718 research outputs found
Suggestive Annotation: A Deep Active Learning Framework for Biomedical Image Segmentation
Image segmentation is a fundamental problem in biomedical image analysis.
Recent advances in deep learning have achieved promising results on many
biomedical image segmentation benchmarks. However, due to large variations in
biomedical images (different modalities, image settings, objects, noise, etc),
to utilize deep learning on a new application, it usually needs a new set of
training data. This can incur a great deal of annotation effort and cost,
because only biomedical experts can annotate effectively, and often there are
too many instances in images (e.g., cells) to annotate. In this paper, we aim
to address the following question: With limited effort (e.g., time) for
annotation, what instances should be annotated in order to attain the best
performance? We present a deep active learning framework that combines fully
convolutional network (FCN) and active learning to significantly reduce
annotation effort by making judicious suggestions on the most effective
annotation areas. We utilize uncertainty and similarity information provided by
FCN and formulate a generalized version of the maximum set cover problem to
determine the most representative and uncertain areas for annotation. Extensive
experiments using the 2015 MICCAI Gland Challenge dataset and a lymph node
ultrasound image segmentation dataset show that, using annotation suggestions
by our method, state-of-the-art segmentation performance can be achieved by
using only 50% of training data.Comment: Accepted at MICCAI 201
Finding Connected Dense -Subgraphs
Given a connected graph on vertices and a positive integer ,
a subgraph of on vertices is called a -subgraph in . We design
combinatorial approximation algorithms for finding a connected -subgraph in
such that its density is at least a factor
of the density of the densest -subgraph
in (which is not necessarily connected). These particularly provide the
first non-trivial approximations for the densest connected -subgraph problem
on general graphs
Budget-restricted utility games with ordered strategic decisions
We introduce the concept of budget games. Players choose a set of tasks and
each task has a certain demand on every resource in the game. Each resource has
a budget. If the budget is not enough to satisfy the sum of all demands, it has
to be shared between the tasks. We study strategic budget games, where the
budget is shared proportionally. We also consider a variant in which the order
of the strategic decisions influences the distribution of the budgets. The
complexity of the optimal solution as well as existence, complexity and quality
of equilibria are analyzed. Finally, we show that the time an ordered budget
game needs to convergence towards an equilibrium may be exponential
Computing Stable Coalitions: Approximation Algorithms for Reward Sharing
Consider a setting where selfish agents are to be assigned to coalitions or
projects from a fixed set P. Each project k is characterized by a valuation
function; v_k(S) is the value generated by a set S of agents working on project
k. We study the following classic problem in this setting: "how should the
agents divide the value that they collectively create?". One traditional
approach in cooperative game theory is to study core stability with the
implicit assumption that there are infinite copies of one project, and agents
can partition themselves into any number of coalitions. In contrast, we
consider a model with a finite number of non-identical projects; this makes
computing both high-welfare solutions and core payments highly non-trivial.
The main contribution of this paper is a black-box mechanism that reduces the
problem of computing a near-optimal core stable solution to the purely
algorithmic problem of welfare maximization; we apply this to compute an
approximately core stable solution that extracts one-fourth of the optimal
social welfare for the class of subadditive valuations. We also show much
stronger results for several popular sub-classes: anonymous, fractionally
subadditive, and submodular valuations, as well as provide new approximation
algorithms for welfare maximization with anonymous functions. Finally, we
establish a connection between our setting and the well-studied simultaneous
auctions with item bidding; we adapt our results to compute approximate pure
Nash equilibria for these auctions.Comment: Under Revie
Limitations to Frechet's Metric Embedding Method
Frechet's classical isometric embedding argument has evolved to become a
major tool in the study of metric spaces. An important example of a Frechet
embedding is Bourgain's embedding. The authors have recently shown that for
every e>0 any n-point metric space contains a subset of size at least n^(1-e)
which embeds into l_2 with distortion O(\log(2/e) /e). The embedding we used is
non-Frechet, and the purpose of this note is to show that this is not
coincidental. Specifically, for every e>0, we construct arbitrarily large
n-point metric spaces, such that the distortion of any Frechet embedding into
l_p on subsets of size at least n^{1/2 + e} is \Omega((\log n)^{1/p}).Comment: 10 pages, 1 figur
Approximating k-Forest with Resource Augmentation: A Primal-Dual Approach
In this paper, we study the -forest problem in the model of resource
augmentation. In the -forest problem, given an edge-weighted graph ,
a parameter , and a set of demand pairs , the
objective is to construct a minimum-cost subgraph that connects at least
demands. The problem is hard to approximate---the best-known approximation
ratio is . Furthermore, -forest is as hard to
approximate as the notoriously-hard densest -subgraph problem.
While the -forest problem is hard to approximate in the worst-case, we
show that with the use of resource augmentation, we can efficiently approximate
it up to a constant factor.
First, we restate the problem in terms of the number of demands that are {\em
not} connected. In particular, the objective of the -forest problem can be
viewed as to remove at most demands and find a minimum-cost subgraph that
connects the remaining demands. We use this perspective of the problem to
explain the performance of our algorithm (in terms of the augmentation) in a
more intuitive way.
Specifically, we present a polynomial-time algorithm for the -forest
problem that, for every , removes at most demands and has
cost no more than times the cost of an optimal algorithm
that removes at most demands
Line-distortion, Bandwidth and Path-length of a graph
We investigate the minimum line-distortion and the minimum bandwidth problems
on unweighted graphs and their relations with the minimum length of a
Robertson-Seymour's path-decomposition. The length of a path-decomposition of a
graph is the largest diameter of a bag in the decomposition. The path-length of
a graph is the minimum length over all its path-decompositions. In particular,
we show:
- if a graph can be embedded into the line with distortion , then
admits a Robertson-Seymour's path-decomposition with bags of diameter at most
in ;
- for every class of graphs with path-length bounded by a constant, there
exist an efficient constant-factor approximation algorithm for the minimum
line-distortion problem and an efficient constant-factor approximation
algorithm for the minimum bandwidth problem;
- there is an efficient 2-approximation algorithm for computing the
path-length of an arbitrary graph;
- AT-free graphs and some intersection families of graphs have path-length at
most 2;
- for AT-free graphs, there exist a linear time 8-approximation algorithm for
the minimum line-distortion problem and a linear time 4-approximation algorithm
for the minimum bandwidth problem
Smoothed Complexity Theory
Smoothed analysis is a new way of analyzing algorithms introduced by Spielman
and Teng (J. ACM, 2004). Classical methods like worst-case or average-case
analysis have accompanying complexity classes, like P and AvgP, respectively.
While worst-case or average-case analysis give us a means to talk about the
running time of a particular algorithm, complexity classes allows us to talk
about the inherent difficulty of problems.
Smoothed analysis is a hybrid of worst-case and average-case analysis and
compensates some of their drawbacks. Despite its success for the analysis of
single algorithms and problems, there is no embedding of smoothed analysis into
computational complexity theory, which is necessary to classify problems
according to their intrinsic difficulty.
We propose a framework for smoothed complexity theory, define the relevant
classes, and prove some first hardness results (of bounded halting and tiling)
and tractability results (binary optimization problems, graph coloring,
satisfiability). Furthermore, we discuss extensions and shortcomings of our
model and relate it to semi-random models.Comment: to be presented at MFCS 201
The Discovery of a Gravitationally Lensed Quasar at z = 6.51
Strong gravitational lensing provides a powerful probe of the physical
properties of quasars and their host galaxies. A high fraction of the most
luminous high-redshift quasars was predicted to be lensed due to magnification
bias. However, no multiple imaged quasar was found at z>5 in previous surveys.
We report the discovery of J043947.08+163415.7, a strongly lensed quasar at
z=6.51, the first such object detected at the epoch of reionization, and the
brightest quasar yet known at z>5. High-resolution HST imaging reveals a
multiple imaged system with a maximum image separation theta ~ 0.2", best
explained by a model of three quasar images lensed by a low luminosity galaxy
at z~0.7, with a magnification factor of ~50. The existence of this source
suggests that a significant population of strongly lensed, high redshift
quasars could have been missed by previous surveys, as standard color selection
techniques would fail when the quasar color is contaminated by the lensing
galaxy.Comment: 8 pages, 4 figures, submitted to ApJ
Fast Distributed Approximation for Max-Cut
Finding a maximum cut is a fundamental task in many computational settings.
Surprisingly, it has been insufficiently studied in the classic distributed
settings, where vertices communicate by synchronously sending messages to their
neighbors according to the underlying graph, known as the or
models. We amend this by obtaining almost optimal
algorithms for Max-Cut on a wide class of graphs in these models. In
particular, for any , we develop randomized approximation
algorithms achieving a ratio of to the optimum for Max-Cut on
bipartite graphs in the model, and on general graphs in the
model.
We further present efficient deterministic algorithms, including a
-approximation for Max-Dicut in our models, thus improving the best known
(randomized) ratio of . Our algorithms make non-trivial use of the greedy
approach of Buchbinder et al. (SIAM Journal on Computing, 2015) for maximizing
an unconstrained (non-monotone) submodular function, which may be of
independent interest
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