Related papers: Compression-based methods for nonparametric densit…

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…

We suggest a new approach to hypothesis testing for ergodic and stationary processes. In contrast to standard methods, the suggested approach gives a possibility to make tests, based on any lossless data compression method even if the…

We describe and experimentally investigate a method to construct forecasting algorithms for stationary and ergodic processes based on universal measures (or so-called universal data compressors). Using some geophysical and economical time…

Most of the world's digital data is currently encoded in a sequential form, and compression methods for sequences have been studied extensively. However, there are many types of non-sequential data for which good compression techniques are…

Suppose there is a large file which should be transmitted (or stored) and there are several (say, m) admissible data-compressors. It seems natural to try all the compressors and then choose the best, i.e. the one that gives the shortest…

Sequential probability assignment and universal compression go hand in hand. We propose sequential probability assignment for non-binary (and large alphabet) sequences with empirical distributions whose parameters are known to be bounded…

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…

We show that Kolmogorov complexity and such its estimators as universal codes (or data compression methods) can be applied for hypotheses testing in a framework of classical mathematical statistics. The methods for identity testing and…

We proposed a learning algorithm for nonparametric estimation and on-line prediction for general stationary ergodic sources. We prepare histograms each of which estimates the probability as a finite distribution, and mixture them with…

Linear models are used in online decision making, such as in machine learning, policy algorithms, and experimentation platforms. Many engineering systems that use linear models achieve computational efficiency through distributed systems…

The predictive advantage of combining several different predictive models is widely accepted. Particularly in time series forecasting problems, this combination is often dynamic to cope with potential non-stationary sources of variation…

Time series account for a large proportion of the data stored in financial, medical and scientific databases. The efficient storage of time series is important in practical applications. In this paper, we propose a novel compression scheme…

The rapid growth of digital data has heightened the demand for efficient lossless compression methods. However, existing algorithms exhibit trade-offs: some achieve high compression ratios, others excel in encoding or decoding speed, and…

We introduce a nonparametric spectral density estimator for continuous-time and continuous-space processes measured at fully irregular locations. Our estimator is constructed using a weighted nonuniform Fourier sum whose weights yield a…

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 evaluation of time series models has traditionally focused on four canonical tasks: forecasting, imputation, anomaly detection, and classification. While these tasks have driven significant progress, they primarily assess task-specific…

In this work a method for statistical analysis of time series is proposed, which is used to obtain solutions to some classical problems of mathematical statistics under the only assumption that the process generating the data is stationary…

The growing popularity of wearable sensors has generated large quantities of temporal physiological and activity data. Ability to analyze this data offers new opportunities for real-time health monitoring and forecasting. However, temporal…

Consider the case where consecutive blocks of N letters of a semi-infinite individual sequence X over a finite-alphabet are being compressed into binary sequences by some one-to-one mapping. No a-priori information about X is available at…

We consider nonparametric or universal sequential hypothesis testing problem when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution. These algorithms are…