25,381 research outputs found
Approximation Algorithms for Correlated Knapsacks and Non-Martingale Bandits
In the stochastic knapsack problem, we are given a knapsack of size B, and a
set of jobs whose sizes and rewards are drawn from a known probability
distribution. However, we know the actual size and reward only when the job
completes. How should we schedule jobs to maximize the expected total reward?
We know O(1)-approximations when we assume that (i) rewards and sizes are
independent random variables, and (ii) we cannot prematurely cancel jobs. What
can we say when either or both of these assumptions are changed?
The stochastic knapsack problem is of interest in its own right, but
techniques developed for it are applicable to other stochastic packing
problems. Indeed, ideas for this problem have been useful for budgeted learning
problems, where one is given several arms which evolve in a specified
stochastic fashion with each pull, and the goal is to pull the arms a total of
B times to maximize the reward obtained. Much recent work on this problem focus
on the case when the evolution of the arms follows a martingale, i.e., when the
expected reward from the future is the same as the reward at the current state.
What can we say when the rewards do not form a martingale?
In this paper, we give constant-factor approximation algorithms for the
stochastic knapsack problem with correlations and/or cancellations, and also
for budgeted learning problems where the martingale condition is not satisfied.
Indeed, we can show that previously proposed LP relaxations have large
integrality gaps. We propose new time-indexed LP relaxations, and convert the
fractional solutions into distributions over strategies, and then use the LP
values and the time ordering information from these strategies to devise a
randomized adaptive scheduling algorithm. We hope our LP formulation and
decomposition methods may provide a new way to address other correlated bandit
problems with more general contexts
SEGMENT3D: A Web-based Application for Collaborative Segmentation of 3D images used in the Shoot Apical Meristem
The quantitative analysis of 3D confocal microscopy images of the shoot
apical meristem helps understanding the growth process of some plants. Cell
segmentation in these images is crucial for computational plant analysis and
many automated methods have been proposed. However, variations in signal
intensity across the image mitigate the effectiveness of those approaches with
no easy way for user correction. We propose a web-based collaborative 3D image
segmentation application, SEGMENT3D, to leverage automatic segmentation
results. The image is divided into 3D tiles that can be either segmented
interactively from scratch or corrected from a pre-existing segmentation.
Individual segmentation results per tile are then automatically merged via
consensus analysis and then stitched to complete the segmentation for the
entire image stack. SEGMENT3D is a comprehensive application that can be
applied to other 3D imaging modalities and general objects. It also provides an
easy way to create supervised data to advance segmentation using machine
learning models
Automated Classification of Airborne Laser Scanning Point Clouds
Making sense of the physical world has always been at the core of mapping. Up
until recently, this has always dependent on using the human eye. Using
airborne lasers, it has become possible to quickly "see" more of the world in
many more dimensions. The resulting enormous point clouds serve as data sources
for applications far beyond the original mapping purposes ranging from flooding
protection and forestry to threat mitigation. In order to process these large
quantities of data, novel methods are required. In this contribution, we
develop models to automatically classify ground cover and soil types. Using the
logic of machine learning, we critically review the advantages of supervised
and unsupervised methods. Focusing on decision trees, we improve accuracy by
including beam vector components and using a genetic algorithm. We find that
our approach delivers consistently high quality classifications, surpassing
classical methods
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