Related papers: Moser-Tardos resampling algorithm, entropy compres…
We consider the RANSAC algorithm in the context of subspace recovery and subspace clustering. We derive some theory and perform some numerical experiments. We also draw some correspondences with the methods of Hardt and Moitra (2013) and…
We introduce a systematic framework to calculate the bipartite entanglement entropy of a compact spatial subsystem in a one-dimensional quantum gas which can be mapped into a noninteracting fermion system. We show that when working with a…
We consider critical models in one dimension. We study the ground state in thermodynamic limit [infinite lattice]. Following Bennett, Bernstein, Popescu, and Schumacher, we use the entropy of a sub-system as a measure of entanglement. We…
We study the approximate string matching and regular expression matching problem for the case when the text to be searched is compressed with the Ziv-Lempel adaptive dictionary compression schemes. We present a time-space trade-off that…
A common approach for sequence tagging tasks based on contextual word representations is to train a machine learning classifier directly on these embedding vectors. This approach has two shortcomings. First, such methods consider single…
Methods for proving functional limit laws are developed for sequences of stochastic processes which allow a recursive distributional decomposition either in time or space. Our approach is an extension of the so-called contraction method to…
We prove theoretically that generalization improves not only through data scaling but also by compressing internal representations. To operationalize this insight, we introduce the Information Bottleneck Language Modeling (IBLM) objective,…
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of…
In the present article we are interested in further investigations for the barotropic compressible Navier-Stokes system endowed with a non-local capillarity we studied in [7]. Thanks to an accurate study of the associated linear system…
Mixture distributions are a workhorse model for multimodal data in information theory, signal processing, and machine learning. Yet even when each component density is simple, the differential entropy of the mixture is notoriously hard to…
Lloyd's algorithm is an iterative method that solves the quantization problem, i.e. the approximation of a target probability measure by a discrete one, and is particularly used in digital applications. This algorithm can be interpreted as…
Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance…
The mathematical analysis on the behavior of the entropy for viscous, compressible, and heat conducting magnetohydrodynamic flows near the vacuum region is a challenging problem as the governing equation for entropy is highly degenerate and…
The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular research tool among physicists, especially when applied to a dynamical system fitting the conditions of validity of the Pesin theorem. The study of time series that are…
We construct suitable metrics for two classes of topological dynamical systems (linear maps on the torus and non-invertible expansive maps on compact spaces) in order to get a lower bound for topological entropy in terms of the resulting…
We study a relaxation of the problem of coupling probability distributions -- a list of samples is generated from one distribution and an accept is declared if any one of these samples is identical to the sample generated from the other…
Local correlation entropy, introduced by Takens in 1983, represents the exponential decay rate of the relative frequency of recurrences in the trajectory of a point, as the embedding dimension grows to infinity. In this paper we study…
For a general class of lattice-spin systems, we prove that an abstract Gaussian concentration bound implies positivity of lower relative entropy density. As a consequence we obtain uniqueness of translation-invariant Gibbs measures from the…
We investigate entropy production in the small-mass (or overdamped) limit of Langevin-Kramers dynamics. The results generalize previous works to provide a rigorous derivation that covers systems with magnetic field as well as anisotropic…
We comment on two randomized algorithms for constructing low-rank matrix decompositions. Both algorithms employ the Subsampled Randomized Hadamard Transform [14]. The first algorithm appeared recently in [9]; here, we provide a novel…