arXiv subjects

Shaowei Lin

Publications and source records attributed to Shaowei Lin.

26 records · Page 2Linked to original sources

arXiv2014

Efficient Data Compression with Error Bound Guarantee in Wireless Sensor Networks

We present a data compression and dimensionality reduction scheme for data fusion and aggregation applications to prevent data congestion and reduce energy consumption at network connecting points such as cluster heads and gateways. Our in-network approach can be easily tuned to analyze the data temporal or spatial correlation using an unsupervised neural network scheme, namely the autoencoders. In particular, our algorithm extracts intrinsic data features from previously collected historical samples to transform the raw data into a low dimensional representation. Moreover, the proposed framework provides an error bound guarantee mechanism. We evaluate the proposed solution using real-world data sets and compare it with traditional methods for temporal and spatial data compression. The experimental validation reveals that our approach outperforms several existing wireless sensor network's data compression methods in terms of compression efficiency and signal reconstruction.

cs.NI↗

arXiv2013

Hypersurfaces and their singularities in partial correlation testing

An asymptotic theory is developed for computing volumes of regions in the parameter space of a directed Gaussian graphical model that are obtained by bounding partial correlations. We study these volumes using the method of real log canonical thresholds from algebraic geometry. Our analysis involves the computation of the singular loci of correlation hypersurfaces. Statistical applications include the strong-faithfulness assumption for the PC-algorithm, and the quantification of confounder bias in causal inference. A detailed analysis is presented for trees, bow-ties, tripartite graphs, and complete graphs.

math.ST↗

arXiv2013

Inverses of symmetric, diagonally dominant positive matrices and applications

We prove tight bounds for the $\infty$-norm of the inverse of symmetric, diagonally dominant positive matrices. We also prove a new lower-bound form of Hadamard's inequality for the determinant of diagonally dominant positive matrices and an improved upper bound for diagonally balanced positive matrices. Applications of our results include numerical stability for linear systems, bounds on inverses of differentiable functions, and consistency of the maximum likelihood equations for maximum entropy graph distributions.

math.FA↗

arXiv2013

Capacity Pre-Log of Noncoherent SIMO Channels via Hironaka's Theorem

We find the capacity pre-log of a temporally correlated Rayleigh block-fading SIMO channel in the noncoherent setting. It is well known that for block-length L and rank of the channel covariance matrix equal to Q, the capacity pre-log in the SISO case is given by 1-Q/L. Here, Q/L can be interpreted as the pre-log penalty incurred by channel uncertainty. Our main result reveals that, by adding only one receive antenna, this penalty can be reduced to 1/L and can, hence, be made to vanish in the large-L limit, even if Q/L remains constant as L goes to infinity. Intuitively, even though the SISO channels between the transmit antenna and the two receive antennas are statistically independent, the transmit signal induces enough statistical dependence between the corresponding receive signals for the second receive antenna to be able to resolve the uncertainty associated with the first receive antenna's channel and thereby make the overall system appear coherent. The proof of our main theorem is based on a deep result from algebraic geometry known as Hironaka's Theorem on the Resolution of Singularities.

cs.IT↗

arXiv2011

Tropical secant graphs of monomial curves

The first secant variety of a projective monomial curve is a threefold with an action by a one-dimensional torus. Its tropicalization is a three-dimensional fan with a one-dimensional lineality space, so the tropical threefold is represented by a balanced graph. Our main result is an explicit construction of that graph. As a consequence, we obtain algorithms to effectively compute the multidegree and Chow polytope of an arbitrary projective monomial curve. This generalizes an earlier degree formula due to Ranestad. The combinatorics underlying our construction is rather delicate, and it is based on a refinement of the theory of geometric tropicalization due to Hacking, Keel and Tevelev.

math.AG↗

arXiv2011

Noncoherent SIMO Pre-Log via Resolution of Singularities

We establish a lower bound on the noncoherent capacity pre-log of a temporally correlated Rayleigh block-fading single-input multiple-output (SIMO) channel. Our result holds for arbitrary rank Q of the channel correlation matrix, arbitrary block-length L > Q, and arbitrary number of receive antennas R, and includes the result in Morgenshtern et al. (2010) as a special case. It is well known that the capacity pre-log for this channel in the single-input single-output (SISO) case is given by 1-Q/L, where Q/L is the penalty incurred by channel uncertainty. Our result reveals that this penalty can be reduced to 1/L by adding only one receive antenna, provided that L \geq 2Q - 1 and the channel correlation matrix satisfies mild technical conditions. The main technical tool used to prove our result is Hironaka's celebrated theorem on resolution of singularities in algebraic geometry.

cs.IT↗

arXiv2009

Polynomial relations among principal minors of a 4x4-matrix

The image of the principal minor map for n x n-matrices is shown to be closed. In the 19th century, Nansen and Muir studied the implicitization problem of finding all relations among principal minors when n=4. We complete their partial results by constructing explicit polynomials of degree 12 that scheme-theoretically define this affine variety and also its projective closure in $\PP^{15}$. The latter is the main component in the singular locus of the 2 x 2 x 2 x 2-hyperdeterminant.

math.AG↗

arXiv2009

Marginal Likelihood Integrals for Mixtures of Independence Models

Inference in Bayesian statistics involves the evaluation of marginal likelihood integrals. We present algebraic algorithms for computing such integrals exactly for discrete data of small sample size. Our methods apply to both uniform priors and Dirichlet priors. The underlying statistical models are mixtures of independent distributions, or, in geometric language, secant varieties of Segre-Veronese varieties.

stat.CO↗