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We consider the problem of estimating the mean and covariance of a distribution from i.i.d. samples in the presence of a fraction of malicious noise. This is in contrast to much recent work where the noise itself is assumed to be from a distribution of known type. The agnostic problem includes many interesting special cases, e.g., learning the parameters of(More)
We show an algorithm for solving symmetric diagonally dominant (SDD) linear systems with <i>m</i> non-zero entries to a relative error of <i>&#949;</i> in <i>O</i>(<i>m</i> log<sup>1/2</sup> <i>n</i> log<sup><i>c</i></sup> <i>n</i> log(1/<i>&#949;</i>)) time. Our approach follows the recursive preconditioning framework, which aims to reduce graphs to trees(More)
We present an algorithm that, with high probability, generates a random spanning tree from an edge-weighted undirected graph in (<i>n</i><sup>5/3 </sup><i>m</i><sup>1/3</sup>) time. The tree is sampled from a distribution where the probability of each tree is proportional to the product of its edge weights. This improves upon the previous best algorithm due(More)
In this paper, we begin to address the longstanding algorithmic gap between general and reversible Markov chains. We develop directed analogues of several spectral graph-theoretic tools that had previously been available only in the undirected setting, and for which it was not clear that directed versions even existed. In particular, we provide a notion of(More)
We show that preconditioners constructed by random sampling can perform well without meeting the standard requirements of iterative methods. When applied to graph Laplacians, this leads to ultrasparsifiers that in expectation behave as the nearly-optimal ones given by [Kolla-Makarychev-Saberi-Teng STOC‘10]. Combining this with the recursive preconditioning(More)
We show variants of spectral sparsification routines can preserve the total spanning tree counts of graphs, which by Kirchhoff’s matrix-tree theorem, is equivalent to determinant of a graph Laplacian minor, or equivalently, of any SDDM matrix. Our analyses utilizes this combinatorial connection to bridge between statistical leverage scores / effective(More)
Data acquisition and analysis of various cardiac /transducer signals based on virtual instrument technology is gaining importance. This paper introduces a novel way of automating the diagnosis of cardiac disorders using an expert system developed on the basis of information derived from the analysis of Electrocardiogram (ECG) and also provides the online(More)
In this paper, a liquid level transmitter using cylindrical capacitive sensor and an improved linearized network for capacitance measurement has been proposed to measure the liquid level and to convert level changes into an electrical current which can be transmitted to a remote indicator. The change in capacitance of cylindrical capacitive sensor due to(More)
Small depth networks arise in a variety of network related applications, often in the form of maximum flow and maximum weighted matching. Recent works have generalized such methods to include costs arising from concave functions. In this paper we give an algorithm that takes a depth D network and strictly increasing concave weight functions of flows on the(More)
Brain Tumors are detected efficiently by using the Magnetic Resonance Imaging (MRI) techniques. The extracted MRI image is sensitive to noise which limits the visibility of certain characteristics of the image. This unwanted noise can be disintegrated and curtailed from the original Image by using the non linear digital median filter. The intensification is(More)
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