The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Jianqing Fan - One of the best experts on this subject based on the ideXlab platform.
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Gradient descent with random initialization: fast global convergence for nonconvex phase retrieval
Mathematical Programming, 2019Co-Authors: Yuxin Chen, Yuejie Chi, Jianqing Fan, Cong MaAbstract:This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest \(\varvec{x}^{\natural }\in {\mathbb {R}}^{n}\) from m quadratic equations/samples \(y_{i}=(\varvec{a}_{i}^{\top }\varvec{x}^{\natural })^{2}, 1\le i\le m\). This problem, also dubbed as phase retrieval, spans multiple domains including physical sciences and machine learning. We investigate the efficacy of gradient descent (or Wirtinger flow) designed for the nonconvex least squares problem. We prove that under Gaussian designs, gradient descent—when randomly initialized—yields an \(\epsilon \)-accurate solution in \(O\big (\log n+\log (1/\epsilon )\big )\) iterations given nearly minimal samples, thus achieving near-optimal computational and sample complexities at once. This provides the first global convergence guarantee concerning vanilla gradient descent for phase retrieval, without the need of (i) carefully-designed initialization, (ii) sample splitting, or (iii) sophisticated saddle-point escaping schemes. All of these are achieved by exploiting the Statistical models in analyzing optimization algorithms, via a leave-one-out approach that enables the decoupling of certain Statistical Dependency between the gradient descent iterates and the data.
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gradient descent with random initialization fast global convergence for nonconvex phase retrieval
arXiv: Machine Learning, 2018Co-Authors: Yuxin Chen, Yuejie Chi, Jianqing FanAbstract:This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest $\mathbf{x}^{\natural}\in\mathbb{R}^{n}$ from $m$ quadratic equations/samples $y_{i}=(\mathbf{a}_{i}^{\top}\mathbf{x}^{\natural})^{2}$, $1\leq i\leq m$. This problem, also dubbed as phase retrieval, spans multiple domains including physical sciences and machine learning. We investigate the efficiency of gradient descent (or Wirtinger flow) designed for the nonconvex least squares problem. We prove that under Gaussian designs, gradient descent --- when randomly initialized --- yields an $\epsilon$-accurate solution in $O\big(\log n+\log(1/\epsilon)\big)$ iterations given nearly minimal samples, thus achieving near-optimal computational and sample complexities at once. This provides the first global convergence guarantee concerning vanilla gradient descent for phase retrieval, without the need of (i) carefully-designed initialization, (ii) sample splitting, or (iii) sophisticated saddle-point escaping schemes. All of these are achieved by exploiting the Statistical models in analyzing optimization algorithms, via a leave-one-out approach that enables the decoupling of certain Statistical Dependency between the gradient descent iterates and the data.
Martijn P Van Den Heuvel - One of the best experts on this subject based on the ideXlab platform.
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biological characteristics of connection wise resting state functional connectivity strength
Cerebral Cortex, 2019Co-Authors: Rory Pijnenburg, Lianne H Scholtens, Wim Vanduffel, Dante Mantini, Martijn P Van Den Heuvel, Lisa Feldman BarrettAbstract:Functional connectivity is defined as the Statistical Dependency of neurophysiological activity between 2 separate brain areas. To investigate the biological characteristics of resting-state functional connectivity (rsFC)-and in particular the significance of connection-wise variation in time-series correlations-rsFC was compared with strychnine-based connectivity measured in the macaque. Strychnine neuronography is a historical technique that induces activity in cortical areas through means of local administration of the substance strychnine. Strychnine causes local disinhibition through GABA suppression and leads to subsequent activation of functional pathways. Multiple resting-state fMRI recordings were acquired in 4 macaques (examining in total 299 imaging runs) from which a group-averaged rsFC matrix was constructed. rsFC was observed to be higher (P < 0.0001) between region-pairs with a strychnine-based connection as compared with region-pairs with no strychnine-based connection present. In particular, higher resting-state connectivity was observed in connections that were relatively stronger (weak < moderate < strong; P < 0.01) and in connections that were bidirectional (P < 0.0001) instead of unidirectional in strychnine-based connectivity. Our results imply that the level of correlation between brain areas as extracted from resting-state fMRI relates to the strength of underlying interregional functional pathways.
G A Mian - One of the best experts on this subject based on the ideXlab platform.
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An Improved Context Adaptive Binary Arithmetic Coder for the H.264/AVC Standard
2014Co-Authors: Simone Milani, G A MianAbstract:During the last years, the increment of video transmissions over wireless channels has created the need for increasingly-efficient coding algorithms that are capable of coding the video information with a reduced number of bits. Among them, the H.264 coder provides the best performance in terms of video quality and reduced bit rates thanks to many enhanced coding solutions that were included in it. One of the most effective is its adaptive arithmetic coder that esti-mates the probability of each syntax element via an elabo-rate structure of contexts. However, the coder can be signif-icantly improved exploiting the Statistical Dependency in the transformed signal. The DCT coefficients of a single trans-form block or of a macroblock are correlated among each other. This Statistical Dependency makes it possible a better estimation of the bit probability with respect to the context counters defined by the standard. For this purpose, the prob-ability mass function of the different bit planes in a block of coefficient can be estimated through a graphical model as-sociated to a Directed Acyclic Graph (DAG). Experimental results report that the adoption of a DAG model leads to 10% reduction of the bit stream size for a given quality or, other-wise, a quality increment between 0 5 and 1 dB at the same bit rate. 1
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an improved context adaptive binary arithmetic coder for the h 264 avc standard
European Signal Processing Conference, 2006Co-Authors: Simone Milani, G A MianAbstract:During the last years, the increment of video transmissions over wireless channels has created the need for increasingly-efficient coding algorithms that are capable of coding the video information with a reduced number of bits. Among them, the H.264 coder provides the best performance in terms of video quality and reduced bit rates thanks to many enhanced coding solutions that were included in it. One of the most effective is its adaptive arithmetic coder that estimates the probability of each syntax element via an elaborate structure of contexts. However, the coder can be significantly improved exploiting the Statistical Dependency in the transformed signal. The DCT coefficients of a single transform block or of a macroblock are correlated among each other. This Statistical Dependency makes it possible a better estimation of the bit probability with respect to the context counters defined by the standard. For this purpose, the probability mass function of the different bit planes in a block of coefficient can be estimated through a graphical model associated to a Directed Acyclic Graph (DAG). Experimental results report that the adoption of a DAG model leads to 10% reduction of the bit stream size for a given quality or, otherwise, a quality increment between 0.5 and 1 dB at the same bit rate.
Yuxin Chen - One of the best experts on this subject based on the ideXlab platform.
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Gradient descent with random initialization: fast global convergence for nonconvex phase retrieval
Mathematical Programming, 2019Co-Authors: Yuxin Chen, Yuejie Chi, Jianqing Fan, Cong MaAbstract:This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest \(\varvec{x}^{\natural }\in {\mathbb {R}}^{n}\) from m quadratic equations/samples \(y_{i}=(\varvec{a}_{i}^{\top }\varvec{x}^{\natural })^{2}, 1\le i\le m\). This problem, also dubbed as phase retrieval, spans multiple domains including physical sciences and machine learning. We investigate the efficacy of gradient descent (or Wirtinger flow) designed for the nonconvex least squares problem. We prove that under Gaussian designs, gradient descent—when randomly initialized—yields an \(\epsilon \)-accurate solution in \(O\big (\log n+\log (1/\epsilon )\big )\) iterations given nearly minimal samples, thus achieving near-optimal computational and sample complexities at once. This provides the first global convergence guarantee concerning vanilla gradient descent for phase retrieval, without the need of (i) carefully-designed initialization, (ii) sample splitting, or (iii) sophisticated saddle-point escaping schemes. All of these are achieved by exploiting the Statistical models in analyzing optimization algorithms, via a leave-one-out approach that enables the decoupling of certain Statistical Dependency between the gradient descent iterates and the data.
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gradient descent with random initialization fast global convergence for nonconvex phase retrieval
arXiv: Machine Learning, 2018Co-Authors: Yuxin Chen, Yuejie Chi, Jianqing FanAbstract:This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest $\mathbf{x}^{\natural}\in\mathbb{R}^{n}$ from $m$ quadratic equations/samples $y_{i}=(\mathbf{a}_{i}^{\top}\mathbf{x}^{\natural})^{2}$, $1\leq i\leq m$. This problem, also dubbed as phase retrieval, spans multiple domains including physical sciences and machine learning. We investigate the efficiency of gradient descent (or Wirtinger flow) designed for the nonconvex least squares problem. We prove that under Gaussian designs, gradient descent --- when randomly initialized --- yields an $\epsilon$-accurate solution in $O\big(\log n+\log(1/\epsilon)\big)$ iterations given nearly minimal samples, thus achieving near-optimal computational and sample complexities at once. This provides the first global convergence guarantee concerning vanilla gradient descent for phase retrieval, without the need of (i) carefully-designed initialization, (ii) sample splitting, or (iii) sophisticated saddle-point escaping schemes. All of these are achieved by exploiting the Statistical models in analyzing optimization algorithms, via a leave-one-out approach that enables the decoupling of certain Statistical Dependency between the gradient descent iterates and the data.
Simone Milani - One of the best experts on this subject based on the ideXlab platform.
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An Improved Context Adaptive Binary Arithmetic Coder for the H.264/AVC Standard
2014Co-Authors: Simone Milani, G A MianAbstract:During the last years, the increment of video transmissions over wireless channels has created the need for increasingly-efficient coding algorithms that are capable of coding the video information with a reduced number of bits. Among them, the H.264 coder provides the best performance in terms of video quality and reduced bit rates thanks to many enhanced coding solutions that were included in it. One of the most effective is its adaptive arithmetic coder that esti-mates the probability of each syntax element via an elabo-rate structure of contexts. However, the coder can be signif-icantly improved exploiting the Statistical Dependency in the transformed signal. The DCT coefficients of a single trans-form block or of a macroblock are correlated among each other. This Statistical Dependency makes it possible a better estimation of the bit probability with respect to the context counters defined by the standard. For this purpose, the prob-ability mass function of the different bit planes in a block of coefficient can be estimated through a graphical model as-sociated to a Directed Acyclic Graph (DAG). Experimental results report that the adoption of a DAG model leads to 10% reduction of the bit stream size for a given quality or, other-wise, a quality increment between 0 5 and 1 dB at the same bit rate. 1
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an improved context adaptive binary arithmetic coder for the h 264 avc standard
European Signal Processing Conference, 2006Co-Authors: Simone Milani, G A MianAbstract:During the last years, the increment of video transmissions over wireless channels has created the need for increasingly-efficient coding algorithms that are capable of coding the video information with a reduced number of bits. Among them, the H.264 coder provides the best performance in terms of video quality and reduced bit rates thanks to many enhanced coding solutions that were included in it. One of the most effective is its adaptive arithmetic coder that estimates the probability of each syntax element via an elaborate structure of contexts. However, the coder can be significantly improved exploiting the Statistical Dependency in the transformed signal. The DCT coefficients of a single transform block or of a macroblock are correlated among each other. This Statistical Dependency makes it possible a better estimation of the bit probability with respect to the context counters defined by the standard. For this purpose, the probability mass function of the different bit planes in a block of coefficient can be estimated through a graphical model associated to a Directed Acyclic Graph (DAG). Experimental results report that the adoption of a DAG model leads to 10% reduction of the bit stream size for a given quality or, otherwise, a quality increment between 0.5 and 1 dB at the same bit rate.
