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Digital Signatures
Published in Khaleel Ahmad, M. N. Doja, Nur Izura Udzir, Manu Pratap Singh, Emerging Security Algorithms and Techniques, 2019
The BLISS scheme is based on lattice problems and rejection sampling from bimodal Gaussian distribution. The BLISS proposes to hide the secret key s with a small random y by choosing y from a narrow distribution and then performs acceptance–rejection (Casella et al., 2004) so that s is not leaked when y is added to it. Conceptually, the BLISS signs a document by drawing a sample x from g and is accepted with probability f(x)/(M·g(x)), where M is some positive real. The process is repeated until the sample is accepted. In the numerical analysis, rejection sampling is a basic technique used to generate observations from a distribution. It is also commonly called the acceptance–rejection method or “accept–reject algorithm” and is a type of exact simulation method. The key generation, signature, and verification process are extracted from Ducas et al. (2013), as given in the following section (Figure 15.8).
Random Variables, Distributions & Linear Regression
Published in Nailong Zhang, A Tour of Data Science, 2020
Rejection sampling is also a basic algorithm to draw samples for a random variable X given its PDF fX. The basic idea of rejection sampling is to draw samples for a random variable Y with PDF fY and accept the samples with probability fX(x)/(MfY(x)). M is selected such that fX(x)/(MfY(x)) ≤ 1. If the sample generated is rejected, the sampling procedure is repeated until an acceptance. More theoretical details of rejection sampling can be found from wikipedia2. The distribution fY is called proposal distribution.
Sampling
Published in A. C. Faul, A Concise Introduction to Machine Learning, 2019
As with rejection sampling, the choice of the proposal distribution is crucial. Most importantly, it should not be small in regions where f is large. The weighting can only make a correction if an actual sample is drawn from this region.
Probabilistic nod generation model based on speech and estimated utterance categories
Published in Advanced Robotics, 2019
Chaoran Liu, Carlos Ishi, Hiroshi Ishiguro
Assuming the samples in the training set are independently drawn from distribution D with domain , x is the feature space, y is the class label, and I is the importance (i.e. the cost when that sample is misclassified). A previous theorem [21] states that when a sample is drawn from the following distribution: then the optimal error rate classifier for is an optimal cost minimizer for the samples drawn from D. In Equation (2), k is a constant. The rejection sampling scheme states that one can draw samples from distribution , given samples independently drawn from distribution D. In this process, each sample from D is either accepted or rejected given the probability .
On model order priors for Bayesian identification of SISO linear systems
Published in International Journal of Control, 2019
Patricio E. Valenzuela, Thomas B. Schön, Cristian R. Rojas
Thus, given the proposal distribution f, at step i of the MH sampler we generate θ⋆ from f(θ|θ(i)) and check if the conditions (32) are satisfied. If they are not satisfied, we then sample a new parameter θ⋆ until the inequalities (32) are fulfiled. In this manner we guarantee that the samples θ⋆ generated from f belong to Θ. Note that this method can be seen as a rejection sampling procedure.