34,661 research outputs found
Expectile Matrix Factorization for Skewed Data Analysis
Matrix factorization is a popular approach to solving matrix estimation
problems based on partial observations. Existing matrix factorization is based
on least squares and aims to yield a low-rank matrix to interpret the
conditional sample means given the observations. However, in many real
applications with skewed and extreme data, least squares cannot explain their
central tendency or tail distributions, yielding undesired estimates. In this
paper, we propose \emph{expectile matrix factorization} by introducing
asymmetric least squares, a key concept in expectile regression analysis, into
the matrix factorization framework. We propose an efficient algorithm to solve
the new problem based on alternating minimization and quadratic programming. We
prove that our algorithm converges to a global optimum and exactly recovers the
true underlying low-rank matrices when noise is zero. For synthetic data with
skewed noise and a real-world dataset containing web service response times,
the proposed scheme achieves lower recovery errors than the existing matrix
factorization method based on least squares in a wide range of settings.Comment: 8 page main text with 5 page supplementary documents, published in
AAAI 201
Calibration of shrinkage estimators for portfolio optimization
Shrinkage estimators is an area widely studied in statistics. In this paper, we contemplate the role of shrinkage estimators on the construction of the investor's portfolio. We study the performance of shrinking the sample moments to estimate portfolio weights as well as the performance of shrinking the naive sample portfolio weights themselves. We provide a theoretical and empirical analysis of different new methods to calibrate shrinkage estimators within portfolio optimizationPortfolio choice, Estimation error, Shrinkage estimators, Smoothed bootstrap
OMP-type Algorithm with Structured Sparsity Patterns for Multipath Radar Signals
A transmitted, unknown radar signal is observed at the receiver through more
than one path in additive noise. The aim is to recover the waveform of the
intercepted signal and to simultaneously estimate the direction of arrival
(DOA). We propose an approach exploiting the parsimonious time-frequency
representation of the signal by applying a new OMP-type algorithm for
structured sparsity patterns. An important issue is the scalability of the
proposed algorithm since high-dimensional models shall be used for radar
signals. Monte-Carlo simulations for modulated signals illustrate the good
performance of the method even for low signal-to-noise ratios and a gain of 20
dB for the DOA estimation compared to some elementary method
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