10,734 research outputs found
Estimation under group actions: recovering orbits from invariants
Motivated by geometric problems in signal processing, computer vision, and
structural biology, we study a class of orbit recovery problems where we
observe very noisy copies of an unknown signal, each acted upon by a random
element of some group (such as Z/p or SO(3)). The goal is to recover the orbit
of the signal under the group action in the high-noise regime. This generalizes
problems of interest such as multi-reference alignment (MRA) and the
reconstruction problem in cryo-electron microscopy (cryo-EM). We obtain
matching lower and upper bounds on the sample complexity of these problems in
high generality, showing that the statistical difficulty is intricately
determined by the invariant theory of the underlying symmetry group.
In particular, we determine that for cryo-EM with noise variance
and uniform viewing directions, the number of samples required scales as
. We match this bound with a novel algorithm for ab initio
reconstruction in cryo-EM, based on invariant features of degree at most 3. We
further discuss how to recover multiple molecular structures from heterogeneous
cryo-EM samples.Comment: 54 pages. This version contains a number of new result
Adaptive Density Estimation for Generative Models
Unsupervised learning of generative models has seen tremendous progress over
recent years, in particular due to generative adversarial networks (GANs),
variational autoencoders, and flow-based models. GANs have dramatically
improved sample quality, but suffer from two drawbacks: (i) they mode-drop,
i.e., do not cover the full support of the train data, and (ii) they do not
allow for likelihood evaluations on held-out data. In contrast,
likelihood-based training encourages models to cover the full support of the
train data, but yields poorer samples. These mutual shortcomings can in
principle be addressed by training generative latent variable models in a
hybrid adversarial-likelihood manner. However, we show that commonly made
parametric assumptions create a conflict between them, making successful hybrid
models non trivial. As a solution, we propose to use deep invertible
transformations in the latent variable decoder. This approach allows for
likelihood computations in image space, is more efficient than fully invertible
models, and can take full advantage of adversarial training. We show that our
model significantly improves over existing hybrid models: offering GAN-like
samples, IS and FID scores that are competitive with fully adversarial models,
and improved likelihood scores
Pseudo-Random Bit Generator Using Chaotic Seed for Cryptographic Algorithm in Data Protection of Electric Power Consumption
Cryptographic algorithms have played an important role in information security for protecting privacy. The literature provides evidence that many types of chaotic cryptosystems have been proposed. These chaotic systems encode information to obviate its orbital instability and ergodicity. In this work, a pseudo-random cryptographic generator algorithm with a symmetric key, based on chaotic functions, is proposed. Moreover, the algorithm exploits dynamic simplicity and synchronization to generate encryption sub-keys using unpredictable seeds, extracted from a chaotic zone, in order to increase their level of randomness. Also, it is applied to a simulated electrical energy consumption signal and implemented on a prototype, using low hardware resources, to measure physical variables; hence, the unpredictability degree was statistically analyzed using the resulting cryptogram. It is shown that the pseudo-random sequences produced by the cryptographic key generator have acceptable properties with respect to randomness, which are validated in this paper using National Institute of Standards and Technology (NIST) statistical tests. To complement the evaluation of the encrypted data, the Lena image is coded and its metrics are compared with those reported in the literature, yielding some useful results
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