415 research outputs found
Properties and use of CMB power spectrum likelihoods
Fast robust methods for calculating likelihoods from CMB observations on
small scales generally rely on approximations based on a set of power spectrum
estimators and their covariances. We investigate the optimality of these
approximation, how accurate the covariance needs to be, and how to estimate the
covariance from simulations. For a simple case with azimuthal symmetry we
compare optimality of hybrid pseudo-C_l CMB power spectrum estimators with the
exact result, indicating that the loss of information is not negligible, but
neither is it enough to have a large effect on standard parameter constraints.
We then discuss the number of samples required to estimate the covariance from
simulations, with and without a good analytic approximation, and assess the use
of shrinkage estimators. Finally we discuss how to combine an approximate
high-ell likelihood with a more exact low-ell harmonic-space likelihood as a
practical method for accurate likelihood calculation on all scales.Comment: 15 pages, 11 figures; updated to match version accepted by PR
A simple scheme for allocating capital in a foreign exchange proprietary trading firm
We present a model of capital allocation in a foreign exchange proprietary trading firm. The owner allocates capital to individual traders, who operate within strict risk limits. Traders specialize in individual currencies, but are given discretion over their choice of trading rule. The owner provides the simple formula that determines position sizes – a formula that does not require estimation of the firm-level covariance matrix. We provide supporting empirical evidence of excess risk-adjusted returns to the firm-level portfolio, and we discuss a modification of the model in which the owner dictates the choice of trading rule
Detection of brain functional-connectivity difference in post-stroke patients using group-level covariance modeling
Functional brain connectivity, as revealed through distant correlations in
the signals measured by functional Magnetic Resonance Imaging (fMRI), is a
promising source of biomarkers of brain pathologies. However, establishing and
using diagnostic markers requires probabilistic inter-subject comparisons.
Principled comparison of functional-connectivity structures is still a
challenging issue. We give a new matrix-variate probabilistic model suitable
for inter-subject comparison of functional connectivity matrices on the
manifold of Symmetric Positive Definite (SPD) matrices. We show that this model
leads to a new algorithm for principled comparison of connectivity coefficients
between pairs of regions. We apply this model to comparing separately
post-stroke patients to a group of healthy controls. We find
neurologically-relevant connection differences and show that our model is more
sensitive that the standard procedure. To the best of our knowledge, these
results are the first report of functional connectivity differences between a
single-patient and a group and thus establish an important step toward using
functional connectivity as a diagnostic tool
An Evolutionary Optimization Approach to Risk Parity Portfolio Selection
In this paper we present an evolutionary optimization approach to solve the
risk parity portfolio selection problem. While there exist convex optimization
approaches to solve this problem when long-only portfolios are considered, the
optimization problem becomes non-trivial in the long-short case. To solve this
problem, we propose a genetic algorithm as well as a local search heuristic.
This algorithmic framework is able to compute solutions successfully. Numerical
results using real-world data substantiate the practicability of the approach
presented in this paper
Adaptive Evolutionary Clustering
In many practical applications of clustering, the objects to be clustered
evolve over time, and a clustering result is desired at each time step. In such
applications, evolutionary clustering typically outperforms traditional static
clustering by producing clustering results that reflect long-term trends while
being robust to short-term variations. Several evolutionary clustering
algorithms have recently been proposed, often by adding a temporal smoothness
penalty to the cost function of a static clustering method. In this paper, we
introduce a different approach to evolutionary clustering by accurately
tracking the time-varying proximities between objects followed by static
clustering. We present an evolutionary clustering framework that adaptively
estimates the optimal smoothing parameter using shrinkage estimation, a
statistical approach that improves a naive estimate using additional
information. The proposed framework can be used to extend a variety of static
clustering algorithms, including hierarchical, k-means, and spectral
clustering, into evolutionary clustering algorithms. Experiments on synthetic
and real data sets indicate that the proposed framework outperforms static
clustering and existing evolutionary clustering algorithms in many scenarios.Comment: To appear in Data Mining and Knowledge Discovery, MATLAB toolbox
available at http://tbayes.eecs.umich.edu/xukevin/affec
Testing linear hypotheses in high-dimensional regressions
For a multivariate linear model, Wilk's likelihood ratio test (LRT)
constitutes one of the cornerstone tools. However, the computation of its
quantiles under the null or the alternative requires complex analytic
approximations and more importantly, these distributional approximations are
feasible only for moderate dimension of the dependent variable, say .
On the other hand, assuming that the data dimension as well as the number
of regression variables are fixed while the sample size grows, several
asymptotic approximations are proposed in the literature for Wilk's \bLa
including the widely used chi-square approximation. In this paper, we consider
necessary modifications to Wilk's test in a high-dimensional context,
specifically assuming a high data dimension and a large sample size .
Based on recent random matrix theory, the correction we propose to Wilk's test
is asymptotically Gaussian under the null and simulations demonstrate that the
corrected LRT has very satisfactory size and power, surely in the large and
large context, but also for moderately large data dimensions like or
. As a byproduct, we give a reason explaining why the standard chi-square
approximation fails for high-dimensional data. We also introduce a new
procedure for the classical multiple sample significance test in MANOVA which
is valid for high-dimensional data.Comment: Accepted 02/2012 for publication in "Statistics". 20 pages, 2 pages
and 2 table
Efficient template attacks
This is the accepted manuscript version. The final published version is available from http://link.springer.com/chapter/10.1007/978-3-319-08302-5_17.Template attacks remain a powerful side-channel technique to eavesdrop on tamper-resistant hardware. They model the probability distribution of leaking signals and noise to guide a search for secret data values. In practice, several numerical obstacles can arise when implementing such attacks with multivariate normal distributions. We propose efficient methods to avoid these. We also demonstrate how to achieve significant performance improvements, both in terms of information extracted and computational cost, by pooling covariance estimates across all data values. We provide a detailed and systematic overview of many different options for implementing such attacks. Our experimental evaluation of all these methods based on measuring the supply current of a byte-load instruction executed in an unprotected 8-bit microcontroller leads to practical guidance for choosing an attack algorithm.Omar Choudary is a recipient of the Google Europe Fellowship in
Mobile Security, and this research is supported in part by this Google Fellowship
Accounting for risk of non linear portfolios: a novel Fourier approach
The presence of non linear instruments is responsible for the emergence of
non Gaussian features in the price changes distribution of realistic
portfolios, even for Normally distributed risk factors. This is especially true
for the benchmark Delta Gamma Normal model, which in general exhibits
exponentially damped power law tails. We show how the knowledge of the model
characteristic function leads to Fourier representations for two standard risk
measures, the Value at Risk and the Expected Shortfall, and for their
sensitivities with respect to the model parameters. We detail the numerical
implementation of our formulae and we emphasizes the reliability and efficiency
of our results in comparison with Monte Carlo simulation.Comment: 10 pages, 12 figures. Final version accepted for publication on Eur.
Phys. J.
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