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1202.3728
|
Reasoning about RoboCup Soccer Narratives
|
cs.AI
|
This paper presents an approach for learning to translate simple narratives,
i.e., texts (sequences of sentences) describing dynamic systems, into coherent
sequences of events without the need for labeled training data. Our approach
incorporates domain knowledge in the form of preconditions and effects of
events, and we show that it outperforms state-of-the-art supervised learning
systems on the task of reconstructing RoboCup soccer games from their
commentaries.
|
1202.3729
|
Suboptimality Bounds for Stochastic Shortest Path Problems
|
cs.AI
|
We consider how to use the Bellman residual of the dynamic programming
operator to compute suboptimality bounds for solutions to stochastic shortest
path problems. Such bounds have been previously established only in the special
case that "all policies are proper," in which case the dynamic programming
operator is known to be a contraction, and have been shown to be easily
computable only in the more limited special case of discounting. Under the
condition that transition costs are positive, we show that suboptimality bounds
can be easily computed even when not all policies are proper. In the general
case when there are no restrictions on transition costs, the analysis is more
complex. But we present preliminary results that show such bounds are possible.
|
1202.3730
|
Sequential Inference for Latent Force Models
|
cs.LG stat.ML
|
Latent force models (LFMs) are hybrid models combining mechanistic principles
with non-parametric components. In this article, we shall show how LFMs can be
equivalently formulated and solved using the state variable approach. We shall
also show how the Gaussian process prior used in LFMs can be equivalently
formulated as a linear statespace model driven by a white noise process and how
inference on the resulting model can be efficiently implemented using Kalman
filter and smoother. Then we shall show how the recently proposed switching LFM
can be reformulated using the state variable approach, and how we can construct
a probabilistic model for the switches by formulating a similar switching LFM
as a switching linear dynamic system (SLDS). We illustrate the performance of
the proposed methodology in simulated scenarios and apply it to inferring the
switching points in GPS data collected from car movement data in urban
environment.
|
1202.3731
|
What Cannot be Learned with Bethe Approximations
|
cs.LG stat.ML
|
We address the problem of learning the parameters in graphical models when
inference is intractable. A common strategy in this case is to replace the
partition function with its Bethe approximation. We show that there exists a
regime of empirical marginals where such Bethe learning will fail. By failure
we mean that the empirical marginals cannot be recovered from the approximated
maximum likelihood parameters (i.e., moment matching is not achieved). We
provide several conditions on empirical marginals that yield outer and inner
bounds on the set of Bethe learnable marginals. An interesting implication of
our results is that there exists a large class of marginals that cannot be
obtained as stable fixed points of belief propagation. Taken together our
results provide a novel approach to analyzing learning with Bethe
approximations and highlight when it can be expected to work or fail.
|
1202.3732
|
Sum-Product Networks: A New Deep Architecture
|
cs.LG cs.AI stat.ML
|
The key limiting factor in graphical model inference and learning is the
complexity of the partition function. We thus ask the question: what are
general conditions under which the partition function is tractable? The answer
leads to a new kind of deep architecture, which we call sum-product networks
(SPNs). SPNs are directed acyclic graphs with variables as leaves, sums and
products as internal nodes, and weighted edges. We show that if an SPN is
complete and consistent it represents the partition function and all marginals
of some graphical model, and give semantics to its nodes. Essentially all
tractable graphical models can be cast as SPNs, but SPNs are also strictly more
general. We then propose learning algorithms for SPNs, based on backpropagation
and EM. Experiments show that inference and learning with SPNs can be both
faster and more accurate than with standard deep networks. For example, SPNs
perform image completion better than state-of-the-art deep networks for this
task. SPNs also have intriguing potential connections to the architecture of
the cortex.
|
1202.3733
|
Lipschitz Parametrization of Probabilistic Graphical Models
|
cs.LG stat.ML
|
We show that the log-likelihood of several probabilistic graphical models is
Lipschitz continuous with respect to the lp-norm of the parameters. We discuss
several implications of Lipschitz parametrization. We present an upper bound of
the Kullback-Leibler divergence that allows understanding methods that penalize
the lp-norm of differences of parameters as the minimization of that upper
bound. The expected log-likelihood is lower bounded by the negative lp-norm,
which allows understanding the generalization ability of probabilistic models.
The exponential of the negative lp-norm is involved in the lower bound of the
Bayes error rate, which shows that it is reasonable to use parameters as
features in algorithms that rely on metric spaces (e.g. classification,
dimensionality reduction, clustering). Our results do not rely on specific
algorithms for learning the structure or parameters. We show preliminary
results for activity recognition and temporal segmentation.
|
1202.3734
|
Efficient Probabilistic Inference with Partial Ranking Queries
|
cs.LG cs.AI stat.ML
|
Distributions over rankings are used to model data in various settings such
as preference analysis and political elections. The factorial size of the space
of rankings, however, typically forces one to make structural assumptions, such
as smoothness, sparsity, or probabilistic independence about these underlying
distributions. We approach the modeling problem from the computational
principle that one should make structural assumptions which allow for efficient
calculation of typical probabilistic queries. For ranking models, "typical"
queries predominantly take the form of partial ranking queries (e.g., given a
user's top-k favorite movies, what are his preferences over remaining movies?).
In this paper, we argue that riffled independence factorizations proposed in
recent literature [7, 8] are a natural structural assumption for ranking
distributions, allowing for particularly efficient processing of partial
ranking queries.
|
1202.3735
|
Noisy-OR Models with Latent Confounding
|
cs.LG stat.ML
|
Given a set of experiments in which varying subsets of observed variables are
subject to intervention, we consider the problem of identifiability of causal
models exhibiting latent confounding. While identifiability is trivial when
each experiment intervenes on a large number of variables, the situation is
more complicated when only one or a few variables are subject to intervention
per experiment. For linear causal models with latent variables Hyttinen et al.
(2010) gave precise conditions for when such data are sufficient to identify
the full model. While their result cannot be extended to discrete-valued
variables with arbitrary cause-effect relationships, we show that a similar
result can be obtained for the class of causal models whose conditional
probability distributions are restricted to a `noisy-OR' parameterization. We
further show that identification is preserved under an extension of the model
that allows for negative influences, and present learning algorithms that we
test for accuracy, scalability and robustness.
|
1202.3736
|
Discovering causal structures in binary exclusive-or skew acyclic models
|
cs.LG stat.ML
|
Discovering causal relations among observed variables in a given data set is
a main topic in studies of statistics and artificial intelligence. Recently,
some techniques to discover an identifiable causal structure have been explored
based on non-Gaussianity of the observed data distribution. However, most of
these are limited to continuous data. In this paper, we present a novel causal
model for binary data and propose a new approach to derive an identifiable
causal structure governing the data based on skew Bernoulli distributions of
external noise. Experimental evaluation shows excellent performance for both
artificial and real world data sets.
|
1202.3737
|
Detecting low-complexity unobserved causes
|
cs.LG stat.ML
|
We describe a method that infers whether statistical dependences between two
observed variables X and Y are due to a "direct" causal link or only due to a
connecting causal path that contains an unobserved variable of low complexity,
e.g., a binary variable. This problem is motivated by statistical genetics.
Given a genetic marker that is correlated with a phenotype of interest, we want
to detect whether this marker is causal or it only correlates with a causal
one. Our method is based on the analysis of the location of the conditional
distributions P(Y|x) in the simplex of all distributions of Y. We report
encouraging results on semi-empirical data.
|
1202.3738
|
Learning Determinantal Point Processes
|
cs.LG cs.AI stat.ML
|
Determinantal point processes (DPPs), which arise in random matrix theory and
quantum physics, are natural models for subset selection problems where
diversity is preferred. Among many remarkable properties, DPPs offer tractable
algorithms for exact inference, including computing marginal probabilities and
sampling; however, an important open question has been how to learn a DPP from
labeled training data. In this paper we propose a natural feature-based
parameterization of conditional DPPs, and show how it leads to a convex and
efficient learning formulation. We analyze the relationship between our model
and binary Markov random fields with repulsive potentials, which are
qualitatively similar but computationally intractable. Finally, we apply our
approach to the task of extractive summarization, where the goal is to choose a
small subset of sentences conveying the most important information from a set
of documents. In this task there is a fundamental tradeoff between sentences
that are highly relevant to the collection as a whole, and sentences that are
diverse and not repetitive. Our parameterization allows us to naturally balance
these two characteristics. We evaluate our system on data from the DUC 2003/04
multi-document summarization task, achieving state-of-the-art results.
|
1202.3739
|
Message-Passing Algorithms for Quadratic Programming Formulations of MAP
Estimation
|
cs.AI cs.DS stat.CO
|
Computing maximum a posteriori (MAP) estimation in graphical models is an
important inference problem with many applications. We present message-passing
algorithms for quadratic programming (QP) formulations of MAP estimation for
pairwise Markov random fields. In particular, we use the concave-convex
procedure (CCCP) to obtain a locally optimal algorithm for the non-convex QP
formulation. A similar technique is used to derive a globally convergent
algorithm for the convex QP relaxation of MAP. We also show that a recently
developed expectation-maximization (EM) algorithm for the QP formulation of MAP
can be derived from the CCCP perspective. Experiments on synthetic and
real-world problems confirm that our new approach is competitive with
max-product and its variations. Compared with CPLEX, we achieve more than an
order-of-magnitude speedup in solving optimally the convex QP relaxation.
|
1202.3740
|
An Efficient Protocol for Negotiation over Combinatorial Domains with
Incomplete Information
|
cs.AI
|
We study the problem of agent-based negotiation in combinatorial domains. It
is difficult to reach optimal agreements in bilateral or multi-lateral
negotiations when the agents' preferences for the possible alternatives are not
common knowledge. Self-interested agents often end up negotiating inefficient
agreements in such situations. In this paper, we present a protocol for
negotiation in combinatorial domains which can lead rational agents to reach
optimal agreements under incomplete information setting. Our proposed protocol
enables the negotiating agents to identify efficient solutions using
distributed search that visits only a small subspace of the whole outcome
space. Moreover, the proposed protocol is sufficiently general that it is
applicable to most preference representation models in combinatorial domains.
We also present results of experiments that demonstrate the feasibility and
computational efficiency of our approach.
|
1202.3741
|
Noisy Search with Comparative Feedback
|
cs.AI
|
We present theoretical results in terms of lower and upper bounds on the
query complexity of noisy search with comparative feedback. In this search
model, the noise in the feedback depends on the distance between query points
and the search target. Consequently, the error probability in the feedback is
not fixed but varies for the queries posed by the search algorithm. Our results
show that a target out of n items can be found in O(log n) queries. We also
show the surprising result that for k possible answers per query, the speedup
is not log k (as for k-ary search) but only log log k in some cases.
|
1202.3742
|
Variational Algorithms for Marginal MAP
|
cs.LG cs.AI cs.IT math.IT stat.ML
|
Marginal MAP problems are notoriously difficult tasks for graphical models.
We derive a general variational framework for solving marginal MAP problems, in
which we apply analogues of the Bethe, tree-reweighted, and mean field
approximations. We then derive a "mixed" message passing algorithm and a
convergent alternative using CCCP to solve the BP-type approximations.
Theoretically, we give conditions under which the decoded solution is a global
or local optimum, and obtain novel upper bounds on solutions. Experimentally we
demonstrate that our algorithms outperform related approaches. We also show
that EM and variational EM comprise a special case of our framework.
|
1202.3743
|
Belief change with noisy sensing in the situation calculus
|
cs.AI
|
Situation calculus has been applied widely in artificial intelligence to
model and reason about actions and changes in dynamic systems. Since actions
carried out by agents will cause constant changes of the agents' beliefs, how
to manage these changes is a very important issue. Shapiro et al. [22] is one
of the studies that considered this issue. However, in this framework, the
problem of noisy sensing, which often presents in real-world applications, is
not considered. As a consequence, noisy sensing actions in this framework will
lead to an agent facing inconsistent situation and subsequently the agent
cannot proceed further. In this paper, we investigate how noisy sensing actions
can be handled in iterated belief change within the situation calculus
formalism. We extend the framework proposed in [22] with the capability of
managing noisy sensings. We demonstrate that an agent can still detect the
actual situation when the ratio of noisy sensing actions vs. accurate sensing
actions is limited. We prove that our framework subsumes the iterated belief
change strategy in [22] when all sensing actions are accurate. Furthermore, we
prove that our framework can adequately handle belief introspection, mistaken
beliefs, belief revision and belief update even with noisy sensing, as done in
[22] with accurate sensing actions only.
|
1202.3744
|
Improving the Scalability of Optimal Bayesian Network Learning with
External-Memory Frontier Breadth-First Branch and Bound Search
|
cs.AI
|
Previous work has shown that the problem of learning the optimal structure of
a Bayesian network can be formulated as a shortest path finding problem in a
graph and solved using A* search. In this paper, we improve the scalability of
this approach by developing a memory-efficient heuristic search algorithm for
learning the structure of a Bayesian network. Instead of using A*, we propose a
frontier breadth-first branch and bound search that leverages the layered
structure of the search graph of this problem so that no more than two layers
of the graph, plus solution reconstruction information, need to be stored in
memory at a time. To further improve scalability, the algorithm stores most of
the graph in external memory, such as hard disk, when it does not fit in RAM.
Experimental results show that the resulting algorithm solves significantly
larger problems than the current state of the art.
|
1202.3745
|
Order-of-Magnitude Influence Diagrams
|
cs.AI
|
In this paper, we develop a qualitative theory of influence diagrams that can
be used to model and solve sequential decision making tasks when only
qualitative (or imprecise) information is available. Our approach is based on
an order-of-magnitude approximation of both probabilities and utilities and
allows for specifying partially ordered preferences via sets of utility values.
We also propose a dedicated variable elimination algorithm that can be applied
for solving order-of-magnitude influence diagrams.
|
1202.3746
|
Asymptotic Efficiency of Deterministic Estimators for Discrete
Energy-Based Models: Ratio Matching and Pseudolikelihood
|
cs.LG stat.ML
|
Standard maximum likelihood estimation cannot be applied to discrete
energy-based models in the general case because the computation of exact model
probabilities is intractable. Recent research has seen the proposal of several
new estimators designed specifically to overcome this intractability, but
virtually nothing is known about their theoretical properties. In this paper,
we present a generalized estimator that unifies many of the classical and
recently proposed estimators. We use results from the standard asymptotic
theory for M-estimators to derive a generic expression for the asymptotic
covariance matrix of our generalized estimator. We apply these results to study
the relative statistical efficiency of classical pseudolikelihood and the
recently-proposed ratio matching estimator.
|
1202.3747
|
Reconstructing Pompeian Households
|
cs.LG stat.ML
|
A database of objects discovered in houses in the Roman city of Pompeii
provides a unique view of ordinary life in an ancient city. Experts have used
this collection to study the structure of Roman households, exploring the
distribution and variability of tasks in architectural spaces, but such
approaches are necessarily affected by modern cultural assumptions. In this
study we present a data-driven approach to household archeology, treating it as
an unsupervised labeling problem. This approach scales to large data sets and
provides a more objective complement to human interpretation.
|
1202.3748
|
Conditional Restricted Boltzmann Machines for Structured Output
Prediction
|
cs.LG stat.ML
|
Conditional Restricted Boltzmann Machines (CRBMs) are rich probabilistic
models that have recently been applied to a wide range of problems, including
collaborative filtering, classification, and modeling motion capture data.
While much progress has been made in training non-conditional RBMs, these
algorithms are not applicable to conditional models and there has been almost
no work on training and generating predictions from conditional RBMs for
structured output problems. We first argue that standard Contrastive
Divergence-based learning may not be suitable for training CRBMs. We then
identify two distinct types of structured output prediction problems and
propose an improved learning algorithm for each. The first problem type is one
where the output space has arbitrary structure but the set of likely output
configurations is relatively small, such as in multi-label classification. The
second problem is one where the output space is arbitrarily structured but
where the output space variability is much greater, such as in image denoising
or pixel labeling. We show that the new learning algorithms can work much
better than Contrastive Divergence on both types of problems.
|
1202.3749
|
Compact Mathematical Programs For DEC-MDPs With Structured Agent
Interactions
|
cs.AI
|
To deal with the prohibitive complexity of calculating policies in
Decentralized MDPs, researchers have proposed models that exploit structured
agent interactions. Settings where most agent actions are independent except
for few actions that affect the transitions and/or rewards of other agents can
be modeled using Event-Driven Interactions with Complex Rewards (EDI-CR).
Finding the optimal joint policy can be formulated as an optimization problem.
However, existing formulations are too verbose and/or lack optimality
guarantees. We propose a compact Mixed Integer Linear Program formulation of
EDI-CR instances. The key insight is that most action sequences of a group of
agents have the same effect on a given agent. This allows us to treat these
sequences similarly and use fewer variables. Experiments show that our
formulation is more compact and leads to faster solution times and better
solutions than existing formulations.
|
1202.3750
|
Fractional Moments on Bandit Problems
|
cs.LG stat.ML
|
Reinforcement learning addresses the dilemma between exploration to find
profitable actions and exploitation to act according to the best observations
already made. Bandit problems are one such class of problems in stateless
environments that represent this explore/exploit situation. We propose a
learning algorithm for bandit problems based on fractional expectation of
rewards acquired. The algorithm is theoretically shown to converge on an
eta-optimal arm and achieve O(n) sample complexity. Experimental results show
the algorithm incurs substantially lower regrets than parameter-optimized
eta-greedy and SoftMax approaches and other low sample complexity
state-of-the-art techniques.
|
1202.3751
|
Dynamic Mechanism Design for Markets with Strategic Resources
|
cs.GT cs.AI
|
The assignment of tasks to multiple resources becomes an interesting game
theoretic problem, when both the task owner and the resources are strategic. In
the classical, nonstrategic setting, where the states of the tasks and
resources are observable by the controller, this problem is that of finding an
optimal policy for a Markov decision process (MDP). When the states are held by
strategic agents, the problem of an efficient task allocation extends beyond
that of solving an MDP and becomes that of designing a mechanism. Motivated by
this fact, we propose a general mechanism which decides on an allocation rule
for the tasks and resources and a payment rule to incentivize agents'
participation and truthful reports. In contrast to related dynamic strategic
control problems studied in recent literature, the problem studied here has
interdependent values: the benefit of an allocation to the task owner is not
simply a function of the characteristics of the task itself and the allocation,
but also of the state of the resources. We introduce a dynamic extension of
Mezzetti's two phase mechanism for interdependent valuations. In this changed
setting, the proposed dynamic mechanism is efficient, within period ex-post
incentive compatible, and within period ex-post individually rational.
|
1202.3752
|
Multidimensional counting grids: Inferring word order from disordered
bags of words
|
cs.IR cs.CL cs.LG stat.ML
|
Models of bags of words typically assume topic mixing so that the words in a
single bag come from a limited number of topics. We show here that many sets of
bag of words exhibit a very different pattern of variation than the patterns
that are efficiently captured by topic mixing. In many cases, from one bag of
words to the next, the words disappear and new ones appear as if the theme
slowly and smoothly shifted across documents (providing that the documents are
somehow ordered). Examples of latent structure that describe such ordering are
easily imagined. For example, the advancement of the date of the news stories
is reflected in a smooth change over the theme of the day as certain evolving
news stories fall out of favor and new events create new stories. Overlaps
among the stories of consecutive days can be modeled by using windows over
linearly arranged tight distributions over words. We show here that such
strategy can be extended to multiple dimensions and cases where the ordering of
data is not readily obvious. We demonstrate that this way of modeling
covariation in word occurrences outperforms standard topic models in
classification and prediction tasks in applications in biology, text modeling
and computer vision.
|
1202.3753
|
Partial Order MCMC for Structure Discovery in Bayesian Networks
|
cs.LG stat.ML
|
We present a new Markov chain Monte Carlo method for estimating posterior
probabilities of structural features in Bayesian networks. The method draws
samples from the posterior distribution of partial orders on the nodes; for
each sampled partial order, the conditional probabilities of interest are
computed exactly. We give both analytical and empirical results that suggest
the superiority of the new method compared to previous methods, which sample
either directed acyclic graphs or linear orders on the nodes.
|
1202.3754
|
A Geometric Traversal Algorithm for Reward-Uncertain MDPs
|
cs.AI
|
Markov decision processes (MDPs) are widely used in modeling decision making
problems in stochastic environments. However, precise specification of the
reward functions in MDPs is often very difficult. Recent approaches have
focused on computing an optimal policy based on the minimax regret criterion
for obtaining a robust policy under uncertainty in the reward function. One of
the core tasks in computing the minimax regret policy is to obtain the set of
all policies that can be optimal for some candidate reward function. In this
paper, we propose an efficient algorithm that exploits the geometric properties
of the reward function associated with the policies. We also present an
approximate version of the method for further speed up. We experimentally
demonstrate that our algorithm improves the performance by orders of magnitude.
|
1202.3755
|
Iterated risk measures for risk-sensitive Markov decision processes with
discounted cost
|
cs.GT cs.AI q-fin.RM
|
We demonstrate a limitation of discounted expected utility, a standard
approach for representing the preference to risk when future cost is
discounted. Specifically, we provide an example of the preference of a decision
maker that appears to be rational but cannot be represented with any discounted
expected utility. A straightforward modification to discounted expected utility
leads to inconsistent decision making over time. We will show that an iterated
risk measure can represent the preference that cannot be represented by any
discounted expected utility and that the decisions based on the iterated risk
measure are consistent over time.
|
1202.3756
|
Price Updating in Combinatorial Prediction Markets with Bayesian
Networks
|
cs.GT cs.AI
|
To overcome the #P-hardness of computing/updating prices in logarithm market
scoring rule-based (LMSR-based) combinatorial prediction markets, Chen et al.
[5] recently used a simple Bayesian network to represent the prices of
securities in combinatorial predictionmarkets for tournaments, and showed that
two types of popular securities are structure preserving. In this paper, we
significantly extend this idea by employing Bayesian networks in general
combinatorial prediction markets. We reveal a very natural connection between
LMSR-based combinatorial prediction markets and probabilistic belief
aggregation,which leads to a complete characterization of all structure
preserving securities for decomposable network structures. Notably, the main
results by Chen et al. [5] are corollaries of our characterization. We then
prove that in order for a very basic set of securities to be structure
preserving, the graph of the Bayesian network must be decomposable. We also
discuss some approximation techniques for securities that are not structure
preserving.
|
1202.3757
|
Identifiability of Causal Graphs using Functional Models
|
cs.LG stat.ML
|
This work addresses the following question: Under what assumptions on the
data generating process can one infer the causal graph from the joint
distribution? The approach taken by conditional independence-based causal
discovery methods is based on two assumptions: the Markov condition and
faithfulness. It has been shown that under these assumptions the causal graph
can be identified up to Markov equivalence (some arrows remain undirected)
using methods like the PC algorithm. In this work we propose an alternative by
defining Identifiable Functional Model Classes (IFMOCs). As our main theorem we
prove that if the data generating process belongs to an IFMOC, one can identify
the complete causal graph. To the best of our knowledge this is the first
identifiability result of this kind that is not limited to linear functional
relationships. We discuss how the IFMOC assumption and the Markov and
faithfulness assumptions relate to each other and explain why we believe that
the IFMOC assumption can be tested more easily on given data. We further
provide a practical algorithm that recovers the causal graph from finitely many
data; experiments on simulated data support the theoretical findings.
|
1202.3758
|
Nonparametric Divergence Estimation with Applications to Machine
Learning on Distributions
|
cs.LG stat.ML
|
Low-dimensional embedding, manifold learning, clustering, classification, and
anomaly detection are among the most important problems in machine learning.
The existing methods usually consider the case when each instance has a fixed,
finite-dimensional feature representation. Here we consider a different
setting. We assume that each instance corresponds to a continuous probability
distribution. These distributions are unknown, but we are given some i.i.d.
samples from each distribution. Our goal is to estimate the distances between
these distributions and use these distances to perform low-dimensional
embedding, clustering/classification, or anomaly detection for the
distributions. We present estimation algorithms, describe how to apply them for
machine learning tasks on distributions, and show empirical results on
synthetic data, real word images, and astronomical data sets.
|
1202.3759
|
Compressed Inference for Probabilistic Sequential Models
|
cs.AI
|
Hidden Markov models (HMMs) and conditional random fields (CRFs) are two
popular techniques for modeling sequential data. Inference algorithms designed
over CRFs and HMMs allow estimation of the state sequence given the
observations. In several applications, estimation of the state sequence is not
the end goal; instead the goal is to compute some function of it. In such
scenarios, estimating the state sequence by conventional inference techniques,
followed by computing the functional mapping from the estimate is not
necessarily optimal. A more formal approach is to directly infer the final
outcome from the observations. In particular, we consider the specific
instantiation of the problem where the goal is to find the state trajectories
without exact transition points and derive a novel polynomial time inference
algorithm that outperforms vanilla inference techniques. We show that this
particular problem arises commonly in many disparate applications and present
experiments on three of them: (1) Toy robot tracking; (2) Single stroke
character recognition; (3) Handwritten word recognition.
|
1202.3760
|
Fast MCMC sampling for Markov jump processes and continuous time
Bayesian networks
|
stat.ME cs.LG stat.ML
|
Markov jump processes and continuous time Bayesian networks are important
classes of continuous time dynamical systems. In this paper, we tackle the
problem of inferring unobserved paths in these models by introducing a fast
auxiliary variable Gibbs sampler. Our approach is based on the idea of
uniformization, and sets up a Markov chain over paths by sampling a finite set
of virtual jump times and then running a standard hidden Markov model forward
filtering-backward sampling algorithm over states at the set of extant and
virtual jump times. We demonstrate significant computational benefits over a
state-of-the-art Gibbs sampler on a number of continuous time Bayesian
networks.
|
1202.3761
|
New Probabilistic Bounds on Eigenvalues and Eigenvectors of Random
Kernel Matrices
|
cs.LG stat.ML
|
Kernel methods are successful approaches for different machine learning
problems. This success is mainly rooted in using feature maps and kernel
matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel
matrix, while for other methods the spectral information can be used to
estimate the excess risk. An important question remains on how close the sample
eigenvalues/eigenvectors are to the population values. In this paper, we
improve earlier results on concentration bounds for eigenvalues of general
kernel matrices. For distance and inner product kernel functions, e.g. radial
basis functions, we provide new concentration bounds, which are characterized
by the eigenvalues of the sample covariance matrix. Meanwhile, the obstacles
for sharper bounds are accounted for and partially addressed. As a case study,
we derive a concentration inequality for sample kernel target-alignment.
|
1202.3762
|
Symbolic Dynamic Programming for Discrete and Continuous State MDPs
|
cs.AI
|
Many real-world decision-theoretic planning problems can be naturally modeled
with discrete and continuous state Markov decision processes (DC-MDPs). While
previous work has addressed automated decision-theoretic planning for DCMDPs,
optimal solutions have only been defined so far for limited settings, e.g.,
DC-MDPs having hyper-rectangular piecewise linear value functions. In this
work, we extend symbolic dynamic programming (SDP) techniques to provide
optimal solutions for a vastly expanded class of DCMDPs. To address the
inherent combinatorial aspects of SDP, we introduce the XADD - a continuous
variable extension of the algebraic decision diagram (ADD) - that maintains
compact representations of the exact value function. Empirically, we
demonstrate an implementation of SDP with XADDs on various DC-MDPs, showing the
first optimal automated solutions to DCMDPs with linear and nonlinear piecewise
partitioned value functions and showing the advantages of constraint-based
pruning for XADDs.
|
1202.3763
|
An Efficient Algorithm for Computing Interventional Distributions in
Latent Variable Causal Models
|
cs.LG stat.ML
|
Probabilistic inference in graphical models is the task of computing marginal
and conditional densities of interest from a factorized representation of a
joint probability distribution. Inference algorithms such as variable
elimination and belief propagation take advantage of constraints embedded in
this factorization to compute such densities efficiently. In this paper, we
propose an algorithm which computes interventional distributions in latent
variable causal models represented by acyclic directed mixed graphs(ADMGs). To
compute these distributions efficiently, we take advantage of a recursive
factorization which generalizes the usual Markov factorization for DAGs and the
more recent factorization for ADMGs. Our algorithm can be viewed as a
generalization of variable elimination to the mixed graph case. We show our
algorithm is exponential in the mixed graph generalization of treewidth.
|
1202.3764
|
Adjustment Criteria in Causal Diagrams: An Algorithmic Perspective
|
cs.AI
|
Identifying and controlling bias is a key problem in empirical sciences.
Causal diagram theory provides graphical criteria for deciding whether and how
causal effects can be identified from observed (nonexperimental) data by
covariate adjustment. Here we prove equivalences between existing as well as
new criteria for adjustment and we provide a new simplified but still
equivalent notion of d-separation. These lead to efficient algorithms for two
important tasks in causal diagram analysis: (1) listing minimal covariate
adjustments (with polynomial delay); and (2) identifying the subdiagram
involved in biasing paths (in linear time). Our results improve upon existing
exponential-time solutions for these problems, enabling users to assess the
effects of covariate adjustment on diagrams with tens to hundreds of variables
interactively in real time.
|
1202.3765
|
Learning mixed graphical models from data with p larger than n
|
stat.ME cs.LG stat.ML
|
Structure learning of Gaussian graphical models is an extensively studied
problem in the classical multivariate setting where the sample size n is larger
than the number of random variables p, as well as in the more challenging
setting when p>>n. However, analogous approaches for learning the structure of
graphical models with mixed discrete and continuous variables when p>>n remain
largely unexplored. Here we describe a statistical learning procedure for this
problem based on limited-order correlations and assess its performance with
synthetic and real data.
|
1202.3766
|
Robust learning Bayesian networks for prior belief
|
cs.LG stat.ML
|
Recent reports have described that learning Bayesian networks are highly
sensitive to the chosen equivalent sample size (ESS) in the Bayesian Dirichlet
equivalence uniform (BDeu). This sensitivity often engenders some unstable or
undesirable results. This paper describes some asymptotic analyses of BDeu to
explain the reasons for the sensitivity and its effects. Furthermore, this
paper presents a proposal for a robust learning score for ESS by eliminating
the sensitive factors from the approximation of log-BDeu.
|
1202.3767
|
Distributed Anytime MAP Inference
|
cs.AI
|
We present a distributed anytime algorithm for performing MAP inference in
graphical models. The problem is formulated as a linear programming relaxation
over the edges of a graph. The resulting program has a constraint structure
that allows application of the Dantzig-Wolfe decomposition principle.
Subprograms are defined over individual edges and can be computed in a
distributed manner. This accommodates solutions to graphs whose state space
does not fit in memory. The decomposition master program is guaranteed to
compute the optimal solution in a finite number of iterations, while the
solution converges monotonically with each iteration. Formulating the MAP
inference problem as a linear program allows additional (global) constraints to
be defined; something not possible with message passing algorithms.
Experimental results show that our algorithm's solution quality outperforms
most current algorithms and it scales well to large problems.
|
1202.3768
|
The Structure of Signals: Causal Interdependence Models for Games of
Incomplete Information
|
cs.GT cs.AI
|
Traditional economic models typically treat private information, or signals,
as generated from some underlying state. Recent work has explicated alternative
models, where signals correspond to interpretations of available information.
We show that the difference between these formulations can be sharply cast in
terms of causal dependence structure, and employ graphical models to illustrate
the distinguishing characteristics. The graphical representation supports
inferences about signal patterns in the interpreted framework, and suggests how
results based on the generated model can be extended to more general
situations. Specific insights about bidding games in classical auction
mechanisms derive from qualitative graphical models.
|
1202.3769
|
Sparse matrix-variate Gaussian process blockmodels for network modeling
|
cs.LG stat.ML
|
We face network data from various sources, such as protein interactions and
online social networks. A critical problem is to model network interactions and
identify latent groups of network nodes. This problem is challenging due to
many reasons. For example, the network nodes are interdependent instead of
independent of each other, and the data are known to be very noisy (e.g.,
missing edges). To address these challenges, we propose a new relational model
for network data, Sparse Matrix-variate Gaussian process Blockmodel (SMGB). Our
model generalizes popular bilinear generative models and captures nonlinear
network interactions using a matrix-variate Gaussian process with latent
membership variables. We also assign sparse prior distributions on the latent
membership variables to learn sparse group assignments for individual network
nodes. To estimate the latent variables efficiently from data, we develop an
efficient variational expectation maximization method. We compared our
approaches with several state-of-the-art network models on both synthetic and
real-world network datasets. Experimental results demonstrate SMGBs outperform
the alternative approaches in terms of discovering latent classes or predicting
unknown interactions.
|
1202.3770
|
Hierarchical Maximum Margin Learning for Multi-Class Classification
|
cs.LG stat.ML
|
Due to myriads of classes, designing accurate and efficient classifiers
becomes very challenging for multi-class classification. Recent research has
shown that class structure learning can greatly facilitate multi-class
learning. In this paper, we propose a novel method to learn the class structure
for multi-class classification problems. The class structure is assumed to be a
binary hierarchical tree. To learn such a tree, we propose a maximum separating
margin method to determine the child nodes of any internal node. The proposed
method ensures that two classgroups represented by any two sibling nodes are
most separable. In the experiments, we evaluate the accuracy and efficiency of
the proposed method over other multi-class classification methods on real world
large-scale problems. The results show that the proposed method outperforms
benchmark methods in terms of accuracy for most datasets and performs
comparably with other class structure learning methods in terms of efficiency
for all datasets.
|
1202.3771
|
Tightening MRF Relaxations with Planar Subproblems
|
cs.LG stat.ML
|
We describe a new technique for computing lower-bounds on the minimum energy
configuration of a planar Markov Random Field (MRF). Our method successively
adds large numbers of constraints and enforces consistency over binary
projections of the original problem state space. These constraints are
represented in terms of subproblems in a dual-decomposition framework that is
optimized using subgradient techniques. The complete set of constraints we
consider enforces cycle consistency over the original graph. In practice we
find that the method converges quickly on most problems with the addition of a
few subproblems and outperforms existing methods for some interesting classes
of hard potentials.
|
1202.3772
|
Rank/Norm Regularization with Closed-Form Solutions: Application to
Subspace Clustering
|
cs.LG cs.NA stat.ML
|
When data is sampled from an unknown subspace, principal component analysis
(PCA) provides an effective way to estimate the subspace and hence reduce the
dimension of the data. At the heart of PCA is the Eckart-Young-Mirsky theorem,
which characterizes the best rank k approximation of a matrix. In this paper,
we prove a generalization of the Eckart-Young-Mirsky theorem under all
unitarily invariant norms. Using this result, we obtain closed-form solutions
for a set of rank/norm regularized problems, and derive closed-form solutions
for a general class of subspace clustering problems (where data is modelled by
unions of unknown subspaces). From these results we obtain new theoretical
insights and promising experimental results.
|
1202.3773
|
Measuring the Hardness of Stochastic Sampling on Bayesian Networks with
Deterministic Causalities: the k-Test
|
cs.AI
|
Approximate Bayesian inference is NP-hard. Dagum and Luby defined the Local
Variance Bound (LVB) to measure the approximation hardness of Bayesian
inference on Bayesian networks, assuming the networks model strictly positive
joint probability distributions, i.e. zero probabilities are not permitted.
This paper introduces the k-test to measure the approximation hardness of
inference on Bayesian networks with deterministic causalities in the
probability distribution, i.e. when zero conditional probabilities are
permitted. Approximation by stochastic sampling is a widely-used inference
method that is known to suffer from inefficiencies due to sample rejection. The
k-test predicts when rejection rates of stochastic sampling a Bayesian network
will be low, modest, high, or when sampling is intractable.
|
1202.3774
|
Risk Bounds for Infinitely Divisible Distribution
|
stat.ML cs.LG
|
In this paper, we study the risk bounds for samples independently drawn from
an infinitely divisible (ID) distribution. In particular, based on a martingale
method, we develop two deviation inequalities for a sequence of random
variables of an ID distribution with zero Gaussian component. By applying the
deviation inequalities, we obtain the risk bounds based on the covering number
for the ID distribution. Finally, we analyze the asymptotic convergence of the
risk bound derived from one of the two deviation inequalities and show that the
convergence rate of the bound is faster than the result for the generic i.i.d.
empirical process (Mendelson, 2003).
|
1202.3775
|
Kernel-based Conditional Independence Test and Application in Causal
Discovery
|
cs.LG stat.ML
|
Conditional independence testing is an important problem, especially in
Bayesian network learning and causal discovery. Due to the curse of
dimensionality, testing for conditional independence of continuous variables is
particularly challenging. We propose a Kernel-based Conditional Independence
test (KCI-test), by constructing an appropriate test statistic and deriving its
asymptotic distribution under the null hypothesis of conditional independence.
The proposed method is computationally efficient and easy to implement.
Experimental results show that it outperforms other methods, especially when
the conditioning set is large or the sample size is not very large, in which
case other methods encounter difficulties.
|
1202.3776
|
Smoothing Multivariate Performance Measures
|
cs.LG stat.ML
|
A Support Vector Method for multivariate performance measures was recently
introduced by Joachims (2005). The underlying optimization problem is currently
solved using cutting plane methods such as SVM-Perf and BMRM. One can show that
these algorithms converge to an eta accurate solution in O(1/Lambda*e)
iterations, where lambda is the trade-off parameter between the regularizer and
the loss function. We present a smoothing strategy for multivariate performance
scores, in particular precision/recall break-even point and ROCArea. When
combined with Nesterov's accelerated gradient algorithm our smoothing strategy
yields an optimization algorithm which converges to an eta accurate solution in
O(min{1/e,1/sqrt(lambda*e)}) iterations. Furthermore, the cost per iteration of
our scheme is the same as that of SVM-Perf and BMRM. Empirical evaluation on a
number of publicly available datasets shows that our method converges
significantly faster than cutting plane methods without sacrificing
generalization ability.
|
1202.3777
|
Belief Propagation by Message Passing in Junction Trees: Computing Each
Message Faster Using GPU Parallelization
|
cs.AI cs.DC
|
Compiling Bayesian networks (BNs) to junction trees and performing belief
propagation over them is among the most prominent approaches to computing
posteriors in BNs. However, belief propagation over junction tree is known to
be computationally intensive in the general case. Its complexity may increase
dramatically with the connectivity and state space cardinality of Bayesian
network nodes. In this paper, we address this computational challenge using GPU
parallelization. We develop data structures and algorithms that extend existing
junction tree techniques, and specifically develop a novel approach to
computing each belief propagation message in parallel. We implement our
approach on an NVIDIA GPU and test it using BNs from several applications.
Experimentally, we study how junction tree parameters affect parallelization
opportunities and hence the performance of our algorithm. We achieve speedups
ranging from 0.68 to 9.18 for the BNs studied.
|
1202.3778
|
Sparse Topical Coding
|
cs.LG stat.ML
|
We present sparse topical coding (STC), a non-probabilistic formulation of
topic models for discovering latent representations of large collections of
data. Unlike probabilistic topic models, STC relaxes the normalization
constraint of admixture proportions and the constraint of defining a normalized
likelihood function. Such relaxations make STC amenable to: 1) directly control
the sparsity of inferred representations by using sparsity-inducing
regularizers; 2) be seamlessly integrated with a convex error function (e.g.,
SVM hinge loss) for supervised learning; and 3) be efficiently learned with a
simply structured coordinate descent algorithm. Our results demonstrate the
advantages of STC and supervised MedSTC on identifying topical meanings of
words and improving classification accuracy and time efficiency.
|
1202.3779
|
Testing whether linear equations are causal: A free probability theory
approach
|
cs.LG stat.ML
|
We propose a method that infers whether linear relations between two
high-dimensional variables X and Y are due to a causal influence from X to Y or
from Y to X. The earlier proposed so-called Trace Method is extended to the
regime where the dimension of the observed variables exceeds the sample size.
Based on previous work, we postulate conditions that characterize a causal
relation between X and Y. Moreover, we describe a statistical test and argue
that both causal directions are typically rejected if there is a common cause.
A full theoretical analysis is presented for the deterministic case but our
approach seems to be valid for the noisy case, too, for which we additionally
present an approach based on a sparsity constraint. The discussed method yields
promising results for both simulated and real world data.
|
1202.3782
|
Graphical Models for Bandit Problems
|
cs.LG cs.AI stat.ML
|
We introduce a rich class of graphical models for multi-armed bandit problems
that permit both the state or context space and the action space to be very
large, yet succinctly specify the payoffs for any context-action pair. Our main
result is an algorithm for such models whose regret is bounded by the number of
parameters and whose running time depends only on the treewidth of the graph
substructure induced by the action space.
|
1202.3807
|
An Adaptive Mechanism for Accurate Query Answering under Differential
Privacy
|
cs.DB
|
We propose a novel mechanism for answering sets of count- ing queries under
differential privacy. Given a workload of counting queries, the mechanism
automatically selects a different set of "strategy" queries to answer
privately, using those answers to derive answers to the workload. The main
algorithm proposed in this paper approximates the optimal strategy for any
workload of linear counting queries. With no cost to the privacy guarantee, the
mechanism improves significantly on prior approaches and achieves near-optimal
error for many workloads, when applied under (\epsilon, \delta)-differential
privacy. The result is an adaptive mechanism which can help users achieve good
utility without requiring that they reason carefully about the best formulation
of their task.
|
1202.3884
|
A feature extraction technique based on character geometry for character
recognition
|
cs.CV
|
This paper describes a geometry based technique for feature extraction
applicable to segmentation-based word recognition systems. The proposed system
extracts the geometric features of the character contour. This features are
based on the basic line types that forms the character skeleton. The system
gives a feature vector as its output. The feature vectors so generated from a
training set, were then used to train a pattern recognition engine based on
Neural Networks so that the system can be benchmarked.
|
1202.3887
|
Extended Mixture of MLP Experts by Hybrid of Conjugate Gradient Method
and Modified Cuckoo Search
|
cs.AI
|
This paper investigates a new method for improving the learning algorithm of
Mixture of Experts (ME) model using a hybrid of Modified Cuckoo Search (MCS)
and Conjugate Gradient (CG) as a second order optimization technique. The CG
technique is combined with Back-Propagation (BP) algorithm to yield a much more
efficient learning algorithm for ME structure. In addition, the experts and
gating networks in enhanced model are replaced by CG based Multi-Layer
Perceptrons (MLPs) to provide faster and more accurate learning. The CG is
considerably depends on initial weights of connections of Artificial Neural
Network (ANN), so, a metaheuristic algorithm, the so-called Modified Cuckoo
Search is applied in order to select the optimal weights. The performance of
proposed method is compared with Gradient Decent Based ME (GDME) and Conjugate
Gradient Based ME (CGME) in classification and regression problems. The
experimental results show that hybrid MSC and CG based ME (MCS-CGME) has faster
convergence and better performance in utilized benchmark data sets.
|
1202.3890
|
PAC Bounds for Discounted MDPs
|
cs.LG
|
We study upper and lower bounds on the sample-complexity of learning
near-optimal behaviour in finite-state discounted Markov Decision Processes
(MDPs). For the upper bound we make the assumption that each action leads to at
most two possible next-states and prove a new bound for a UCRL-style algorithm
on the number of time-steps when it is not Probably Approximately Correct
(PAC). The new lower bound strengthens previous work by being both more general
(it applies to all policies) and tighter. The upper and lower bounds match up
to logarithmic factors.
|
1202.3910
|
Performance of Amplify-and-Forward Multihop Transmission over Relay
Clusters with Different Routing Strategies
|
cs.IT math.IT
|
We Consider a multihop relay network in which two terminals are communicating
with each other via a number of cluster of relays. Performance of such networks
depends on the routing protocols employed. In this paper, we find the
expressions for the average symbol error probability (ASEP) performance of
amplify-and-forward (AF) multihop transmission for the simplest routing
protocol in which the relay transmits using the channel having the best symbol
to noise ratio (SNR). The ASEP performance of a better protocol proposed in [1]
known as the adhoc protocol is also analyzed. The derived expressions for the
performance are a convenient tool to analyze the performance of AF multihop
transmission over relay clusters. Monte-Carlo simulations verify the
correctness of the proposed formulation and are in agreement with analytical
results. Furthermore, we propose new generalized protocols termed as last-n-hop
selection protocol, the dual path protocol, the forward- backward last-n-hop
selection protocol, and the forward-backward dual path protocol, to get
improved ASEP performances. The ASEP performance of these proposed schemes is
analysed by computer simulations. It is shown that close to optimal performance
can be achieved by using the last-n-hop selection protocol and its
forward-backward variant. The complexity of the protocols is also studied.
|
1202.3913
|
Greedy Adaptive Compression in Signal-Plus-Noise Models
|
cs.IT math.IT
|
The purpose of this article is to examine the greedy adaptive measurement
policy in the context of a linear Guassian measurement model with an
optimization criterion based on information gain. In the special case of
sequential scalar measurements, we provide sufficient conditions under which
the greedy policy actually is optimal in the sense of maximizing the net
information gain. In the general setting, we also discuss cases where the
greedy policy is not optimal.
|
1202.3914
|
A formal proof of the optimal frame setting for Dynamic-Frame Aloha with
known population size
|
cs.IT math.IT
|
In Dynamic-Frame Aloha subsequent frame lengths must be optimally chosen to
maximize throughput. When the initial population size ${\cal N}$ is known,
numerical evaluations show that the maximum efficiency is achieved by setting
the frame length equal to the backlog size at each subsequent frame; however,
at best of our knowledge, a formal proof of this result is still missing, and
is provided here. As byproduct, we also prove that the asymptotical efficiency
in the optimal case is $e^{-1}$, provide upper and lower bounds for the length
of the entire transmission period and show that its asymptotical behaviour is
$\sim ne-\zeta \ln (n)$, with $\zeta=0.5/\ln(1-e^{-1})$.
|
1202.3957
|
Alternating register automata on finite words and trees
|
cs.DB cs.FL cs.LO
|
We study alternating register automata on data words and data trees in
relation to logics. A data word (resp. data tree) is a word (resp. tree) whose
every position carries a label from a finite alphabet and a data value from an
infinite domain. We investigate one-way automata with alternating control over
data words or trees, with one register for storing data and comparing them for
equality. This is a continuation of the study started by Demri, Lazic and
Jurdzinski. From the standpoint of register automata models, this work aims at
two objectives: (1) simplifying the existent decidability proofs for the
emptiness problem for alternating register automata; and (2) exhibiting
decidable extensions for these models. From the logical perspective, we show
that (a) in the case of data words, satisfiability of LTL with one register and
quantification over data values is decidable; and (b) the satisfiability
problem for the so-called forward fragment of XPath on XML documents is
decidable, even in the presence of DTDs and even of key constraints. The
decidability is obtained through a reduction to the automata model introduced.
This fragment contains the child, descendant, next-sibling and
following-sibling axes, as well as data equality and inequality tests.
|
1202.3987
|
Beyond the Blacklist: Modeling Malware Spread and the Effect of
Interventions
|
cs.CR cs.SI
|
Malware spread among websites and between websites and clients is an
increasing problem. Search engines play an important role in directing users to
websites and are a natural control point for intervening, using mechanisms such
as blacklisting. The paper presents a simple Markov model of malware spread
through large populations of websites and studies the effect of two
interventions that might be deployed by a search provider: blacklisting
infected web pages by removing them from search results entirely and a
generalization of blacklisting, called depreferencing, in which a website's
ranking is decreased by a fixed percentage each time period the site remains
infected. We analyze and study the trade-offs between infection exposure and
traffic loss due to false positives (the cost to a website that is incorrectly
blacklisted) for different interventions. As expected, we find that
interventions are most effective when websites are slow to remove infections.
Surprisingly, we also find that low infection or recovery rates can increase
traffic loss due to false positives. Our analysis also shows that heavy-tailed
distributions of website popularity, as documented in many studies, leads to
high sample variance of all measured outcomes. These result implies that it
will be difficult to determine empirically whether certain website
interventions are effective, and it suggests that theoretical models such as
the one described in this paper have an important role to play in improving web
security.
|
1202.3993
|
Internet Topology over Time
|
cs.NI cs.SI
|
There are few studies that look closely at how the topology of the Internet
evolves over time; most focus on snapshots taken at a particular point in time.
In this paper, we investigate the evolution of the topology of the Autonomous
Systems graph of the Internet, examining how eight commonly-used topological
measures change from January 2002 to January 2010. We find that the
distributions of most of the measures remain unchanged, except for average path
length and clustering coefficient. The average path length has slowly and
steadily increased since 2005 and the average clustering coefficient has
steadily declined. We hypothesize that these changes are due to changes in
peering policies as the Internet evolves. We also investigate a surprising
feature, namely that the maximum degree has changed little, an aspect that
cannot be captured without modeling link deletion. Our results suggest that
evaluating models of the Internet graph by comparing steady-state generated
topologies to snapshots of the real data is reasonable for many measures.
However, accurately matching time-variant properties is more difficult, as we
demonstrate by evaluating ten well-known models against the 2010 data.
|
1202.4002
|
Generalized Principal Component Analysis (GPCA)
|
cs.CV cs.LG
|
This paper presents an algebro-geometric solution to the problem of
segmenting an unknown number of subspaces of unknown and varying dimensions
from sample data points. We represent the subspaces with a set of homogeneous
polynomials whose degree is the number of subspaces and whose derivatives at a
data point give normal vectors to the subspace passing through the point. When
the number of subspaces is known, we show that these polynomials can be
estimated linearly from data; hence, subspace segmentation is reduced to
classifying one point per subspace. We select these points optimally from the
data set by minimizing certain distance function, thus dealing automatically
with moderate noise in the data. A basis for the complement of each subspace is
then recovered by applying standard PCA to the collection of derivatives
(normal vectors). Extensions of GPCA that deal with data in a high- dimensional
space and with an unknown number of subspaces are also presented. Our
experiments on low-dimensional data show that GPCA outperforms existing
algebraic algorithms based on polynomial factorization and provides a good
initialization to iterative techniques such as K-subspaces and Expectation
Maximization. We also present applications of GPCA to computer vision problems
such as face clustering, temporal video segmentation, and 3D motion
segmentation from point correspondences in multiple affine views.
|
1202.4008
|
Modeling Internet-Scale Policies for Cleaning up Malware
|
cs.NI cs.CR cs.MA
|
An emerging consensus among policy makers is that interventions undertaken by
Internet Service Providers are the best way to counter the rising incidence of
malware. However, assessing the suitability of countermeasures at this scale is
hard. In this paper, we use an agent-based model, called ASIM, to investigate
the impact of policy interventions at the Autonomous System level of the
Internet. For instance, we find that coordinated intervention by the
0.2%-biggest ASes is more effective than uncoordinated efforts adopted by 30%
of all ASes. Furthermore, countermeasures that block malicious transit traffic
appear more effective than ones that block outgoing traffic. The model allows
us to quantify and compare positive externalities created by different
countermeasures. Our results give an initial indication of the types and levels
of intervention that are most cost-effective at large scale.
|
1202.4033
|
Energy Efficient Greedy Link Scheduling and Power Control in wireless
networks
|
cs.NI cs.IT math.IT
|
We consider the problem of joint link scheduling and power control for
wireless networks with average transmission power constraints. Due to the high
computational complexity of the optimal policies, we extend the class of greedy
link scheduling policies to handle average power constraints. We develop a
greedy link scheduling and power control scheme GECS, with provable performance
guarantees.
We show that the performance of our greedy scheduler can be characterized
using the Local Pooling Factor (LPF) of a network graph, which has been
previously used to characterize the stability of the Greedy Maximal Scheduling
(GMS) policy for wireless networks. We also simulate the performance of GECS on
wireless network, and compare its performance to another candidate greedy link
scheduling and power control policy.
|
1202.4034
|
PAR-Aware Large-Scale Multi-User MIMO-OFDM Downlink
|
cs.IT math.IT
|
We investigate an orthogonal frequency-division multiplexing (OFDM)-based
downlink transmission scheme for large-scale multi-user (MU) multiple-input
multiple-output (MIMO) wireless systems. The use of OFDM causes a high
peak-to-average (power) ratio (PAR), which necessitates expensive and
power-inefficient radio-frequency (RF) components at the base station. In this
paper, we present a novel downlink transmission scheme, which exploits the
massive degrees-of-freedom available in large-scale MU-MIMO-OFDM systems to
achieve low PAR. Specifically, we propose to jointly perform MU precoding, OFDM
modulation, and PAR reduction by solving a convex optimization problem. We
develop a corresponding fast iterative truncation algorithm (FITRA) and show
numerical results to demonstrate tremendous PAR-reduction capabilities. The
significantly reduced linearity requirements eventually enable the use of
low-cost RF components for the large-scale MU-MIMO-OFDM downlink.
|
1202.4041
|
Simple transmission strategies for interference channel
|
cs.IT math.IT
|
In this paper, we investigate performances of simple transmission strategies.
We first consider two user SISO Gaussian symmetric interference channel (IC)
for which Etkin, Tse and Wang proposed a scheme (ETW scheme) which achieves one
bit gap to the capacity. We compare performance of point-to-point (p2p) codes
with that of the ETW scheme in practical range of transmitter power. It turns
out that p2p coding scheme performs better or as nearly good as the ETW scheme.
Next, we consider K user SISO Gaussian symmetric IC. We define interference
regimes for K user SISO Gaussian symmetric IC and provide closed-form
characterization of the symmetric rate achieved by the p2p scheme and the ETW
scheme. Using this characterization, we evaluate performances of simple
strategies with K=3, and show the similar trend to two user case.
|
1202.4044
|
Robust computation of linear models by convex relaxation
|
cs.IT math.IT stat.CO stat.ML
|
Consider a dataset of vector-valued observations that consists of noisy
inliers, which are explained well by a low-dimensional subspace, along with
some number of outliers. This work describes a convex optimization problem,
called REAPER, that can reliably fit a low-dimensional model to this type of
data. This approach parameterizes linear subspaces using orthogonal projectors,
and it uses a relaxation of the set of orthogonal projectors to reach the
convex formulation. The paper provides an efficient algorithm for solving the
REAPER problem, and it documents numerical experiments which confirm that
REAPER can dependably find linear structure in synthetic and natural data. In
addition, when the inliers lie near a low-dimensional subspace, there is a
rigorous theory that describes when REAPER can approximate this subspace.
|
1202.4050
|
On the Sample Complexity of Predictive Sparse Coding
|
cs.LG stat.ML
|
The goal of predictive sparse coding is to learn a representation of examples
as sparse linear combinations of elements from a dictionary, such that a
learned hypothesis linear in the new representation performs well on a
predictive task. Predictive sparse coding algorithms recently have demonstrated
impressive performance on a variety of supervised tasks, but their
generalization properties have not been studied. We establish the first
generalization error bounds for predictive sparse coding, covering two
settings: 1) the overcomplete setting, where the number of features k exceeds
the original dimensionality d; and 2) the high or infinite-dimensional setting,
where only dimension-free bounds are useful. Both learning bounds intimately
depend on stability properties of the learned sparse encoder, as measured on
the training sample. Consequently, we first present a fundamental stability
result for the LASSO, a result characterizing the stability of the sparse codes
with respect to perturbations to the dictionary. In the overcomplete setting,
we present an estimation error bound that decays as \tilde{O}(sqrt(d k/m)) with
respect to d and k. In the high or infinite-dimensional setting, we show a
dimension-free bound that is \tilde{O}(sqrt(k^2 s / m)) with respect to k and
s, where s is an upper bound on the number of non-zeros in the sparse code for
any training data point.
|
1202.4063
|
Comparing SVM and Naive Bayes classifiers for text categorization with
Wikitology as knowledge enrichment
|
cs.AI cs.IR
|
The activity of labeling of documents according to their content is known as
text categorization. Many experiments have been carried out to enhance text
categorization by adding background knowledge to the document using knowledge
repositories like Word Net, Open Project Directory (OPD), Wikipedia and
Wikitology. In our previous work, we have carried out intensive experiments by
extracting knowledge from Wikitology and evaluating the experiment on Support
Vector Machine with 10- fold cross-validations. The results clearly indicate
Wikitology is far better than other knowledge bases. In this paper we are
comparing Support Vector Machine (SVM) and Na\"ive Bayes (NB) classifiers under
text enrichment through Wikitology. We validated results with 10-fold cross
validation and shown that NB gives an improvement of +28.78%, on the other hand
SVM gives an improvement of +6.36% when compared with baseline results. Na\"ive
Bayes classifier is better choice when external enriching is used through any
external knowledge base.
|
1202.4087
|
Epidemic spreading on interconnected networks
|
cond-mat.dis-nn cs.SI physics.soc-ph
|
Many real networks are not isolated from each other but form networks of
networks, often interrelated in non trivial ways. Here, we analyze an epidemic
spreading process taking place on top of two interconnected complex networks.
We develop a heterogeneous mean field approach that allows us to calculate the
conditions for the emergence of an endemic state. Interestingly, a global
endemic state may arise in the coupled system even though the epidemics is not
able to propagate on each network separately, and even when the number of
coupling connections is small. Our analytic results are successfully confronted
against large-scale numerical simulations.
|
1202.4098
|
Energy-Efficient Sensing and Communication of Parallel Gaussian Sources
|
cs.IT math.IT
|
Energy efficiency is a key requirement in the design of wireless sensor
networks. While most theoretical studies only account for the energy
requirements of communication, the sensing process, which includes measurements
and compression, can also consume comparable energy. In this paper, the problem
of sensing and communicating parallel sources is studied by accounting for the
cost of both communication and sensing. In the first formulation of the
problem, the sensor has a separate energy budget for sensing and a rate budget
for communication, while, in the second, it has a single energy budget for both
tasks. Assuming that sources with larger variances have lower sensing costs,
the optimal allocation of sensing energy and rate that minimizes the overall
distortion is derived for the first problem. Moreover, structural results on
the solution of the second problem are derived under the assumption that the
sources with larger variances are transmitted on channels with lower noise.
Closed-form solutions are also obtained for the case where the energy budget is
sufficiently large. For an arbitrary order on the variances and costs, the
optimal solution to the first problem is also obtained numerically and compared
with several suboptimal strategies.
|
1202.4107
|
Unsupervised Threshold for Automatic Extraction of Dolphin Dorsal Fin
Outlines from Digital Photographs in DARWIN (Digital Analysis and Recognition
of Whale Images on a Network)
|
cs.CV
|
At least two software packages---DARWIN, Eckerd College, and FinScan, Texas
A&M---exist to facilitate the identification of cetaceans---whales, dolphins,
porpoises---based upon the naturally occurring features along the edges of
their dorsal fins. Such identification is useful for biological studies of
population, social interaction, migration, etc. The process whereby fin
outlines are extracted in current fin-recognition software packages is manually
intensive and represents a major user input bottleneck: it is both time
consuming and visually fatiguing. This research aims to develop automated
methods (employing unsupervised thresholding and morphological processing
techniques) to extract cetacean dorsal fin outlines from digital photographs
thereby reducing manual user input. Ideally, automatic outline generation will
improve the overall user experience and improve the ability of the software to
correctly identify cetaceans. Various transformations from color to gray space
were examined to determine which produced a grayscale image in which a suitable
threshold could be easily identified. To assist with unsupervised thresholding,
a new metric was developed to evaluate the jaggedness of figures ("pixelarity")
in an image after thresholding. The metric indicates how cleanly a threshold
segments background and foreground elements and hence provides a good measure
of the quality of a given threshold. This research results in successful
extractions in roughly 93% of images, and significantly reduces user-input
time.
|
1202.4144
|
Towards an efficient prover for the C1 paraconsistent logic
|
cs.LO cs.AI
|
The KE inference system is a tableau method developed by Marco Mondadori
which was presented as an improvement, in the computational efficiency sense,
over Analytic Tableaux. In the literature, there is no description of a theorem
prover based on the KE method for the C1 paraconsistent logic. Paraconsistent
logics have several applications, such as in robot control and medicine. These
applications could benefit from the existence of such a prover. We present a
sound and complete KE system for C1, an informal specification of a strategy
for the C1 prover as well as problem families that can be used to evaluate
provers for C1. The C1 KE system and the strategy described in this paper will
be used to implement a KE based prover for C1, which will be useful for those
who study and apply paraconsistent logics.
|
1202.4170
|
Classification by Ensembles of Neural Networks
|
cs.NE cond-mat.dis-nn
|
We introduce a new procedure for training of artificial neural networks by
using the approximation of an objective function by arithmetic mean of an
ensemble of selected randomly generated neural networks, and apply this
procedure to the classification (or pattern recognition) problem. This approach
differs from the standard one based on the optimization theory. In particular,
any neural network from the mentioned ensemble may not be an approximation of
the objective function.
|
1202.4174
|
Perception Lie Paradox: Mathematically Proved Uncertainty about Humans
Perception Similarity
|
q-bio.NC cs.AI
|
Agents' judgment depends on perception and previous knowledge. Assuming that
previous knowledge depends on perception, we can say that judgment depends on
perception. So, if judgment depends on perception, can agents judge that they
have the same perception? In few words, this is the addressed paradox through
this document. While illustrating on the paradox, it's found that to reach
agreement in communication, it's not necessary for parties to have the same
perception however the necessity is to have perception correspondence. The
attempted solution to this paradox reveals a potential uncertainty in judging
the matter thus supporting the skeptical view of the problem. Moreover,
relating perception to intelligence, the same uncertainty is inherited by
judging the level of intelligence of an agent compared to others not
necessarily from the same kind (e.g. machine intelligence compared to human
intelligence). Using a proposed simple mathematical model for perception and
action, a tool is developed to construct scenarios, and the problem is
addressed mathematically such that conclusions are drawn systematically based
on mathematically defined properties. When it comes to formalization,
philosophical arguments and views become more visible and explicit.
|
1202.4177
|
$Q$- and $A$-Learning Methods for Estimating Optimal Dynamic Treatment
Regimes
|
stat.ME cs.AI
|
In clinical practice, physicians make a series of treatment decisions over
the course of a patient's disease based on his/her baseline and evolving
characteristics. A dynamic treatment regime is a set of sequential decision
rules that operationalizes this process. Each rule corresponds to a decision
point and dictates the next treatment action based on the accrued information.
Using existing data, a key goal is estimating the optimal regime, that, if
followed by the patient population, would yield the most favorable outcome on
average. Q- and A-learning are two main approaches for this purpose. We provide
a detailed account of these methods, study their performance, and illustrate
them using data from a depression study.
|
1202.4180
|
On Finding Sub-optimum Signature Matrices for Overloaded CDMA Systems
|
cs.IT math.IT
|
The objective of this paper is to design optimal signature matrices for
binary inputs. For the determination of such optimal codes, we need certain
measures as objective functions. The sum-channel capacity and Bit Error Rate
(BER) measures are typical methods for the evaluation of signature matrices. In
this paper, in addition to these measures, we use distance criteria to evaluate
the optimality of signature matrices. The Genetic Algorithm (GA) and Particle
Swarm Optimization (PSO) are used to search the optimum signature matrices
based on these three measures (Sum channel capacity, BER and Distance). Since
the GA and PSO algorithms become computationally expensive for large signature
matrices, we propose suboptimal large signature matrices that can be derived
from small suboptimal matrices.
|
1202.4190
|
Generalized FMD Detection for Spectrum Sensing Under Low Signal-to-Noise
Ratio
|
cs.AI
|
Spectrum sensing is a fundamental problem in cognitive radio. We propose a
function of covariance matrix based detection algorithm for spectrum sensing in
cognitive radio network. Monotonically increasing property of function of
matrix involving trace operation is utilized as the cornerstone for this
algorithm. The advantage of proposed algorithm is it works under extremely low
signal-to-noise ratio, like lower than -30 dB with limited sample data.
Theoretical analysis of threshold setting for the algorithm is discussed. A
performance comparison between the proposed algorithm and other
state-of-the-art methods is provided, by the simulation on captured digital
television (DTV) signal.
|
1202.4207
|
Regularized Robust Coding for Face Recognition
|
cs.CV
|
Recently the sparse representation based classification (SRC) has been
proposed for robust face recognition (FR). In SRC, the testing image is coded
as a sparse linear combination of the training samples, and the representation
fidelity is measured by the l2-norm or l1-norm of the coding residual. Such a
sparse coding model assumes that the coding residual follows Gaussian or
Laplacian distribution, which may not be effective enough to describe the
coding residual in practical FR systems. Meanwhile, the sparsity constraint on
the coding coefficients makes SRC's computational cost very high. In this
paper, we propose a new face coding model, namely regularized robust coding
(RRC), which could robustly regress a given signal with regularized regression
coefficients. By assuming that the coding residual and the coding coefficient
are respectively independent and identically distributed, the RRC seeks for a
maximum a posterior solution of the coding problem. An iteratively reweighted
regularized robust coding (IR3C) algorithm is proposed to solve the RRC model
efficiently. Extensive experiments on representative face databases demonstrate
that the RRC is much more effective and efficient than state-of-the-art sparse
representation based methods in dealing with face occlusion, corruption,
lighting and expression changes, etc.
|
1202.4232
|
Boundary Conditions of Subharmonic Oscillations in
Fixed-Switching-Frequency DC-DC Converters
|
cs.SY math.DS nlin.CD
|
Design-oriented boundary conditions for subharmonic oscillations are of great
interest recently. Based on a subharmonic oscillation boundary condition
reported in a PhD thesis more than a decade ago, extended new boundary
conditions are derived in closed forms for general switching DC-DC converters.
Sampled-data and harmonic balance analyses are applied and generate equivalent
results. It is shown that equivalent series resistance causes the boundary
conditions for voltage/current mode control to have similar forms. Some
recently reported boundary conditions become special cases in view of the
general boundary conditions derived. New Nyquist-like design-oriented plots are
proposed to predict or prevent the occurrence of the subharmonic oscillation.
The relation between the crossover frequency and the subharmonic oscillation is
also analyzed.
|
1202.4237
|
A Simple Unsupervised Color Image Segmentation Method based on MRF-MAP
|
cs.CV
|
Color image segmentation is an important topic in the image processing field.
MRF-MAP is often adopted in the unsupervised segmentation methods, but their
performance are far behind recent interactive segmentation tools supervised by
user inputs. Furthermore, the existing related unsupervised methods also suffer
from the low efficiency, and high risk of being trapped in the local optima,
because MRF-MAP is currently solved by iterative frameworks with inaccurate
initial color distribution models. To address these problems, the letter
designs an efficient method to calculate the energy functions approximately in
the non-iteration style, and proposes a new binary segmentation algorithm based
on the slightly tuned Lanczos eigensolver. The experiments demonstrate that the
new algorithm achieves competitive performance compared with two state-of-art
segmentation methods.
|
1202.4261
|
Immuno-inspired robotic applications: a review
|
cs.RO
|
Artificial immune systems primarily mimic the adaptive nature of biological
immune functions. Their ability to adapt to varying pathogens makes such
systems a suitable choice for various robotic applications. Generally,
AIS-based robotic applications map local instantaneous sensory information into
either an antigen or a co-stimulatory signal, according to the choice of
representation schema. Algorithms then use relevant immune functions to output
either evolved antibodies or maturity of dendritic cells, in terms of actuation
signals. It is observed that researchers, in an attempt to solve the problem in
hand, do not try to replicate the biological immunity but select necessary
immune functions instead, resulting in an ad-hoc manner these applications are
reported. Authors, therefore, present a comprehensive review of immuno-inspired
robotic applications in an attempt to categorize them according to underlying
immune definitions. Implementation details are tabulated in terms of
corresponding mathematical expressions and their representation schema that
include binary, real or hybrid data. Limitations of reported applications are
also identified in light of modern immunological interpretations. As a result
of this study, authors suggest a renewed focus on innate immunity and also
emphasize that immunological representations should benefit from robot
embodiment and must be extended to include modern trends.
|
1202.4329
|
Global Networks of Trade and Bits
|
physics.soc-ph cs.SI physics.data-an
|
Considerable efforts have been made in recent years to produce detailed
topologies of the Internet. Although Internet topology data have been brought
to the attention of a wide and somewhat diverse audience of scholars, so far
they have been overlooked by economists. In this paper, we suggest that such
data could be effectively treated as a proxy to characterize the size of the
"digital economy" at country level and outsourcing: thus, we analyse the
topological structure of the network of trade in digital services (trade in
bits) and compare it with that of the more traditional flow of manufactured
goods across countries. To perform meaningful comparisons across networks with
different characteristics, we define a stochastic benchmark for the number of
connections among each country-pair, based on hypergeometric distribution.
Original data are thus filtered by means of different thresholds, so that we
only focus on the strongest links, i.e., statistically significant links. We
find that trade in bits displays a sparser and less hierarchical network
structure, which is more similar to trade in high-skill manufactured goods than
total trade. Lastly, distance plays a more prominent role in shaping the
network of international trade in physical goods than trade in digital
services.
|
1202.4331
|
Strong Backdoors to Nested Satisfiability
|
cs.DS cs.AI cs.CC math.CO
|
Knuth (1990) introduced the class of nested formulas and showed that their
satisfiability can be decided in polynomial time. We show that, parameterized
by the size of a smallest strong backdoor set to the target class of nested
formulas, checking the satisfiability of any CNF formula is fixed-parameter
tractable. Thus, for any k>0, the satisfiability problem can be solved in
polynomial time for any formula F for which there exists a variable set B of
size at most k such that for every truth assignment t to B, the formula F[t] is
nested; moreover, the degree of the polynomial is independent of k.
Our algorithm uses the grid-minor theorem of Robertson and Seymour (1986) to
either find that the incidence graph of the formula has bounded treewidth - a
case that is solved using model checking for monadic second order logic - or to
find many vertex-disjoint obstructions in the incidence graph. For the latter
case, new combinatorial arguments are used to find a small backdoor set.
Combining both cases leads to an approximation algorithm producing a strong
backdoor set whose size is upper bounded by a function of the optimum. Going
through all assignments to this set of variables and using Knuth's algorithm,
the satisfiability of the input formula is decided.
|
1202.4361
|
Discrete logarithm computations over finite fields using Reed-Solomon
codes
|
math.NT cs.IT math.IT
|
Cheng and Wan have related the decoding of Reed-Solomon codes to the
computation of discrete logarithms over finite fields, with the aim of proving
the hardness of their decoding. In this work, we experiment with solving the
discrete logarithm over GF(q^h) using Reed-Solomon decoding. For fixed h and q
going to infinity, we introduce an algorithm (RSDL) needing O (h! q^2)
operations over GF(q), operating on a q x q matrix with (h+2) q non-zero
coefficients. We give faster variants including an incremental version and
another one that uses auxiliary finite fields that need not be subfields of
GF(q^h); this variant is very practical for moderate values of q and h. We
include some numerical results of our first implementations.
|
1202.4372
|
Linear approach to the orbiting spacecraft thermal problem
|
cs.CE cs.SY physics.class-ph
|
We develop a linear method for solving the nonlinear differential equations
of a lumped-parameter thermal model of a spacecraft moving in a closed orbit.
Our method, based on perturbation theory, is compared with heuristic
linearizations of the same equations. The essential feature of the linear
approach is that it provides a decomposition in thermal modes, like the
decomposition of mechanical vibrations in normal modes. The stationary periodic
solution of the linear equations can be alternately expressed as an explicit
integral or as a Fourier series. We apply our method to a minimal thermal model
of a satellite with ten isothermal parts (nodes) and we compare the method with
direct numerical integration of the nonlinear equations. We briefly study the
computational complexity of our method for general thermal models of orbiting
spacecraft and conclude that it is certainly useful for reduced models and
conceptual design but it can also be more efficient than the direct integration
of the equations for large models. The results of the Fourier series
computations for the ten-node satellite model show that the periodic solution
at the second perturbative order is sufficiently accurate.
|
1202.4375
|
The Stochastic Reach-Avoid Problem and Set Characterization for
Diffusions
|
math.OC cs.SY
|
In this article we approach a class of stochastic reachability problems with
state constraints from an optimal control perspective. Preceding approaches to
solving these reachability problems are either confined to the deterministic
setting or address almost-sure stochastic requirements. In contrast, we propose
a methodology to tackle problems with less stringent requirements than almost
sure. To this end, we first establish a connection between two distinct
stochastic reach-avoid problems and three classes of stochastic optimal control
problems involving discontinuous payoff functions. Subsequently, we focus on
solutions of one of the classes of stochastic optimal control problems---the
exit-time problem, which solves both the two reach-avoid problems mentioned
above. We then derive a weak version of a dynamic programming principle (DPP)
for the corresponding value function; in this direction our contribution
compared to the existing literature is to develop techniques that admit
discontinuous payoff functions. Moreover, based on our DPP, we provide an
alternative characterization of the value function as a solution of a partial
differential equation in the sense of discontinuous viscosity solutions, along
with boundary conditions both in Dirichlet and viscosity senses. Theoretical
justifications are also discussed to pave the way for deployment of
off-the-shelf PDE solvers for numerical computations. Finally, we validate the
performance of the proposed framework on the stochastic Zermelo navigation
problem.
|
1202.4385
|
An Overview of Local Capacity in Wireless Networks
|
cs.IT cs.NI math.IT
|
This article introduces a metric for performance evaluation of medium access
schemes in wireless ad hoc networks known as local capacity. Although deriving
the end-to-end capacity of wireless ad hoc networks is a difficult problem, the
local capacity framework allows us to quantify the average information rate
received by a receiver node randomly located in the network. In this article,
the basic network model and analytical tools are first discussed and applied to
a simple network to derive the local capacity of various medium access schemes.
Our goal is to identify the most optimal scheme and also to see how does it
compare with more practical medium access schemes. We analyzed grid pattern
schemes where simultaneous transmitters are positioned in a regular grid
pattern, ALOHA schemes where simultaneous transmitters are dispatched according
to a uniform Poisson distribution and exclusion schemes where simultaneous
transmitters are dispatched according to an exclusion rule such as node
coloring and carrier sense schemes. Our analysis shows that local capacity is
optimal when simultaneous transmitters are positioned in a grid pattern based
on equilateral triangles and our results show that this optimal local capacity
is at most double the local capacity of ALOHA based scheme. Our results also
show that node coloring and carrier sense schemes approach the optimal local
capacity by an almost negligible difference. At the end, we also discuss the
shortcomings in our model as well as future research directions.
|
1202.4387
|
Locally Linear Embedding Clustering Algorithm for Natural Imagery
|
math.GT cs.CG cs.CV
|
The ability to characterize the color content of natural imagery is an
important application of image processing. The pixel by pixel coloring of
images may be viewed naturally as points in color space, and the inherent
structure and distribution of these points affords a quantization, through
clustering, of the color information in the image. In this paper, we present a
novel topologically driven clustering algorithm that permits segmentation of
the color features in a digital image. The algorithm blends Locally Linear
Embedding (LLE) and vector quantization by mapping color information to a lower
dimensional space, identifying distinct color regions, and classifying pixels
together based on both a proximity measure and color content. It is observed
that these techniques permit a significant reduction in color resolution while
maintaining the visually important features of images.
|
1202.4393
|
An Exploration of Social Identity: The Geography and Politics of
News-Sharing Communities in Twitter
|
physics.soc-ph cs.CY cs.SI nlin.AO
|
The importance of collective social action in current events is manifest in
the Arab Spring and Occupy movements. Electronic social media have become a
pervasive channel for social interactions, and a basis of collective social
response to information. The study of social media can reveal how individual
actions combine to become the collective dynamics of society. Characterizing
the groups that form spontaneously may reveal both how individuals
self-identify and how they will act together. Here we map the social,
political, and geographical properties of news-sharing communities on Twitter,
a popular micro-blogging platform. We track user-generated messages that
contain links to New York Times online articles and we label users according to
the topic of the links they share, their geographic location, and their
self-descriptive keywords. When users are clustered based on who follows whom
in Twitter, we find social groups separate by whether they are interested in
local (NY), national (US) or global (cosmopolitan) issues. The national group
subdivides into liberal, conservative and other, the latter being a diverse but
mostly business oriented group with sports, arts and other splinters. The
national political groups are based across the US but are distinct from the
national group that is broadly interested in a variety of topics. A person who
is cosmopolitan associates with others who are cosmopolitan, and a US liberal /
conservative associates with others who are US liberal / conservative, creating
separated social groups with those identities. The existence of "citizens" of
local, national and cosmopolitan communities is a basis for dialog and action
at each of these levels of societal organization.
|
1202.4411
|
Localization and Spreading of Diseases in Complex Networks
|
physics.soc-ph cond-mat.dis-nn cs.SI physics.bio-ph
|
Using the SIS model on unweighted and weighted networks, we consider the
disease localization phenomenon. In contrast to the well-recognized point of
view that diseases infect a finite fraction of vertices right above the
epidemic threshold, we show that diseases can be localized on a finite number
of vertices, where hubs and edges with large weights are centers of
localization. Our results follow from the analysis of standard models of
networks and empirical data for real-world networks.
|
1202.4425
|
Relay Channel with Orthogonal Components and Structured Interference
Known at the Source
|
cs.IT math.IT
|
A relay channel with orthogonal components that is affected by an
interference signal that is noncausally available only at the source is
studied. The interference signal has structure in that it is produced by
another transmitter communicating with its own destination. Moreover, the
interferer is not willing to adjust its communication strategy to minimize the
interference. Knowledge of the interferer's signal may be acquired by the
source, for instance, by exploiting HARQ retransmissions on the interferer's
link. The source can then utilize the relay not only for communicating its own
message, but also for cooperative interference mitigation at the destination by
informing the relay about the interference signal. Proposed transmission
strategies are based on partial decode-and-forward (PDF) relaying and leverage
the interference structure. Achievable schemes are derived for discrete
memoryless models, Gaussian and Ricean fading channels. Furthermore, optimal
strategies are identified in some special cases. Finally, numerical results
bring insight into the advantages of utilizing the interference structure at
the source, relay or destination.
|
1202.4438
|
On Channels with Action-Dependent States
|
cs.IT math.IT
|
Action-dependent channels model scenarios in which transmission takes place
in two successive phases. In the first phase, the encoder selects an "action"
sequence, with the twofold aim of conveying information to the receiver and of
affecting in a desired way the state of the channel to be used in the second
phase. In the second phase, communication takes place in the presence the
mentioned action-dependent state. In this work, two extensions of the original
action-dependent channel are studied. In the first, the decoder is interested
in estimating not only the message, but also the state sequence within an
average per-letter distortion. Under the constraint of common knowledge (i.e.,
the decoder's estimate of the state must be recoverable also at the encoder)
and assuming non-causal state knowledge at the encoder in the second phase, we
obtain a single-letter characterization of the achievable rate-distortion-cost
trade-off. In the second extension, we study an action-dependent degraded
broadcast channel. Under the assumption that the encoder knows the state
sequence causally in the second phase, the capacity-cost region is identified.
Various examples, including Gaussian channels and a model with a "probing"
encoder, are also provided to show the advantage of a proper joint design of
the two communication phases.
|
1202.4446
|
Fast and Accurate Frequency Estimation Using Sliding DFT
|
cs.SY
|
Frequency Estimation of a complex exponential is a problem relevant to a
large number of fields. In this paper a computationally efficient and accurate
frequency estimator is presented using the guaranteed stable Sliding DFT which
gives stability as well as computational efficiency. The estimator approaches
Jacobsen's estimator and Candan's estimator for large N with an extra
correction term multiplied to it for the stabilization of the sliding DFT.
Simulation results show that the performance of the proposed estimator were
found to be better than Jacobsen's estimator and Candan's estimator.
|
1202.4465
|
MAV Stabilization using Machine Learning and Onboard Sensors
|
cs.RO cs.AI
|
In many situations, Miniature Aerial Vehicles (MAVs) are limited to using
only on-board sensors for navigation. This limits the data available to
algorithms used for stabilization and localization, and current control methods
are often insufficient to allow reliable hovering in place or trajectory
following. In this research, we explore using machine learning to predict the
drift (flight path errors) of an MAV while executing a desired flight path.
This predicted drift will allow the MAV to adjust it's flightpath to maintain a
desired course.
|
1202.4473
|
The best of both worlds: stochastic and adversarial bandits
|
cs.LG cs.DS
|
We present a new bandit algorithm, SAO (Stochastic and Adversarial Optimal),
whose regret is, essentially, optimal both for adversarial rewards and for
stochastic rewards. Specifically, SAO combines the square-root worst-case
regret of Exp3 (Auer et al., SIAM J. on Computing 2002) and the
(poly)logarithmic regret of UCB1 (Auer et al., Machine Learning 2002) for
stochastic rewards. Adversarial rewards and stochastic rewards are the two main
settings in the literature on (non-Bayesian) multi-armed bandits. Prior work on
multi-armed bandits treats them separately, and does not attempt to jointly
optimize for both. Our result falls into a general theme of achieving good
worst-case performance while also taking advantage of "nice" problem instances,
an important issue in the design of algorithms with partially known inputs.
|
1202.4478
|
(weak) Calibration is Computationally Hard
|
cs.GT cs.AI cs.LG stat.ML
|
We show that the existence of a computationally efficient calibration
algorithm, with a low weak calibration rate, would imply the existence of an
efficient algorithm for computing approximate Nash equilibria - thus implying
the unlikely conclusion that every problem in PPAD is solvable in polynomial
time.
|
1202.4482
|
Metabolic cost as an organizing principle for cooperative learning
|
q-bio.NC cs.LG nlin.AO
|
This paper investigates how neurons can use metabolic cost to facilitate
learning at a population level. Although decision-making by individual neurons
has been extensively studied, questions regarding how neurons should behave to
cooperate effectively remain largely unaddressed. Under assumptions that
capture a few basic features of cortical neurons, we show that constraining
reward maximization by metabolic cost aligns the information content of actions
with their expected reward. Thus, metabolic cost provides a mechanism whereby
neurons encode expected reward into their outputs. Further, aside from reducing
energy expenditures, imposing a tight metabolic constraint also increases the
accuracy of empirical estimates of rewards, increasing the robustness of
distributed learning. Finally, we present two implementations of metabolically
constrained learning that confirm our theoretical finding. These results
suggest that metabolic cost may be an organizing principle underlying the
neural code, and may also provide a useful guide to the design and analysis of
other cooperating populations.
|
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