19 research outputs found
Non-monotone Submodular Maximization with Nearly Optimal Adaptivity and Query Complexity
Submodular maximization is a general optimization problem with a wide range
of applications in machine learning (e.g., active learning, clustering, and
feature selection). In large-scale optimization, the parallel running time of
an algorithm is governed by its adaptivity, which measures the number of
sequential rounds needed if the algorithm can execute polynomially-many
independent oracle queries in parallel. While low adaptivity is ideal, it is
not sufficient for an algorithm to be efficient in practice---there are many
applications of distributed submodular optimization where the number of
function evaluations becomes prohibitively expensive. Motivated by these
applications, we study the adaptivity and query complexity of submodular
maximization. In this paper, we give the first constant-factor approximation
algorithm for maximizing a non-monotone submodular function subject to a
cardinality constraint that runs in adaptive rounds and makes
oracle queries in expectation. In our empirical study, we use
three real-world applications to compare our algorithm with several benchmarks
for non-monotone submodular maximization. The results demonstrate that our
algorithm finds competitive solutions using significantly fewer rounds and
queries.Comment: 12 pages, 8 figure
Streaming Algorithms for Submodular Function Maximization
We consider the problem of maximizing a nonnegative submodular set function
subject to a -matchoid
constraint in the single-pass streaming setting. Previous work in this context
has considered streaming algorithms for modular functions and monotone
submodular functions. The main result is for submodular functions that are {\em
non-monotone}. We describe deterministic and randomized algorithms that obtain
a -approximation using -space, where is
an upper bound on the cardinality of the desired set. The model assumes value
oracle access to and membership oracles for the matroids defining the
-matchoid constraint.Comment: 29 pages, 7 figures, extended abstract to appear in ICALP 201
TimeMachine: Timeline Generation for Knowledge-Base Entities
We present a method called TIMEMACHINE to generate a timeline of events and
relations for entities in a knowledge base. For example for an actor, such a
timeline should show the most important professional and personal milestones
and relationships such as works, awards, collaborations, and family
relationships. We develop three orthogonal timeline quality criteria that an
ideal timeline should satisfy: (1) it shows events that are relevant to the
entity; (2) it shows events that are temporally diverse, so they distribute
along the time axis, avoiding visual crowding and allowing for easy user
interaction, such as zooming in and out; and (3) it shows events that are
content diverse, so they contain many different types of events (e.g., for an
actor, it should show movies and marriages and awards, not just movies). We
present an algorithm to generate such timelines for a given time period and
screen size, based on submodular optimization and web-co-occurrence statistics
with provable performance guarantees. A series of user studies using Mechanical
Turk shows that all three quality criteria are crucial to produce quality
timelines and that our algorithm significantly outperforms various baseline and
state-of-the-art methods.Comment: To appear at ACM SIGKDD KDD'15. 12pp, 7 fig. With appendix. Demo and
other info available at http://cs.stanford.edu/~althoff/timemachine
Adversarially Robust Submodular Maximization under Knapsack Constraints
We propose the first adversarially robust algorithm for monotone submodular
maximization under single and multiple knapsack constraints with scalable
implementations in distributed and streaming settings. For a single knapsack
constraint, our algorithm outputs a robust summary of almost optimal (up to
polylogarithmic factors) size, from which a constant-factor approximation to
the optimal solution can be constructed. For multiple knapsack constraints, our
approximation is within a constant-factor of the best known non-robust
solution.
We evaluate the performance of our algorithms by comparison to natural
robustifications of existing non-robust algorithms under two objectives: 1)
dominating set for large social network graphs from Facebook and Twitter
collected by the Stanford Network Analysis Project (SNAP), 2) movie
recommendations on a dataset from MovieLens. Experimental results show that our
algorithms give the best objective for a majority of the inputs and show strong
performance even compared to offline algorithms that are given the set of
removals in advance.Comment: To appear in KDD 201