4,663 research outputs found
Isoelastic Agents and Wealth Updates in Machine Learning Markets
Recently, prediction markets have shown considerable promise for developing
flexible mechanisms for machine learning. In this paper, agents with isoelastic
utilities are considered. It is shown that the costs associated with
homogeneous markets of agents with isoelastic utilities produce equilibrium
prices corresponding to alpha-mixtures, with a particular form of mixing
component relating to each agent's wealth. We also demonstrate that wealth
accumulation for logarithmic and other isoelastic agents (through payoffs on
prediction of training targets) can implement both Bayesian model updates and
mixture weight updates by imposing different market payoff structures. An
iterative algorithm is given for market equilibrium computation. We demonstrate
that inhomogeneous markets of agents with isoelastic utilities outperform state
of the art aggregate classifiers such as random forests, as well as single
classifiers (neural networks, decision trees) on a number of machine learning
benchmarks, and show that isoelastic combination methods are generally better
than their logarithmic counterparts.Comment: Appears in Proceedings of the 29th International Conference on
Machine Learning (ICML 2012
Algorithm for SIS and MultiSIS problems
SIS problem has numerous applications in cryptography. Known algorithms for
solving that problem are exponential in complexity. A new algorithm is
suggested in this note, its complexity is sub-exponential for a range of
parameters
Containing epidemic outbreaks by message-passing techniques
The problem of targeted network immunization can be defined as the one of
finding a subset of nodes in a network to immunize or vaccinate in order to
minimize a tradeoff between the cost of vaccination and the final (stationary)
expected infection under a given epidemic model. Although computing the
expected infection is a hard computational problem, simple and efficient
mean-field approximations have been put forward in the literature in recent
years. The optimization problem can be recast into a constrained one in which
the constraints enforce local mean-field equations describing the average
stationary state of the epidemic process. For a wide class of epidemic models,
including the susceptible-infected-removed and the
susceptible-infected-susceptible models, we define a message-passing approach
to network immunization that allows us to study the statistical properties of
epidemic outbreaks in the presence of immunized nodes as well as to find
(nearly) optimal immunization sets for a given choice of parameters and costs.
The algorithm scales linearly with the size of the graph and it can be made
efficient even on large networks. We compare its performance with topologically
based heuristics, greedy methods, and simulated annealing
Resampling: an improvement of Importance Sampling in varying population size models
Sequential importance sampling algorithms have been defined to estimate
likelihoods in models of ancestral population processes. However, these
algorithms are based on features of the models with constant population size,
and become inefficient when the population size varies in time, making
likelihood-based inferences difficult in many demographic situations. In this
work, we modify a previous sequential importance sampling algorithm to improve
the efficiency of the likelihood estimation. Our procedure is still based on
features of the model with constant size, but uses a resampling technique with
a new resampling probability distribution depending on the pairwise composite
likelihood. We tested our algorithm, called sequential importance sampling with
resampling (SISR) on simulated data sets under different demographic cases. In
most cases, we divided the computational cost by two for the same accuracy of
inference, in some cases even by one hundred. This study provides the first
assessment of the impact of such resampling techniques on parameter inference
using sequential importance sampling, and extends the range of situations where
likelihood inferences can be easily performed
Effect of collisions on neutrino flavor inhomogeneity in a dense neutrino gas
We investigate the stability, with respect to spatial inhomogeneity, of a
two-dimensional dense neutrino gas. The system exhibits growth of seed
inhomogeneity due to nonlinear coherent neutrino self-interactions. In the
absence of incoherent collisional effects, we observe a dependence of this
instability growth rate on the neutrino mass spectrum: the normal neutrino mass
hierarchy exhibits spatial instability over a larger range of neutrino number
density compared to that of the inverted case. We further consider the effect
of elastic incoherent collisions of the neutrinos with a static background of
heavy, nucleon-like scatterers. At small scales, the growth of flavor
instability can be suppressed by collisions. At large length scales we find,
perhaps surprisingly, that for inverted neutrino mass hierarchy incoherent
collisions fail to suppress flavor instabilities, independent of the coupling
strength.Comment: 10 pages, 6 figures Version accepted in PLB. Minor changes. Title
change
Epidemic Thresholds with External Agents
We study the effect of external infection sources on phase transitions in
epidemic processes. In particular, we consider an epidemic spreading on a
network via the SIS/SIR dynamics, which in addition is aided by external agents
- sources unconstrained by the graph, but possessing a limited infection rate
or virulence. Such a model captures many existing models of externally aided
epidemics, and finds use in many settings - epidemiology, marketing and
advertising, network robustness, etc. We provide a detailed characterization of
the impact of external agents on epidemic thresholds. In particular, for the
SIS model, we show that any external infection strategy with constant virulence
either fails to significantly affect the lifetime of an epidemic, or at best,
sustains the epidemic for a lifetime which is polynomial in the number of
nodes. On the other hand, a random external-infection strategy, with rate
increasing linearly in the number of infected nodes, succeeds under some
conditions to sustain an exponential epidemic lifetime. We obtain similar sharp
thresholds for the SIR model, and discuss the relevance of our results in a
variety of settings.Comment: 12 pages, 2 figures (to appear in INFOCOM 2014
Skellam shrinkage: Wavelet-based intensity estimation for inhomogeneous Poisson data
The ubiquity of integrating detectors in imaging and other applications
implies that a variety of real-world data are well modeled as Poisson random
variables whose means are in turn proportional to an underlying vector-valued
signal of interest. In this article, we first show how the so-called Skellam
distribution arises from the fact that Haar wavelet and filterbank transform
coefficients corresponding to measurements of this type are distributed as sums
and differences of Poisson counts. We then provide two main theorems on Skellam
shrinkage, one showing the near-optimality of shrinkage in the Bayesian setting
and the other providing for unbiased risk estimation in a frequentist context.
These results serve to yield new estimators in the Haar transform domain,
including an unbiased risk estimate for shrinkage of Haar-Fisz
variance-stabilized data, along with accompanying low-complexity algorithms for
inference. We conclude with a simulation study demonstrating the efficacy of
our Skellam shrinkage estimators both for the standard univariate wavelet test
functions as well as a variety of test images taken from the image processing
literature, confirming that they offer substantial performance improvements
over existing alternatives.Comment: 27 pages, 8 figures, slight formatting changes; submitted for
publicatio
Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources
Light incident on a layer of scattering material such as a piece of sugar or
white paper forms a characteristic speckle pattern in transmission and
reflection. The information hidden in the correlations of the speckle pattern
with varying frequency, polarization and angle of the incident light can be
exploited for applications such as biomedical imaging and high-resolution
microscopy. Conventional computational models for multi-frequency optical
response involve multiple solution runs of Maxwell's equations with
monochromatic sources. Exponential Krylov subspace time solvers are promising
candidates for improving efficiency of such models, as single monochromatic
solution can be reused for the other frequencies without performing full
time-domain computations at each frequency. However, we show that the
straightforward implementation appears to have serious limitations. We further
propose alternative ways for efficient solution through Krylov subspace
methods. Our methods are based on two different splittings of the unknown
solution into different parts, each of which can be computed efficiently.
Experiments demonstrate a significant gain in computation time with respect to
the standard solvers.Comment: 22 pages, 4 figure
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