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Neri Merhav - One of the best experts on this subject based on the ideXlab platform.
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data processing inequalities based on a certain Structured Class of information measures with application to estimation theory
IEEE Transactions on Information Theory, 2012Co-Authors: Neri MerhavAbstract:We study data-processing inequalities that are derived from a certain Class of generalized information measures, where a series of convex functions and multiplicative likelihood ratios is nested alternately. While these information measures can be viewed as a special case of the most general Zakai-Ziv generalized information measure, this special nested structure calls for attention and motivates our study. Specifically, a certain choice of the convex functions leads to an information measure that extends the notion of the Bhattacharyya distance (or the Chernoff divergence): While the ordinary Bhattacharyya distance is based on the (weighted) geometric mean of two replicas of the channel's conditional distribution, the more general information measure allows an arbitrary number of such replicas. We apply the data-processing inequality induced by this information measure to a detailed study of lower bounds of parameter estimation under additive white Gaussian noise (AWGN) and show that in certain cases, tighter bounds can be obtained by using more than two replicas. While the resulting lower bound may not compete favorably with the best bounds available for the ordinary AWGN channel, the advantage of the new lower bound, relative to the other bounds, becomes significant in the presence of channel uncertainty, like unknown fading. This different behavior in the presence of channel uncertainty is explained by the convexity property of the information measure.
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data processing inequalities based on a certain Structured Class of information measures with application to estimation theory
International Symposium on Information Theory, 2012Co-Authors: Neri MerhavAbstract:We study data processing inequalities (DPI's) that are derived from a certain Class of generalized information measures, where a series of convex functions and multiplicative likelihood ratios are nested alternately. A certain choice of the convex functions leads to an information measure that extends the notion of the Bhattacharyya distance: While the ordinary Bhattacharyya distance is based on the geometric mean of two replicas of the channel's conditional distribution, the more general one allows an arbitrary number of replicas. We apply the DPI induced by this information measure to a detailed study of lower bounds of parameter estimation under additive white Gaussian noise (AWGN) and show that in certain cases, tighter bounds can be obtained by using more than two replicas. While the resulting bound may not compete favorably with the best bounds available for the ordinary AWGN channel, the advantage of the new lower bound, becomes significant in the presence of channel uncertainty, like unknown fading. This is explained by the convexity property of the information measure.
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data processing inequalities based on a certain Structured Class of information measures with application to estimation theory
arXiv: Information Theory, 2011Co-Authors: Neri MerhavAbstract:We study data processing inequalities that are derived from a certain Class of generalized information measures, where a series of convex functions and multiplicative likelihood ratios are nested alternately. While these information measures can be viewed as a special case of the most general Zakai-Ziv generalized information measure, this special nested structure calls for attention and motivates our study. Specifically, a certain choice of the convex functions leads to an information measure that extends the notion of the Bhattacharyya distance (or the Chernoff divergence): While the ordinary Bhattacharyya distance is based on the (weighted) geometric mean of two replicas of the channel's conditional distribution, the more general information measure allows an arbitrary number of such replicas. We apply the data processing inequality induced by this information measure to a detailed study of lower bounds of parameter estimation under additive white Gaussian noise (AWGN) and show that in certain cases, tighter bounds can be obtained by using more than two replicas. While the resulting lower bound may not compete favorably with the best bounds available for the ordinary AWGN channel, the advantage of the new lower bound, relative to the other bounds, becomes significant in the presence of channel uncertainty, like unknown fading. This different behavior in the presence of channel uncertainty is explained by the convexity property of the information measure.
Huang Jing - One of the best experts on this subject based on the ideXlab platform.
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Obstructions for local tournament orientation completions
2021Co-Authors: Hsu Kevin, Huang JingAbstract:The orientation completion problem for a Class of oriented graphs asks whether a given partially oriented graph can be completed to an oriented graph in the Class by orienting the unoriented edges of the partially oriented graph. Orientation completion problems have been studied recently for several Classes of oriented graphs, yielding both polynomial time solutions as well as NP-completeness results. Local tournaments are a well-Structured Class of oriented graphs that generalize tournaments and their underlying graphs are intimately related to proper circular-arc graphs. According to Skrien, a connected graph can be oriented as a local tournament if and only if it is a proper circular-arc graph. Proper interval graphs are precisely the graphs which can be oriented as acyclic local tournaments. It has been proved that the orientation completion problems for the Classes of local tournaments and acyclic local tournaments are both polynomial time solvable. In this paper we characterize the partially oriented graphs that can be completed to local tournaments by determining the complete list of obstructions. These are in a sense minimal partially oriented graphs that cannot be completed to local tournaments. The result may be viewed as an extension of the well-known forbidden subgraph characterization of proper circular-arc graphs obtained by Tucker. The complete list of obstructions for acyclic local tournament orientation completions has been given in a companion paper.Comment: 45 pages, 14 figure
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Obstructions for acyclic local tournament orientation completions
2020Co-Authors: Hsu Kevin, Huang JingAbstract:The orientation completion problem for a fixed Class of oriented graphs asks whether a given partially oriented graph can be completed to an oriented graph in the Class. Orientation completion problems have been studied recently for several Classes of oriented graphs, yielding both polynomial time solutions and NP-completeness results. Local tournaments are a well-Structured Class of oriented graphs that generalize tournaments and their underlying graphs are intimately related to proper circular-arc graphs. Proper interval graphs are precisely those which can be oriented as acyclic local tournaments. It has been proved that the orientation completion problems for local tournaments and acyclic local tournaments are both polynomial time solvable. In this paper we identify the obstructions for acyclic local tournament orientation completions. These are in a sense minimal partially oriented graphs that cannot be completed to acyclic local tournaments. Our description of the obstructions imply that they can be recognized in polynomial time. In a companion paper we will determine all obstructions for local tournament orientation completions.Comment: 13 pages, 2 figure
Hsu Kevin - One of the best experts on this subject based on the ideXlab platform.
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Obstructions for local tournament orientation completions
2021Co-Authors: Hsu Kevin, Huang JingAbstract:The orientation completion problem for a Class of oriented graphs asks whether a given partially oriented graph can be completed to an oriented graph in the Class by orienting the unoriented edges of the partially oriented graph. Orientation completion problems have been studied recently for several Classes of oriented graphs, yielding both polynomial time solutions as well as NP-completeness results. Local tournaments are a well-Structured Class of oriented graphs that generalize tournaments and their underlying graphs are intimately related to proper circular-arc graphs. According to Skrien, a connected graph can be oriented as a local tournament if and only if it is a proper circular-arc graph. Proper interval graphs are precisely the graphs which can be oriented as acyclic local tournaments. It has been proved that the orientation completion problems for the Classes of local tournaments and acyclic local tournaments are both polynomial time solvable. In this paper we characterize the partially oriented graphs that can be completed to local tournaments by determining the complete list of obstructions. These are in a sense minimal partially oriented graphs that cannot be completed to local tournaments. The result may be viewed as an extension of the well-known forbidden subgraph characterization of proper circular-arc graphs obtained by Tucker. The complete list of obstructions for acyclic local tournament orientation completions has been given in a companion paper.Comment: 45 pages, 14 figure
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Obstructions for acyclic local tournament orientation completions
2020Co-Authors: Hsu Kevin, Huang JingAbstract:The orientation completion problem for a fixed Class of oriented graphs asks whether a given partially oriented graph can be completed to an oriented graph in the Class. Orientation completion problems have been studied recently for several Classes of oriented graphs, yielding both polynomial time solutions and NP-completeness results. Local tournaments are a well-Structured Class of oriented graphs that generalize tournaments and their underlying graphs are intimately related to proper circular-arc graphs. Proper interval graphs are precisely those which can be oriented as acyclic local tournaments. It has been proved that the orientation completion problems for local tournaments and acyclic local tournaments are both polynomial time solvable. In this paper we identify the obstructions for acyclic local tournament orientation completions. These are in a sense minimal partially oriented graphs that cannot be completed to acyclic local tournaments. Our description of the obstructions imply that they can be recognized in polynomial time. In a companion paper we will determine all obstructions for local tournament orientation completions.Comment: 13 pages, 2 figure
Viswanathan Sambasivan Abhinav - One of the best experts on this subject based on the ideXlab platform.
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New Information-Theoretic Analyses and Algorithmic Methods for Parameter Estimation in Structured Data Settings and Plenoptic Imaging Models
2020Co-Authors: Viswanathan Sambasivan AbhinavAbstract:University of Minnesota Ph.D. dissertation. August 2020. Major: Electrical Engineering. Advisor: Jarvis Haupt. 1 computer file (PDF); 127 pages.Parameter estimation problems involve estimating an unknown quantity (or parameter) of interest, from a set of data (or observations) that contains some information about the parameter. Such problems are ubiquitous and widely studied across diverse disciplines in science and engineering including, but not limited to, physics, computer science, signal processing, computational genomics, and economics. Information-theoretic limits of a parameter estimation problem quantify the best-achievable performance (under a suitable metric), thus establishing the fundamental difficulty of solving the problem. A central theme of the first two parts of this work is to develop information-theoretic tools to analyze the fundamental limits of estimating parameters from noisy data under two very different settings: (1) the parameter of interest belongs to Structured Class of signals, and (2) a concise forward model relating the observations to the parameters is analytically challenging to obtain. The first part of this work examines the fundamental error characteristics of a general Class of matrix completion problems, where the matrix of interest is a product of two a priori unknown matrices, one of which is sparse, and the observations are noisy. Our main contributions come in the form of minimax lower bounds for the expected per-element squared error for this problem under several common noise models. Our results establish that the error bounds derived in (Soni et al. 2016) for complexity-regularized maximum likelihood estimators achieve, up to multiplicative constants and logarithmic factors, the minimax error rates under certain (mild) conditions. The rest of this work focuses on plenoptic imaging, which usually involves taking multiple single snapshot images of a scene, collected across time (videos), wavelength (multi-spectral cameras), and from multiple vantage points (light field sensor arrays), thus providing substantially more information about a given scene than conventional imaging. For this thrust, we first focus on assessing the fundamental limits of scene parameter estimation in plenoptic imaging systems, with an eye towards passive indirect imaging problems. We develop a general framework to obtain lower bounds on the variance of unbiased estimators for scene parameter estimation from noisy plenoptic data. The novelty of this work lies in the use of computer graphics rendering software to synthesize the (often-complicated) forward mapping to evaluate the Hammersley-Chapman-Robbins lower bound (HCR-LB), which is at least as tight as the more commonly used Cramer-Rao lower bound. When the rendering software yields inexact estimates of the forward mapping, we analyze the effects of such inaccuracies on the HCR-LB both theoretically and via simulations, and provide a method to obtain upper and lower intervals for the true HCR-LB. The final part of this work explores algorithmic methods for Non-Line-of-Sight (NLOS) imaging from (noisy) plenoptic data, where the aim is to recover a hidden scene of interest from noisy measurements that arise from reflections off a scattering surface, e.g. a wall, or the floor. We use the insight that plenoptic data is highly Structured due to parallax and/or motion in the hidden scene and propose a multi-way Total Variation (TV) regularized inversion methodology to leverage this structure and recover hidden scenes. We demonstrate our recovery algorithm on real-world plenoptic data measurements at visible and Long-Wave InfraRed (LWIR) wavelengths. Experiments in LWIR (or thermal) imaging shows that it is possible to reliably image human subjects around a corner, nearly in real-time, using our framework
Catherine Woods - One of the best experts on this subject based on the ideXlab platform.
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what sustains long term adherence to Structured physical activity after a cardiac event
Journal of Aging and Physical Activity, 2012Co-Authors: Antonia M Martin, Catherine WoodsAbstract:Purpose: Research addressing methods to sustain long-term adherence to physical activity among older adults is needed. This study investigated the motivations and supports deemed necessary to adhere to a community-based cardiac rehabilitation (CBCR) program by individuals with established coronary heart disease. Methods: Twenty-four long-term adherers (15 men, 9 women; age 67.7 ± 16.7 yr) took part in focus-group discussions. Results: Constant comparative analysis supported previous research in terms of the importance of referral procedures, social support, and knowledge of health benefits in influencing uptake and adherence to CBCR. Results also highlighted the routine of a Structured Class and task-, barrier-, and recovery-specific self-efficacy as necessary to sustain long-term adherence for this specific clinical group. Discussion: Older adults themselves provide rich information on how to successfully support their long-term adherence to Structured exercise sessions. Further research into how to buil...
