Algorithmic statistics, prediction and machine learning

Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation. In this paper we extend this framework in two directions. First, the explanations are not only interesting in themselves but also used for prediction: we want to know what kind of data we may reasonably expect in similar situations (repeating the same experiment). We show that some kind of hierarchy can be constructed both in terms of algorithmic statistics and using the notion of a priori probability, and these two approaches turn out to be equivalent. Second, a more realistic approach that goes back to machine learning theory, assumes that we have not a single data string $x$ but some set of "positive examples" $x_1,\ldots,x_l$ that all belong to some unknown set $A$, a property that we want to learn. We want this set $A$ to contain all positive examples and to be as small and simple as possible. We show how algorithmic statistic can be extended to cover this situation.Comment: 22 page

Predictions and algorithmic statistics for infinite sequence

Consider the following prediction problem. Assume that there is a block box that produces bits according to some unknown computable distribution on the binary tree. We know first $n$ bits $x_1 x_2 \ldots x_n$. We want to know the probability of the event that that the next bit is equal to $1$. Solomonoff suggested to use universal semimeasure $m$ for solving this task. He proved that for every computable distribution $P$ and for every $b \in \{0,1\}$ the following holds: $$\sum_{n=1}^{\infty}\sum_{x: l(x)=n} P(x) (P(b | x) - m(b | x))^2 < \infty\ .$$ However, Solomonoff's method has a negative aspect: Hutter and Muchnik proved that there are an universal semimeasure $m$, computable distribution $P$ and a random (in Martin-L{\"o}f sense) sequence $x_1 x_2\ldots$ such that $\lim_{n \to \infty} P(x_{n+1} | x_1\ldots x_n) - m(x_{n+1} | x_1\ldots x_n) \nrightarrow 0$. We suggest a new way for prediction. For every finite string $x$ we predict the new bit according to the best (in some sence) distribution for $x$. We prove the similar result as Solomonoff theorem for our way of prediction. Also we show that our method of prediction has no that negative aspect as Solomonoff's method.Comment: 12 page

Stochasticity in Algorithmic Statistics for Polynomial Time

A fundamental notion in Algorithmic Statistics is that of a stochastic object, i.e., an object having a simple plausible explanation. Informally, a probability distribution is a plausible explanation for x if it looks likely that x was drawn at random with respect to that distribution. In this paper, we suggest three definitions of a plausible statistical hypothesis for Algorithmic Statistics with polynomial time bounds, which are called acceptability, plausibility and optimality. Roughly speaking, a probability distribution m is called an acceptable explanation for x, if x possesses all properties decidable by short programs in a short time and shared by almost all objects (with respect to m). Plausibility is a similar notion, however this time we require x to possess all properties T decidable even by long programs in a short time and shared by almost all objects. To compensate the increase in program length, we strengthen the notion of `almost all\u27 - the longer the program recognizing the property is, the more objects must share the property. Finally, a probability distribution m is called an optimal explanation for x if m(x) is large. Almost all our results hold under some plausible complexity theoretic assumptions. Our main result states that for acceptability and plausibility there are infinitely many non-stochastic objects, i.e. objects that do not have simple plausible (acceptable) explanations. Using the same techniques, we show that the distinguishing complexity of a string x can be super-logarithmically less than the conditional complexity of x with condition r for almost all r (for polynomial time bounded programs). Finally, we study relationships between the introduced notions

LOCAL IRRIGATION METHODS FOR VEGETABLE PRODUCTION IN SOUTH OF RUSSIA

In the Southern Federal District, where the Volgograd region occupies a significant territory, cultivation of vegetable crops is impossible without irrigation. There was a large number of wide-spread sprinklers in the USSR. Each unit of this system watered at least 60 to70 hectares, required a lot of water pressure that resulted in high operating costs. Therefore, currently, such local irrigation methods as drip and subsoil irrigation have a broad development perspective. Both irrigation methods favorably differ from sprinkling by a significant increase in yield of vegetable crops, irrigation water saving, ease of operation and rapid investment return. In this regard, the main goal of our research, conducted at Volgograd State Agricultural University, is development of techniques and technologies for drip and subsoil irrigation that allow receiving projected vegetable yields while maintaining soil fertility and environmental safety. The research have shown that it is possible to obtain planned yields of 60, 70 and 80 t/ha of zucchini and table beet using drip irrigation in steppe zone of southern Russia on light chestnut soils. Therefore, it is necessary to observe irrigation regimes with maintaining pre-irrigation moisture (PIM) 75-85-75 and 85% of field moisture capacity (FMC) simultaneously with application of calculated doses of mineral fertilizers. Moreover, it is important to apply increased doses of mineral fertilizers with decrease in intensity of irrigation regime due to reduction in soil moisture content to 75% of FMC. The planned radish yield of 80 tons per hectare with subsoil irrigation can be obtained in variants with differentiated soil moisture 75-85-75% of FMC and 1.4 m distance n t between humidifiers, and also maintaining constant soil moisture at 85% of FMC at plots with 1.2 and 1.4 m distances

Precision improvement of MEMS gyros for indoor mobile robots with horizontal motion inspired by methods of TRIZ

In the paper, the problem of precision improvement for the MEMS gyrosensors on indoor robots with horizontal motion is solved by methods of TRIZ ("the theory of inventive problem solving").Comment: 6 pages, the paper is accepted to 9th IEEE International Conference on Nano/Micro Engineered and Molecular Systems, Hawaii, USA (IEEE-NEMS 2014) as an oral presentatio