Algorithmic statistics: forty years later

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 a "good model" is introduced, a natural question arises: it is possible that for some piece of data there is no good model? If yes, how often these bad ("non-stochastic") data appear "in real life"? Another, more technical motivation comes from algorithmic information theory. In this theory a notion of complexity of a finite object (=amount of information in this object) is introduced; it assigns to every object some number, called its algorithmic complexity (or Kolmogorov complexity). Algorithmic statistic provides a more fine-grained classification: for each finite object some curve is defined that characterizes its behavior. It turns out that several different definitions give (approximately) the same curve. In this survey we try to provide an exposition of the main results in the field (including full proofs for the most important ones), as well as some historical comments. We assume that the reader is familiar with the main notions of algorithmic information (Kolmogorov complexity) theory.Comment: Missing proofs adde

The Universal Plausibility Metric (UPM) & Principle (UPP)

<p>Abstract</p> <p>Background</p> <p>Mere possibility is not an adequate basis for asserting scientific plausibility. A precisely defined universal bound is needed beyond which the assertion of <it>plausibility</it>, particularly in life-origin models, can be considered operationally falsified. But can something so seemingly relative and subjective as plausibility ever be quantified? Amazingly, the answer is, "Yes." A method of objectively measuring the plausibility of any chance hypothesis (The Universal Plausibility Metric [UPM]) is presented. A numerical inequality is also provided whereby any chance hypothesis can be definitively falsified when its UPM metric of ξ is < 1 (The Universal Plausibility Principle [UPP]). Both UPM and UPP pre-exist and are independent of any experimental design and data set.</p> <p>Conclusion</p> <p>No low-probability hypothetical plausibility assertion should survive peer-review without subjection to the UPP inequality standard of formal falsification (ξ < 1).</p

RECURSIA-RRT:Recursive translatable point-set pattern discovery with removal of redundant translators

We introduce two algorithms, RECURSIA and RRT, designed to increase the compression factor achievable using point-set cover algorithms based on the SIA and SIATEC pattern discovery algorithms. SIA computes the maximal translatable patterns (MTPs) in a point set, while SIATEC computes the translational equivalence class (TEC) of every MTP in a point set, where the TEC of an MTP is the set of translationally invariant occurrences of that MTP in the point set. In its output, SIATEC encodes each MTP TEC as a pair, , where P is the first occurrence of the MTP and V is the set of non-zero vectors that map P onto its other occurrences. RECURSIA recursively applies a TEC cover algorithm to the pattern P, in each TEC, , that it discovers. RRT attempts to remove translators from V in each TEC without reducing the total set of points covered by the TEC. When evaluated with COSIATEC, SIATECCompress and Forth's algorithm on the JKU Patterns Development Database, using RECURSIA with or without RRT increased compression factor and recall but reduced precision. Using RRT alone increased compression factor and reduced recall and precision, but had a smaller effect than RECURSIA.Comment: Submitted to 12th International Workshop on Machine Learning and Music (https://musml2019.weebly.com/

We Must Choose The Simplest Physical Theory: Levin-Li-Vitányi Theorem And Its Potential Physical Applications

. If several physical theories are consistent with the same experimental data, which theory should we choose? Physicists often choose the simplest theory; this principle (explicitly formulated by Occam) is one of the basic principles of physical reasoning. However, until recently, this principle was mainly a heuristic because it uses the informal notion of simplicity. With the explicit notion of simplicity coming from the Algorithmic Information theory, it is possible not only to formalize this principle in a way that is consistent with its traditional usage in physics, but also to prove this principle, or, to be more precise, deduce it from the fundamentals of mathematical statistics as the choice corresponding to the least informative prior measure. Potential physical applications of this formalization (due to Li and Vit&apos;anyi) are presented. In particular, we show that, on the qualitative level, most fundamental ideas of physics can be re-formulated as natural steps towards choosing..