multi-class logistic regression, label
propagation, and L1-regularization
Information Structure Design in Team Decision Problems
We consider a problem of information structure design in team decision
problems and team games. We propose simple, scalable greedy algorithms for
adding a set of extra information links to optimize team performance and
resilience to non-cooperative and adversarial agents. We show via a simple
counterexample that the set function mapping additional information links to
team performance is in general not supermodular. Although this implies that the
greedy algorithm is not accompanied by worst-case performance guarantees, we
illustrate through numerical experiments that it can produce effective and
often optimal or near optimal information structure modifications
Theories for influencer identification in complex networks
In social and biological systems, the structural heterogeneity of interaction
networks gives rise to the emergence of a small set of influential nodes, or
influencers, in a series of dynamical processes. Although much smaller than the
entire network, these influencers were observed to be able to shape the
collective dynamics of large populations in different contexts. As such, the
successful identification of influencers should have profound implications in
various real-world spreading dynamics such as viral marketing, epidemic
outbreaks and cascading failure. In this chapter, we first summarize the
centrality-based approach in finding single influencers in complex networks,
and then discuss the more complicated problem of locating multiple influencers
from a collective point of view. Progress rooted in collective influence
theory, belief-propagation and computer science will be presented. Finally, we
present some applications of influencer identification in diverse real-world
systems, including online social platforms, scientific publication, brain
networks and socioeconomic systems.Comment: 24 pages, 6 figure
On combinatorial optimisation in analysis of protein-protein interaction and protein folding networks
Abstract: Protein-protein interaction networks and protein folding networks represent prominent research topics at the intersection of bioinformatics and network science. In this paper, we present a study of these networks from combinatorial optimisation point of view. Using a combination of classical heuristics and stochastic optimisation techniques, we were able to identify several interesting combinatorial properties of biological networks of the COSIN project. We obtained optimal or near-optimal solutions to maximum clique and chromatic number problems for these networks. We also explore patterns of both non-overlapping and overlapping cliques in these networks. Optimal or near-optimal solutions to partitioning of these networks into non-overlapping cliques and to maximum independent set problem were discovered. Maximal cliques are explored by enumerative techniques. Domination in these networks is briefly studied, too. Applications and extensions of our findings are discussed
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