Related papers: Sequential Recurrence-Based Multidimensional Unive…
Time series constitute a challenging data type for machine learning algorithms, due to their highly variable lengths and sparse labeling in practice. In this paper, we tackle this challenge by proposing an unsupervised method to learn…
We propose a universal ensemble for random selection of rate-distortion codes, which is asymptotically optimal in a sample-wise sense. According to this ensemble, each reproduction vector, $\hbx$, is selected independently at random under…
We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a…
The Lempel-Ziv parsing of a string (LZ77 for short) is one of the most important and widely-used algorithmic tools in data compression and string processing. We show that the Lempel-Ziv parsing of a string of length $n$ on an alphabet of…
A mainstream type of current self-supervised learning methods pursues a general-purpose representation that can be well transferred to downstream tasks, typically by optimizing on a given pretext task such as instance discrimination. In…
As it is known, universal codes, which estimate the entropy rate consistently, exist for stationary ergodic sources over finite alphabets but not over countably infinite ones. We generalize universal coding as the problem of universal…
Motivated from the fact that universal source coding on countably infinite alphabets is not feasible, this work introduces the notion of almost lossless source coding. Analog to the weak variable-length source coding problem studied by Han…
Computation on compressed strings is one of the key approaches to processing massive data sets. We consider local subsequence recognition problems on strings compressed by straight-line programs (SLP), which is closely related to…
We show that the typical coordinate-wise encoding of multivariate ergodic source into prescribed alphabets has the entropy profile close to the convolution of the entropy profile of the source and the modular polymatroid that is determined…
Sequence processing has long been a central area of machine learning research. Recurrent neural nets have been successful in processing sequences for a number of tasks; however, they are known to be both ineffective and computationally…
Motivated by the established notion of storage codes, we consider sets of infinite sequences over a finite alphabet such that every $k$-tuple of consecutive entries is uniquely recoverable from its $l$-neighborhood in the sequence. We…
The well-known dictionary-based algorithms of the Lempel-Ziv (LZ) 77 family are the basis of several universal lossless compression techniques. These algorithms are asymmetric regarding encoding/decoding time and memory requirements, with…
LP-type problems such as the Minimum Enclosing Ball (MEB), Linear Support Vector Machine (SVM), Linear Programming (LP), and Semidefinite Programming (SDP) are fundamental combinatorial optimization problems, with many important…
In this paper, the context dependence multilevel pattern matching(in short CDMPM) grammar transform is proposed; based on this grammar transform, the universal lossless data compression algorithm, CDMPM code is then developed. Moreover we…
We introduce the notion of combinatorial encoding of continuous dynamical systems and suggest the first examples, which are the most interesting and important, namely, the combinatorial encoding of a Bernoulli process with continuous state…
There is a class of entropy-coding methods which do not substitute symbols by code words (such as Huffman coding), but operate on intervals or ranges. This class includes three prominent members: conventional arithmetic coding, range…
Homogeneous continued fraction algorithms are multidimensional generalizations of the classical Euclidean algorithm, the dissipative map $$ (x_1,x_2) \in \mathbb{R}_+^2 \longmapsto \left\{\begin{array}{ll} (x_1 - x_2, x_2), & \mbox{if $x_1…
We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a…
We present a framework facilitating the implementation and comparison of text compression algorithms. We evaluate its features by a case study on two novel compression algorithms based on the Lempel-Ziv compression schemes that perform well…
The entropy of an ergodic source is the limit of properly rescaled 1-block entropies of sources obtained applying successive non-sequential recursive pairs substitutions (see P. Grassberger 2002 ArXiv:physics/0207023 and D. Benedetto, E.…