The Experts below are selected from a list of 255 Experts worldwide ranked by ideXlab platform
Han Liu - One of the best experts on this subject based on the ideXlab platform.
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optimal linear estimation under unknown Nonlinear Transform
Neural Information Processing Systems, 2015Co-Authors: Zhaoran Wang, Constantine Caramanis, Han LiuAbstract:Linear regression studies the problem of estimating a model parameter β* ∈ ℝp, from n observations {(yi, xi)}ni=1 from linear model yi = 〈xi, β*〉 + ∊i. We consider a significant generalization in which the relationship between 〈xi, β*〉 and yi is noisy, quantized to a single bit, potentially Nonlinear, noninvertible, as well as unknown. This model is known as the single-index model in statistics, and, among other things, it represents a significant generalization of one-bit compressed sensing. We propose a novel spectral-based estimation procedure and show that we can recover β* in settings (i.e., classes of link function f) where previous algorithms fail. In general, our algorithm requires only very mild restrictions on the (unknown) functional relationship between yi and 〈xi, β*〉. We also consider the high dimensional setting where β* is sparse, and introduce a two-stage nonconvex framework that addresses estimation challenges in high dimensional regimes where p ≫ n. For a broad class of link functions between 〈xi, β*〉 and yi, we establish minimax lower bounds that demonstrate the optimality of our estimators in both the classical and high dimensional regimes.
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Optimal linear estimation under unknown Nonlinear Transform
arXiv: Machine Learning, 2015Co-Authors: Zhaoran Wang, Constantine Caramanis, Han LiuAbstract:Linear regression studies the problem of estimating a model parameter $\beta^* \in \mathbb{R}^p$, from $n$ observations $\{(y_i,\mathbf{x}_i)\}_{i=1}^n$ from linear model $y_i = \langle \mathbf{x}_i,\beta^* \rangle + \epsilon_i$. We consider a significant generalization in which the relationship between $\langle \mathbf{x}_i,\beta^* \rangle$ and $y_i$ is noisy, quantized to a single bit, potentially Nonlinear, noninvertible, as well as unknown. This model is known as the single-index model in statistics, and, among other things, it represents a significant generalization of one-bit compressed sensing. We propose a novel spectral-based estimation procedure and show that we can recover $\beta^*$ in settings (i.e., classes of link function $f$) where previous algorithms fail. In general, our algorithm requires only very mild restrictions on the (unknown) functional relationship between $y_i$ and $\langle \mathbf{x}_i,\beta^* \rangle$. We also consider the high dimensional setting where $\beta^*$ is sparse ,and introduce a two-stage nonconvex framework that addresses estimation challenges in high dimensional regimes where $p \gg n$. For a broad class of link functions between $\langle \mathbf{x}_i,\beta^* \rangle$ and $y_i$, we establish minimax lower bounds that demonstrate the optimality of our estimators in both the classical and high dimensional regimes.
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NIPS - Optimal linear estimation under unknown Nonlinear Transform
Advances in neural information processing systems, 2015Co-Authors: Zhaoran Wang, Constantine Caramanis, Han LiuAbstract:Linear regression studies the problem of estimating a model parameter β* ∈ℝ p , from n observations [Formula: see text] from linear model yi = 〈xi , β*〉 + ε i . We consider a significant generalization in which the relationship between 〈xi , β*〉 and yi is noisy, quantized to a single bit, potentially Nonlinear, noninvertible, as well as unknown. This model is known as the single-index model in statistics, and, among other things, it represents a significant generalization of one-bit compressed sensing. We propose a novel spectral-based estimation procedure and show that we can recover β* in settings (i.e., classes of link function f) where previous algorithms fail. In general, our algorithm requires only very mild restrictions on the (unknown) functional relationship between yi and 〈xi , β*〉. We also consider the high dimensional setting where β* is sparse, and introduce a two-stage nonconvex framework that addresses estimation challenges in high dimensional regimes where p ≫ n. For a broad class of link functions between 〈xi , β*〉 and yi , we establish minimax lower bounds that demonstrate the optimality of our estimators in both the classical and high dimensional regimes.
Ying Sun - One of the best experts on this subject based on the ideXlab platform.
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Nonolinear Transforms In Qrs Detection Algorithms
[1990] Proceedings of the Twelfth Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1Co-Authors: S. Suppappola, Ying SunAbstract:A Nonlinear Transform is typically used in a QRS detection algorithm to estimate the signal energy. In this study five different Nonlinear Transforms on the derivative of the ECG signal are evaluated. These Transforms include squaring, 2-point multiplication, 2-point multiplication with sign consistency, 3-point multiplication, and 3-point multiplication with sign consistency. The AHA ECG data base is used to test the algorithms. We have found that the 3-point multiplication enhances the QRS complex most, and the sign consistency constraint is useful in rejecting abrupt transitions such as the pacer spikes. old is used in the decision stage as previously described [3]. The adaptive threshold is used to increase the sensitivity of QRS detection as the elapsed time from the last QRS increases. Let 2, denote the 1st-order backward difference for the current ECG sample, and yn denote the output from the Nonlinear Transform. The five Nonlinear Transforms under investigation are, respectively, defined as follows:
Shixing Yan - One of the best experts on this subject based on the ideXlab platform.
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Application of modified sign Haar Transform in logic functions
IEICE Electronics Express, 2004Co-Authors: Bogdan J. Falkowski, Shixing YanAbstract:Modified sign Haar Transform with sign Walsh-like structure is introduced in this article. This Nonlinear Transform converts binary/ternary vectors into digital spectral domain and is invertible. Recursive definitions for the calculation of this Transform have been developed. The properties of logic functions and variables in the spectral domain of the modified sign Haar Transform are presented.
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Modified sign Haar Transform
The 2004 47th Midwest Symposium on Circuits and Systems 2004. MWSCAS '04., 1Co-Authors: Bogdan J. Falkowski, Shixing YanAbstract:Modified sign Haar Transform with sign Walsh-like structure is introduced in this article. This Nonlinear Transform converts binary/ternary vectors into digital spectral domain and is invertible. Recursive definitions for the calculation of this Transform have been developed. With its unique and isomorphic properties, this Transform is suitable for security coding in a communication system.
Zhaoran Wang - One of the best experts on this subject based on the ideXlab platform.
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optimal linear estimation under unknown Nonlinear Transform
Neural Information Processing Systems, 2015Co-Authors: Zhaoran Wang, Constantine Caramanis, Han LiuAbstract:Linear regression studies the problem of estimating a model parameter β* ∈ ℝp, from n observations {(yi, xi)}ni=1 from linear model yi = 〈xi, β*〉 + ∊i. We consider a significant generalization in which the relationship between 〈xi, β*〉 and yi is noisy, quantized to a single bit, potentially Nonlinear, noninvertible, as well as unknown. This model is known as the single-index model in statistics, and, among other things, it represents a significant generalization of one-bit compressed sensing. We propose a novel spectral-based estimation procedure and show that we can recover β* in settings (i.e., classes of link function f) where previous algorithms fail. In general, our algorithm requires only very mild restrictions on the (unknown) functional relationship between yi and 〈xi, β*〉. We also consider the high dimensional setting where β* is sparse, and introduce a two-stage nonconvex framework that addresses estimation challenges in high dimensional regimes where p ≫ n. For a broad class of link functions between 〈xi, β*〉 and yi, we establish minimax lower bounds that demonstrate the optimality of our estimators in both the classical and high dimensional regimes.
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Optimal linear estimation under unknown Nonlinear Transform
arXiv: Machine Learning, 2015Co-Authors: Zhaoran Wang, Constantine Caramanis, Han LiuAbstract:Linear regression studies the problem of estimating a model parameter $\beta^* \in \mathbb{R}^p$, from $n$ observations $\{(y_i,\mathbf{x}_i)\}_{i=1}^n$ from linear model $y_i = \langle \mathbf{x}_i,\beta^* \rangle + \epsilon_i$. We consider a significant generalization in which the relationship between $\langle \mathbf{x}_i,\beta^* \rangle$ and $y_i$ is noisy, quantized to a single bit, potentially Nonlinear, noninvertible, as well as unknown. This model is known as the single-index model in statistics, and, among other things, it represents a significant generalization of one-bit compressed sensing. We propose a novel spectral-based estimation procedure and show that we can recover $\beta^*$ in settings (i.e., classes of link function $f$) where previous algorithms fail. In general, our algorithm requires only very mild restrictions on the (unknown) functional relationship between $y_i$ and $\langle \mathbf{x}_i,\beta^* \rangle$. We also consider the high dimensional setting where $\beta^*$ is sparse ,and introduce a two-stage nonconvex framework that addresses estimation challenges in high dimensional regimes where $p \gg n$. For a broad class of link functions between $\langle \mathbf{x}_i,\beta^* \rangle$ and $y_i$, we establish minimax lower bounds that demonstrate the optimality of our estimators in both the classical and high dimensional regimes.
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NIPS - Optimal linear estimation under unknown Nonlinear Transform
Advances in neural information processing systems, 2015Co-Authors: Zhaoran Wang, Constantine Caramanis, Han LiuAbstract:Linear regression studies the problem of estimating a model parameter β* ∈ℝ p , from n observations [Formula: see text] from linear model yi = 〈xi , β*〉 + ε i . We consider a significant generalization in which the relationship between 〈xi , β*〉 and yi is noisy, quantized to a single bit, potentially Nonlinear, noninvertible, as well as unknown. This model is known as the single-index model in statistics, and, among other things, it represents a significant generalization of one-bit compressed sensing. We propose a novel spectral-based estimation procedure and show that we can recover β* in settings (i.e., classes of link function f) where previous algorithms fail. In general, our algorithm requires only very mild restrictions on the (unknown) functional relationship between yi and 〈xi , β*〉. We also consider the high dimensional setting where β* is sparse, and introduce a two-stage nonconvex framework that addresses estimation challenges in high dimensional regimes where p ≫ n. For a broad class of link functions between 〈xi , β*〉 and yi , we establish minimax lower bounds that demonstrate the optimality of our estimators in both the classical and high dimensional regimes.
S. Suppappola - One of the best experts on this subject based on the ideXlab platform.
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Nonolinear Transforms In Qrs Detection Algorithms
[1990] Proceedings of the Twelfth Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1Co-Authors: S. Suppappola, Ying SunAbstract:A Nonlinear Transform is typically used in a QRS detection algorithm to estimate the signal energy. In this study five different Nonlinear Transforms on the derivative of the ECG signal are evaluated. These Transforms include squaring, 2-point multiplication, 2-point multiplication with sign consistency, 3-point multiplication, and 3-point multiplication with sign consistency. The AHA ECG data base is used to test the algorithms. We have found that the 3-point multiplication enhances the QRS complex most, and the sign consistency constraint is useful in rejecting abrupt transitions such as the pacer spikes. old is used in the decision stage as previously described [3]. The adaptive threshold is used to increase the sensitivity of QRS detection as the elapsed time from the last QRS increases. Let 2, denote the 1st-order backward difference for the current ECG sample, and yn denote the output from the Nonlinear Transform. The five Nonlinear Transforms under investigation are, respectively, defined as follows:
