3,145 research outputs found
Cooperative Synchronization in Wireless Networks
Synchronization is a key functionality in wireless network, enabling a wide
variety of services. We consider a Bayesian inference framework whereby network
nodes can achieve phase and skew synchronization in a fully distributed way. In
particular, under the assumption of Gaussian measurement noise, we derive two
message passing methods (belief propagation and mean field), analyze their
convergence behavior, and perform a qualitative and quantitative comparison
with a number of competing algorithms. We also show that both methods can be
applied in networks with and without master nodes. Our performance results are
complemented by, and compared with, the relevant Bayesian Cram\'er-Rao bounds
Geometry Helps to Compare Persistence Diagrams
Exploiting geometric structure to improve the asymptotic complexity of
discrete assignment problems is a well-studied subject. In contrast, the
practical advantages of using geometry for such problems have not been
explored. We implement geometric variants of the Hopcroft--Karp algorithm for
bottleneck matching (based on previous work by Efrat el al.) and of the auction
algorithm by Bertsekas for Wasserstein distance computation. Both
implementations use k-d trees to replace a linear scan with a geometric
proximity query. Our interest in this problem stems from the desire to compute
distances between persistence diagrams, a problem that comes up frequently in
topological data analysis. We show that our geometric matching algorithms lead
to a substantial performance gain, both in running time and in memory
consumption, over their purely combinatorial counterparts. Moreover, our
implementation significantly outperforms the only other implementation
available for comparing persistence diagrams.Comment: 20 pages, 10 figures; extended version of paper published in ALENEX
201
Scaling Graph-based Semi Supervised Learning to Large Number of Labels Using Count-Min Sketch
Graph-based Semi-supervised learning (SSL) algorithms have been successfully
used in a large number of applications. These methods classify initially
unlabeled nodes by propagating label information over the structure of graph
starting from seed nodes. Graph-based SSL algorithms usually scale linearly
with the number of distinct labels (m), and require O(m) space on each node.
Unfortunately, there exist many applications of practical significance with
very large m over large graphs, demanding better space and time complexity. In
this paper, we propose MAD-SKETCH, a novel graph-based SSL algorithm which
compactly stores label distribution on each node using Count-min Sketch, a
randomized data structure. We present theoretical analysis showing that under
mild conditions, MAD-SKETCH can reduce space complexity at each node from O(m)
to O(log m), and achieve similar savings in time complexity as well. We support
our analysis through experiments on multiple real world datasets. We observe
that MAD-SKETCH achieves similar performance as existing state-of-the-art
graph- based SSL algorithms, while requiring smaller memory footprint and at
the same time achieving up to 10x speedup. We find that MAD-SKETCH is able to
scale to datasets with one million labels, which is beyond the scope of
existing graph- based SSL algorithms.Comment: 9 page
Imperfect-Recall Abstractions with Bounds in Games
Imperfect-recall abstraction has emerged as the leading paradigm for
practical large-scale equilibrium computation in incomplete-information games.
However, imperfect-recall abstractions are poorly understood, and only weak
algorithm-specific guarantees on solution quality are known. In this paper, we
show the first general, algorithm-agnostic, solution quality guarantees for
Nash equilibria and approximate self-trembling equilibria computed in
imperfect-recall abstractions, when implemented in the original
(perfect-recall) game. Our results are for a class of games that generalizes
the only previously known class of imperfect-recall abstractions where any
results had been obtained. Further, our analysis is tighter in two ways, each
of which can lead to an exponential reduction in the solution quality error
bound.
We then show that for extensive-form games that satisfy certain properties,
the problem of computing a bound-minimizing abstraction for a single level of
the game reduces to a clustering problem, where the increase in our bound is
the distance function. This reduction leads to the first imperfect-recall
abstraction algorithm with solution quality bounds. We proceed to show a divide
in the class of abstraction problems. If payoffs are at the same scale at all
information sets considered for abstraction, the input forms a metric space.
Conversely, if this condition is not satisfied, we show that the input does not
form a metric space. Finally, we use these results to experimentally
investigate the quality of our bound for single-level abstraction
Sequential Design for Optimal Stopping Problems
We propose a new approach to solve optimal stopping problems via simulation.
Working within the backward dynamic programming/Snell envelope framework, we
augment the methodology of Longstaff-Schwartz that focuses on approximating the
stopping strategy. Namely, we introduce adaptive generation of the stochastic
grids anchoring the simulated sample paths of the underlying state process.
This allows for active learning of the classifiers partitioning the state space
into the continuation and stopping regions. To this end, we examine sequential
design schemes that adaptively place new design points close to the stopping
boundaries. We then discuss dynamic regression algorithms that can implement
such recursive estimation and local refinement of the classifiers. The new
algorithm is illustrated with a variety of numerical experiments, showing that
an order of magnitude savings in terms of design size can be achieved. We also
compare with existing benchmarks in the context of pricing multi-dimensional
Bermudan options.Comment: 24 page
Imbalanced Ensemble Classifier for learning from imbalanced business school data set
Private business schools in India face a common problem of selecting quality
students for their MBA programs to achieve the desired placement percentage.
Generally, such data sets are biased towards one class, i.e., imbalanced in
nature. And learning from the imbalanced dataset is a difficult proposition.
This paper proposes an imbalanced ensemble classifier which can handle the
imbalanced nature of the dataset and achieves higher accuracy in case of the
feature selection (selection of important characteristics of students) cum
classification problem (prediction of placements based on the students'
characteristics) for Indian business school dataset. The optimal value of an
important model parameter is found. Numerical evidence is also provided using
Indian business school dataset to assess the outstanding performance of the
proposed classifier
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