1,127 research outputs found
Online Maximum k-Coverage
We study an online model for the maximum k-vertex-coverage problem, where given a graph G = (V,E) and an integer k, we ask for a subset A ⊆ V, such that |A | = k and the number of edges covered by A is maximized. In our model, at each step i, a new vertex vi is revealed, and we have to decide whether we will keep it or discard it. At any time of the process, only k vertices can be kept in memory; if at some point the current solution already contains k vertices, any inclusion of any new vertex in the solution must entail the irremediable deletion of one vertex of the current solution (a vertex not kept when revealed is irremediably deleted). We propose algorithms for several natural classes of graphs (mainly regular and bipartite), improving on an easy 1/2-competitive ratio. We next settle a set-version of the problem, called maximum k-(set)-coverage problem. For this problem we present an algorithm that improves upon former results for the same model for small and moderate values of k
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
Improving Gaussian mixture latent variable model convergence with Optimal Transport
Generative models with both discrete and continuous latent variables are highly motivated by the structure of many real-world data sets. They present, however, subtleties in training often manifesting in the discrete latent variable not being leveraged. In this paper, we show why such models struggle to train using traditional log-likelihood maximization, and that they are amenable to training using the Optimal Transport framework of Wasserstein Autoencoders. We find our discrete latent variable to be fully leveraged by the model when trained, without any modifications to the objective function or significant fine tuning. Our model generates comparable samples to other approaches while using relatively simple neural networks, since the discrete latent variable carries much of the descriptive burden. Furthermore, the discrete latent provides significant control over generation
Learning Disentangled Representations with the Wasserstein Autoencoder
Disentangled representation learning has undoubtedly benefited from objective function surgery. However, a delicate balancing act of tuning is still required in order to trade off reconstruction fidelity versus disentanglement. Building on previous successes of penalizing the total correlation in the latent variables, we propose TCWAE (Total Correlation Wasserstein Autoencoder). Working in the WAE paradigm naturally enables the separation of the total-correlation term, thus providing disentanglement control over the learned representation, while offering more flexibility in the choice of reconstruction cost. We propose two variants using different KL estimators and analyse in turn the impact of having different ground cost functions and latent regularization terms. Extensive quantitative comparisons on data sets with known generative factors shows that our methods present competitive results relative to state-of-the-art techniques. We further study the trade off between disentanglement and reconstruction on more-difficult data sets with unknown generative factors, where the flexibility of the WAE paradigm leads to improved reconstructions
Maximizing Welfare in Social Networks under a Utility Driven Influence Diffusion Model
Motivated by applications such as viral marketing, the problem of influence
maximization (IM) has been extensively studied in the literature. The goal is
to select a small number of users to adopt an item such that it results in a
large cascade of adoptions by others. Existing works have three key
limitations. (1) They do not account for economic considerations of a user in
buying/adopting items. (2) Most studies on multiple items focus on competition,
with complementary items receiving limited attention. (3) For the network
owner, maximizing social welfare is important to ensure customer loyalty, which
is not addressed in prior work in the IM literature. In this paper, we address
all three limitations and propose a novel model called UIC that combines
utility-driven item adoption with influence propagation over networks. Focusing
on the mutually complementary setting, we formulate the problem of social
welfare maximization in this novel setting. We show that while the objective
function is neither submodular nor supermodular, surprisingly a simple greedy
allocation algorithm achieves a factor of of the optimum
expected social welfare. We develop \textsf{bundleGRD}, a scalable version of
this approximation algorithm, and demonstrate, with comprehensive experiments
on real and synthetic datasets, that it significantly outperforms all
baselines.Comment: 33 page
Replica Placement on Bounded Treewidth Graphs
We consider the replica placement problem: given a graph with clients and
nodes, place replicas on a minimum set of nodes to serve all the clients; each
client is associated with a request and maximum distance that it can travel to
get served and there is a maximum limit (capacity) on the amount of request a
replica can serve. The problem falls under the general framework of capacitated
set covering. It admits an O(\log n)-approximation and it is NP-hard to
approximate within a factor of . We study the problem in terms of
the treewidth of the graph and present an O(t)-approximation algorithm.Comment: An abridged version of this paper is to appear in the proceedings of
WADS'1
A Characterization of Visibility Graphs for Pseudo-Polygons
In this paper, we give a characterization of the visibility graphs of
pseudo-polygons. We first identify some key combinatorial properties of
pseudo-polygons, and we then give a set of five necessary conditions based off
our identified properties. We then prove that these necessary conditions are
also sufficient via a reduction to a characterization of vertex-edge visibility
graphs given by O'Rourke and Streinu
Pricing Multi-Unit Markets
We study the power and limitations of posted prices in multi-unit markets,
where agents arrive sequentially in an arbitrary order. We prove upper and
lower bounds on the largest fraction of the optimal social welfare that can be
guaranteed with posted prices, under a range of assumptions about the
designer's information and agents' valuations. Our results provide insights
about the relative power of uniform and non-uniform prices, the relative
difficulty of different valuation classes, and the implications of different
informational assumptions. Among other results, we prove constant-factor
guarantees for agents with (symmetric) subadditive valuations, even in an
incomplete-information setting and with uniform prices
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
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