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Alexander Stotsky

Publications and source records attributed to Alexander Stotsky.

8 recordsLinked to original sources
arXiv2025

RLS Framework with Segmentation of the Forgetting Profile and Low Rank Updates

This report describes a new regularization approach based on segmentation of the forgetting profile in sliding window least squares estimation. Each segment is designed to enforce specific desirable properties of the estimator such as rapidity, desired condition number of the information matrix, accuracy, numerical stability, etc. The forgetting profile is divided in three segments, where the speed of estimation is ensured by the first segment, which employs rapid exponential forgetting of recent data.The second segment features a decline in the profile and marks the transition to the third segment, characterized by slow exponential forgetting to reduce the condition number of the information matrix using more distant data. Condition number reduction mitigates error propagation, thereby enhancing accuracy and stability. This approach facilitates the incorporation of a priori information regarding signal characteristics (i.e., the expected behavior of the signal) into the estimator. Recursive and computationally efficient algorithm with low rank updates based on new matrix inversion lemma for moving window associated with this regularization approach is developed. New algorithms significantly improve the approximation accuracy of low resolution daily temperature measurements obtained at the Stockholm Old Astronomical Observatory, thereby enhancing the reliability of temperature predictions.

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arXiv2025

Performance Enhancement of the Recursive Least Squares Algorithms with Rank Two Updates

New recursive least squares algorithms with rank two updates (RLSR2) that include both exponential and instantaneous forgetting (implemented via a proper choice of the forgetting factor and the window size) are introduced and systematically associated in this report with well-known RLS algorithms with rank one updates. Moreover, new properties (which can be used for further performance improvement) of the recursive algorithms associated with the convergence of the inverse of information matrix and parameter vector are established in this report. The performance of new algorithms is examined in the problem of estimation of the grid events in the presence of significant harmonic emissions.

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arXiv2025

Development of New Methods for Detection and Control of Credit Card Fraud Attacks

Credit card fraud causes significant financial losses and frequently occurs as fraud attack, defined as short-term sequence of fraudulent transactions associated with high transaction rates and amounts, business areas historically tied to fraud, unusual transaction times and locations and different types of errors. Confidence interval method in the moving window with exponential forgetting is proposed in this report which allows to capture recent changes in the shopping behaviour of the cardholder, detect fraudulent amounts and mitigate the attack. Fraud risk scoring method is used for estimation of the intensity of the fraudulent activity via monitoring of the transaction rates, merchant category codes, times and some other factors for detection of the start of the attack. The development and verification are based on detailed analysis of the transaction patterns from the dataset, which represents an extensive collection of around 24.4 million credit card transactions from IBM financial database. Recommendations for further development of the detection techniques are also presented.

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arXiv2024

Automatic Generation of Examinations in the Automatic Control Courses

Final written examination is the most important part of summative assessment in automatic control courses. Preparation of the examinations with a given number of points according to the concept of Constructive Alignment (which could be the main concept in future automatic control education) takes significant amount of time of the educator and motivates development of a toolkit for automatic compilation of examination problems. A decision support Matlab-LATEX toolkit based on random number generators for selection of examination problems is described in this report to facilitate the alignment. The toolkit allows application of Stepwise Constructive Alignment (a new method described in this report), where the alignment is achieved by a number of software runs associated with random trials. In each step the educator manually selects suitable problems before each run based on evaluation of the random choice from the previous run. Automatic generation of the examination together with solutions for the course 'Process control and measurement techniques' is presented as an example.

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arXiv2023

Richardson Approach or Direct Methods? What to Apply in the Ill-Conditioned Least Squares Problem

This report shows on real data that the direct methods such as LDL decomposition and Gaussian elimination for solving linear systems with ill-conditioned matrices provide inaccurate results due to divisions by very small numbers, which in turn results in peaking phenomena and large estimation errors. Richardson iteration provides accurate results without peaking phenomena since division by small numbers is absent in the Richardson approach. In addition, two preconditioners are considered and compared in the Richardson iteration: 1) the simplest and robust preconditioner based on the maximum row sum matrix norm and 2) the optimal one based on calculation of the eigenvalues. It is shown that the simplest preconditioner is more robust for ill-conditioned case and therefore it is recommended for many applications.

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arXiv2022

Systematic Review of Newton-Schulz Iterations with Unified Factorizations : Integration in the Richardson Method and Application to Robust Failure Detection in Electrical Networks

Systematic overview of Newton-Schulz and Durand iterations with convergence analysis and factorizations is presented in the chronological sequence in unified framework. Practical recommendations for the choice of the order and factorizations of the algorithms and integration into Richardson iteration are given. The simplest combination of Newton-Schulz and Richardson iteration is applied to the parameter estimation problem associated with the failure detection via evaluation of the frequency content of the signals in electrical network. The detection is performed on real data for which the software failure was simulated, which resulted in the rank deficient information matrix. Robust preconditioning for rank deficient matrices is proposed and the efficiency of the approach is demonstrated by simulations via comparison with standard LU decomposition method.

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arXiv2020

Convergence Rate Improvement of Richardson and Newton-Schulz Iterations

Fast convergent, accurate, computationally efficient, parallelizable, and robust matrix inversion and parameter estimation algorithms are required in many time-critical and accuracy-critical applications such as system identification, signal and image processing, network and big data analysis, machine learning and in many others. This paper introduces new composite power series expansion with optionally chosen rates (which can be calculated simultaneously on parallel units with different computational capacities) for further convergence rate improvement of high order Newton-Schulz iteration. New expansion was integrated into the Richardson iteration and resulted in significant convergence rate improvement. The improvement is quantified via explicit transient models for estimation errors and by simulations. In addition, the recursive and computationally efficient version of the combination of Richardson iteration and Newton-Schulz iteration with composite expansion is developed for simultaneous calculations. Moreover, unified factorization is developed in this paper in the form of tool-kit for power series expansion, which results in a new family of computationally efficient Newton-Schulz algorithms.

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