Related papers: A theory of incremental compression
High-energy, large-scale particle colliders in nuclear and high-energy physics generate data at extraordinary rates, reaching up to $1$ terabyte and several petabytes per second, respectively. The development of real-time, high-throughput…
Reductions combine collections of input values with an associative and often commutative operator to produce collections of results. When the same input value contributes to multiple outputs, there is an opportunity to reuse partial…
Kolmogorov complexity theory is used to tell what the algorithmic informational content of a string is. It is defined as the length of the shortest program that describes the string. We present a programming language that can be used to…
Multivariate information theory provides a general and principled framework for understanding how the components of a complex system are connected. Existing analyses are coarse in nature -- built up from characterizations of discrete…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
In this paper we present a general method for information extraction that exploits the features of data compression techniques. We first define and focus our attention on the so-called "dictionary" of a sequence. Dictionaries are…
Scientific computations or measurements may result in huge volumes of data. Often these can be thought of representing a real-valued function on a high-dimensional domain, and can be conceptually arranged in the format of a tensor of high…
A popular approach to sentence compression is to formulate the task as a constrained optimization problem and solve it with integer linear programming (ILP) tools. Unfortunately, dependence on ILP may make the compressor prohibitively slow,…
Recently, sparsity has become a key concept in various areas of applied mathematics, computer science, and electrical engineering. One application of this novel methodology is the separation of data, which is composed of two (or more)…
$\textit{Implicit neural representations}$ (INRs) aim to learn a $\textit{continuous function}$ (i.e., a neural network) to represent an image, where the input and output of the function are pixel coordinates and RGB/Gray values,…
Algorithmic statistics has two different (and almost orthogonal) motivations. From the philosophical point of view, it tries to formalize how the statistics works and why some statistical models are better than others. After this notion of…
The word "complexity" is most often used as a meta--linguistic expression referring to certain intuitive characteristics of a natural system and/or its scientific description. These characteristics may include: sheer amount of data that…
One requirement of maintaining digital information is storage. With the latest advances in the digital world, new emerging media types have required even more storage space to be kept than before. In fact, in many cases it is required to…
We present a fully automatic method for music classification, based only on compression of strings that represent the music pieces. The method uses no background knowledge about music whatsoever: it is completely general and can, without…
We present a new algorithm for incrementally updating the tensor train decomposition of a stream of tensor data. This new algorithm, called the {\em tensor train incremental core expansion} (TT-ICE) improves upon the current…
In this paper, we propose an information-theoretic approach to design the functional representations to extract the hidden common structure shared by a set of random variables. The main idea is to measure the common information between the…
This philosophical paper proposes a modified version of the scientific method, in which large databases are used instead of experimental observations as the necessary empirical ingredient. This change in the source of the empirical data…
Run-Length Encoding (RLE) is one of the most fundamental tools in data compression. However, its compression power drops significantly if there lacks consecutive elements in the sequence. In extreme cases, the output of the encoder may…
According to Algorithmic Information Theory (AIT) -- Intelligent representations compress data into the shortest possible program that can reconstruct its content, exhibiting low Kolmogorov Complexity (KC). In contrast, most visual…
Traditionally, data compression deals with the problem of concisely representing a data source, e.g. a sequence of letters, for the purpose of eventual reproduction (either exact or approximate). In this work we are interested in the case…