arXiv subjects

Jaakko Astola

Publications and source records attributed to Jaakko Astola.

8 recordsLinked to original sources

arXiv2026

Stochastic complexity of vectors containing cluster structure

This paper studies the problem of computing the stochastic probability (shortest code length) of the encoded vectors containing cluster structure using Normalized Maximum Likelihood (NML) model. This is of great theoretical and practical importance in data clustering based on Minimum Description Length (MDL) principle, such as for estimating the best number of clusters and best cluster structure for the data. Straightforward computation of the shortest code length of the vector containing cluster structure based on the NML model requires polynomial time with respect to the size of the vector and number of clusters. We show that this is a tractable problem by introducing a recursion formula for the efficient computation of normalizing constant from the NML model. The time complexity of the new formula is linear opposed to previous polynomial time with respect to the size of the vector and number of clusters.

cs.LG↗

arXiv2011

Advanced phase retrieval: maximum likelihood technique with sparse regularization of phase and amplitude

Sparse modeling is one of the efficient techniques for imaging that allows recovering lost information. In this paper, we present a novel iterative phase-retrieval algorithm using a sparse representation of the object amplitude and phase. The algorithm is derived in terms of a constrained maximum likelihood, where the wave field reconstruction is performed using a number of noisy intensity-only observations with a zero-mean additive Gaussian noise. The developed algorithm enables the optimal solution for the object wave field reconstruction. Our goal is an improvement of the reconstruction quality with respect to the conventional algorithms. Sparse regularization results in advanced reconstruction accuracy, and numerical simulations demonstrate significant enhancement of imaging.

cs.CV↗

arXiv2007

Fast Recursive Coding Based on Grouping of Symbols

A novel fast recursive coding technique is proposed. It operates with only integer values not longer 8 bits and is multiplication free. Recursion the algorithm is based on indirectly provides rather effective coding of symbols for very large alphabets. The code length for the proposed technique can be up to 20-30% less than for arithmetic coding and, in the worst case it is only by 1-3% larger.

cs.IT↗

arXiv2006

Universal Codes as a Basis for Time Series Testing

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 distribution law of the codeword lengths is not known. We apply this approach to the following four problems: goodness-of-fit testing (or identity testing), testing for independence, testing of serial independence and homogeneity testing and suggest nonparametric statistical tests for these problems. It is important to note that practically used so-called archivers can be used for suggested testing.

cs.IT↗

arXiv2005

Universal Codes as a Basis for Nonparametric Testing of Serial Independence for Time Series

We consider a stationary and ergodic source $p$ generated symbols $x_1 ... x_t$ from some finite set $A$ and a null hypothesis $H_0$ that $p$ is Markovian source with memory (or connectivity) not larger than $m, (m >= 0).$ The alternative hypothesis $H_1$ is that the sequence is generated by a stationary and ergodic source, which differs from the source under $H_0$. In particular, if $m= 0$ we have the null hypothesis $H_0$ that the sequence is generated by Bernoully source (or the hypothesis that $x_1 ...x_t$ are independent.) Some new tests which are based on universal codes and universal predictors, are suggested.

cs.IT↗

arXiv2005

Application of Kolmogorov complexity and universal codes to identity testing and nonparametric testing of serial independence for time series

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 nonparametric testing of serial independence for time series are suggested.

cs.CC↗

arXiv2005

Prediction of Large Alphabet Processes and Its Application to Adaptive Source Coding

The problem of predicting a sequence $x_1,x_2,...$ generated by a discrete source with unknown statistics is considered. Each letter $x_{t+1}$ is predicted using information on the word $x_1x_2... x_t$ only. In fact, this problem is a classical problem which has received much attention. Its history can be traced back to Laplace. We address the problem where each $x_i$ belongs to some large (or even infinite) alphabet. A method is presented for which the precision is greater than for known algorithms, where precision is estimated by the Kullback-Leibler divergence. The results can readily be translated to results about adaptive coding.

cs.IT↗

arXiv2005

Fast Codes for Large Alphabets

We address the problem of constructing a fast lossless code in the case when the source alphabet is large. The main idea of the new scheme may be described as follows. We group letters with small probabilities in subsets (acting as super letters) and use time consuming coding for these subsets only, whereas letters in the subsets have the same code length and therefore can be coded fast. The described scheme can be applied to sources with known and unknown statistics.

cs.IT↗