The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Alexander Barg - One of the best experts on this subject based on the ideXlab platform.
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optimal schemes for Discrete Distribution estimation under locally differential privacy
IEEE Transactions on Information Theory, 2018Co-Authors: Alexander BargAbstract:We consider the minimax estimation problem of a Discrete Distribution with support size $k$ under privacy constraints. A privatization scheme is applied to each raw sample independently, and we need to estimate the Distribution of the raw samples from the privatized samples. A positive number $\epsilon $ measures the privacy level of a privatization scheme. For a given $\epsilon $ , we consider the problem of constructing optimal privatization schemes with $\epsilon $ -privacy level, i.e., schemes that minimize the expected estimation loss for the worst-case Distribution. Two schemes known in the literature provide order optimal performance in the high privacy regime where $\epsilon $ is very close to 0, and in the low privacy regime where $e^{\epsilon }\approx k$ , respectively. In this paper, we propose a new family of schemes which substantially improve the performance of the existing schemes in the medium privacy regime when $1\ll e^{\epsilon } \ll k$ . More concretely, we prove that when $3.8 , our schemes reduce the expected estimation loss by 50% under $\ell _{2}^{2}$ metric and by 30% under $\ell _{1}$ metric over the existing schemes. We also prove a lower bound for the region $e^{\epsilon } \ll k$ , which implies that our schemes are order optimal in this regime.
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optimal schemes for Discrete Distribution estimation under local differential privacy
International Symposium on Information Theory, 2017Co-Authors: Alexander BargAbstract:We consider the minimax estimation problem of a Discrete Distribution with support size k under privacy constraints. A privatization scheme is applied to each raw sample independently, and we need to estimate the Distribution of the raw samples from the privatized samples. A positive number ∊ measures the privacy level of a privatization scheme. For a given ∊, we want to find the optimal privatization scheme which minimizes the expected estimation loss for the worst-case Distribution. Two schemes in the literature provide order optimal performance in the high-privacy regime when ∊ is very close to 0, and in the low-privacy regime when e∊ ≈ k, respectively. In this paper, we propose a new family of schemes which substantially improve the performance of the existing schemes in the medium privacy regime when 1 ≪ e∊ ≪ k. More concretely, we prove that when 3.8 2 metric and 30% under l 1 metric over the existing schemes. We also prove a tight lower bound for the whole region e∊ ≪ k, which implies that our schemes are order optimal in this regime.
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optimal schemes for Discrete Distribution estimation under locally differential privacy
arXiv: Learning, 2017Co-Authors: Alexander BargAbstract:We consider the minimax estimation problem of a Discrete Distribution with support size $k$ under privacy constraints. A privatization scheme is applied to each raw sample independently, and we need to estimate the Distribution of the raw samples from the privatized samples. A positive number $\epsilon$ measures the privacy level of a privatization scheme. For a given $\epsilon,$ we consider the problem of constructing optimal privatization schemes with $\epsilon$-privacy level, i.e., schemes that minimize the expected estimation loss for the worst-case Distribution. Two schemes in the literature provide order optimal performance in the high privacy regime where $\epsilon$ is very close to $0,$ and in the low privacy regime where $e^{\epsilon}\approx k,$ respectively. In this paper, we propose a new family of schemes which substantially improve the performance of the existing schemes in the medium privacy regime when $1\ll e^{\epsilon} \ll k.$ More concretely, we prove that when $3.8 < \epsilon <\ln(k/9) ,$ our schemes reduce the expected estimation loss by $50\%$ under $\ell_2^2$ metric and by $30\%$ under $\ell_1$ metric over the existing schemes. We also prove a lower bound for the region $e^{\epsilon} \ll k,$ which implies that our schemes are order optimal in this regime.
Hidefumi Hiura - One of the best experts on this subject based on the ideXlab platform.
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determination of the number of graphene layers Discrete Distribution of the secondary electron intensity stemming from individual graphene layers
Applied Physics Express, 2010Co-Authors: Hidefumi Hiura, Hisao Miyazaki, Kazuhito TsukagoshiAbstract:Using a scanning electron microscope, we observed a reproducible, Discrete Distribution of secondary electron intensity stemming from an atomically thick graphene film on a thick insulating substrate. We found a distinct linear relationship between the relative secondary electron intensity from graphene and the number of layers, provided that a low primary electron acceleration voltage was used. Based on these observations, we propose a practical method to determine the number of graphene layers in a sample. This method is superior to the conventional optical method in terms of its capability to characterize graphene samples with sub-micrometer squares in area on various insulating substrates.
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determination of the number of graphene layers Discrete Distribution of the secondary electron intensity derived from individual graphene layers
arXiv: Materials Science, 2010Co-Authors: Hidefumi Hiura, Hisao Miyazaki, Kazuhito TsukagoshiAbstract:Using a scanning electron microscope, we observed a reproducible, Discrete Distribution of secondary electron intensity stemming from an atomically thick graphene film on a thick insulating substrate. The Discrete Distribution made it possible to uniquely relate the secondary electron intensity to the number of graphene layers. Furthermore, we found a distinct linear relationship between the relative secondary electron intensity from graphene and the number of layers, provided a low primary electron acceleration voltage was used. Based on these observations, we propose a practical method to determine the number of graphene layers in a sample. This method is superior to the conventional optical method in its capability to characterize graphene samples with sub-micrometer squares in area on various insulating substrates.
R.g. Shenoy - One of the best experts on this subject based on the ideXlab platform.
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Discrete-time, Discrete-frequency, time-frequency analysis
IEEE Transactions on Signal Processing, 1998Co-Authors: M.s. Richman, T.w. Parks, R.g. ShenoyAbstract:A formulation of a Discrete-time, Discrete-frequency Wigner Distribution for analysis of Discrete-time, periodic signals is given using an approach involving group representation theory. This approach is motivated by a well-known connection between group theory and the continuous Wigner Distribution. The advantage of this approach is that the resulting Discrete Distribution satisfies mathematical properties analogous to those satisfied by the continuous Distribution. After outlining the relationship between group representation theory and time-frequency analysis, we derive the Discrete Distribution and exhibit many of its mathematical properties. These include time and frequency marginals, the Weyl correspondence, and covariance. In particular, the interpretation of covariance for the Discrete Distribution is shown to be different than that for the continuous Distribution. Finally, we note some unusual features of this Discrete Distribution, which are a consequence of the group-theoretic derivation.
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Discrete-Time, Discrete-Frequency,
1998Co-Authors: M.s. Richman, T.w. Parks, R.g. ShenoyAbstract:A formulation of a Discrete-time, Discrete-frequency Wigner Distribution for analysis of Discrete-time, periodic signals is given using an approach involving group representation theory. This approach is motivated by a well-known connection between group theory and the continuous Wigner Distribution. The ad- vantage of this approach is that the resulting Discrete Distribution satisfies mathematical properties analogous to those satisfied by the continuous Distribution. After outlining the relationship be- tween group representation theory and time-frequency analysis, we derive the Discrete Distribution and exhibit many of its mathe- matical properties. These include time and frequency marginals, the Weyl correspondence, and covariance. In particular, the interpretation of covariance for the Discrete Distribution is shown to be different than that for the continuous Distribution. Finally, we note some unusual features of this Discrete Distribution, which are a consequence of the group-theoretic derivation.
Kazuhito Tsukagoshi - One of the best experts on this subject based on the ideXlab platform.
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determination of the number of graphene layers Discrete Distribution of the secondary electron intensity stemming from individual graphene layers
Applied Physics Express, 2010Co-Authors: Hidefumi Hiura, Hisao Miyazaki, Kazuhito TsukagoshiAbstract:Using a scanning electron microscope, we observed a reproducible, Discrete Distribution of secondary electron intensity stemming from an atomically thick graphene film on a thick insulating substrate. We found a distinct linear relationship between the relative secondary electron intensity from graphene and the number of layers, provided that a low primary electron acceleration voltage was used. Based on these observations, we propose a practical method to determine the number of graphene layers in a sample. This method is superior to the conventional optical method in terms of its capability to characterize graphene samples with sub-micrometer squares in area on various insulating substrates.
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determination of the number of graphene layers Discrete Distribution of the secondary electron intensity derived from individual graphene layers
arXiv: Materials Science, 2010Co-Authors: Hidefumi Hiura, Hisao Miyazaki, Kazuhito TsukagoshiAbstract:Using a scanning electron microscope, we observed a reproducible, Discrete Distribution of secondary electron intensity stemming from an atomically thick graphene film on a thick insulating substrate. The Discrete Distribution made it possible to uniquely relate the secondary electron intensity to the number of graphene layers. Furthermore, we found a distinct linear relationship between the relative secondary electron intensity from graphene and the number of layers, provided a low primary electron acceleration voltage was used. Based on these observations, we propose a practical method to determine the number of graphene layers in a sample. This method is superior to the conventional optical method in its capability to characterize graphene samples with sub-micrometer squares in area on various insulating substrates.
Chuanhai Liu - One of the best experts on this subject based on the ideXlab platform.
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Estimation of Discrete Distributions with a Class of Simplex Constraints
Journal of the American Statistical Association, 2000Co-Authors: Chuanhai LiuAbstract:Abstract Simplex constraints, such as monotonicity and convexity or concavity on the probabilities of a set of Discrete Distributions, are useful for modeling and analyzing Discrete data. This article considers both maximum likelihood estimation and Bayesian estimation of Discrete Distribution with a class of simplex constraints using the Expectation-Maximization (EM) algorithm and the data augmentation (DA) algorithm. The formulation and implementation of EM and DA for binomial, Poisson, hierarchical Poisson-binomial, multinomial, and hierarchical multinomial Distributions are considered in detail and illustrated with examples.