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statistical complexity as a Criterion for the Useful Signal Detection Problem

AUTOMATION AND REMOTE CONTROL 2023年第7期84卷 753-771页

作者： Galyaev, A. A. Lysenko, P. V. Berlin, L. M. Russian Acad Sci Trapeznikov Inst Control Sci Moscow Russia

Three variants of the statistical complexity function, which is used as a criterion in the problem of detection of a useful signal in the signal-noise mixture, are considered. The probability distributions maximizing the considered variants of statistical complexity are obtained analytically and conclusions about the efficiency of using one or another variant for detection problem are made. The comparison of considered information characteristics is shown and analytical results are illustrated on an example of synthesized signals. A method is proposed for selecting the threshold of the information criterion, which can be used in decision rule for useful signal detection in the signal-noise mixture. The choice of the threshold depends a priori on the analytically obtained maximum values. As a result, the complexity based on the total variation demonstrates the best ability of useful signal detection.

关键词： statistical complexity signal detection information divergence

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Asymptotic distribution of the statistical complexity under the multinomial law

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CHAOS SOLITONS & FRACTALS 2025年 193卷

作者： Rey, Andrea Frery, Alejandro C. Gambini, Juliana Univ Nacl Hurlingham UNAHUR Univ Tecnol Nacl LIDEC Buenos Aires Argentina Victoria Univ Wellington Sch Math & Stat Wellington New Zealand

The statistical complexity is a feature computed from a probability function that aims to quantify the structure of the system that produced the observations. It is the product between the normalized Shannon Entropy and the normalized Jensen-Shannon distance between the probability function and the uniform law. We obtain the statistical complexity asymptotic distribution under the Multinomial model, and we validate this result with numerical experiments. We present examples where this asymptotic result provides a good approximation, even in scenarios where the Multinomial model is not strictly valid, such as in applications to Bandt and Pompe ordinal patterns. We provide the R code that implements these functions.

关键词： statistical complexity Asymptotic distribution Multinomial distribution

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Adaptive maximum statistical complexity deconvolution and its application for train axle box bearing fault diagnosis

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2025年 230卷

作者： Gu, Xiaohui Yang, Shaopu Liu, Pengfei Liu, Zechao Liu, Yongqiang Shijiazhuang Tiedao Univ State Key Lab Mech Behav & Syst Safety Traff Engn Shijiazhuang 050043 Peoples R China

Axle box bearing fault diagnosis is challenging due to the fault-induced impulses are often buried in heavy background noise from wheel-rail interaction. Recently, various methods have been devised for extracting the hidden repetitive transients, among which blind deconvolution (BD) has arouse much attention but also suffer from some drawbacks. For example, maximum sparsity based BD techniques are prone to the single impulse yet maximum cyclostationarity based BD methods require the fault period as prior knowledge. In addition, filter length is crucial for BD but often selected by trial-and-error or through additional optimizations. To address these limitations, a new blind deconvolution method, called adaptive maximum statistical complexity deconvolution (AMSCD) is proposed. Firstly, statistical complexity, defined as the product of entropic information and distance-based disequilibrium, is introduced as a novel index for characterizing the repetitive transients, which is less sensitive to the impulsive noise and robust to the cyclostationary interference. Secondly, the blind filter coefficients as well as the filter length are jointly solved by a new variable length grey wolf optimizer, which allows for the simultaneous optimization of BD. At last, the proposed method is examined by both simulated axle box bearing signals with different fault degrees and real signals from a full-scale test rig of train bogie with different speeds. The results indicate its effectiveness and robustness in recovering the weak repetitive transients than some popular BD methods, especially under complex interferences.

关键词： Axle box bearing Blind deconvolution statistical complexity Repetitive transient Variable length grey wolf optimizer

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Assessing biological self-organization patterns using statistical complexity characteristics: a tool for diffusion tensor imaging analysis

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MAGNETIC RESONANCE MATERIALS IN PHYSICS BIOLOGY AND MEDICINE 2024年 1-11页

作者： Senra Filho, Antonio Carlos da S. Murta Junior, Luiz Otavio Paschoal, Andre Monteiro Univ Estadual Campinas Dept Cosm Rays & Chronol Sao Paulo Brazil Univ Sao Paulo Dept Comp & Math Sao Paulo Brazil

ObjectDiffusion-weighted imaging (DWI) and diffusion tensor imaging (DTI) are well-known and powerful imaging techniques for MRI. Although DTI evaluation has evolved continually in recent years, there are still struggles regarding quantitative measurements that can benefit brain areas that are consistently difficult to measure via diffusion-based methods, e.g., gray matter (GM). The present study proposes a new image processing technique based on diffusion distribution evaluation of L & oacute;pez-Ruiz, Mancini and Calbet (LMC) complexity called diffusion complexity (DC).Materials and MethodsThe OASIS-3 and TractoInferno open-science databases for healthy individuals were used, and all the codes are provided as open-source *** DC map showed relevant signal characterization in brain tissues and structures, achieving contrast-to-noise ratio (CNR) gains of approximately 39% and 93%, respectively, compared to those of the FA and ADC *** the special case of GM tissue, the DC map obtains its maximum signal level, showing the possibility of studying cortical and subcortical structures challenging for classical DTI quantitative formalism. The ability to apply the DC technique, which requires the same imaging acquisition for DTI and its potential to provide complementary information to study the brain's GM structures, can be a rich source of information for further neuroscience research and clinical practice.

关键词： Diffusion tensor imaging statistical complexity MRI Brain

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statistical complexity and stochastic resonance of an underdamped bistable periodic potential system excited by Levy noise

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CHAOS SOLITONS & FRACTALS 2024年 179卷

作者： Guo, Yongfeng Ding, Jiaxin Mi, Lina Tiangong Univ Sch Math Sci Tianjin 300387 Peoples R China

This paper focuses on the underdamped bistable potential system's stochastic resonance (SR) phenomenon under Le ' vy noise excitation. The statistical complexity of the system is analyzed under the changes of damping factor, amplitude and frequency of the periodic signal, stability index and skew parameter of Le ' vy noise, and the effects of the changes of above parameters on SR are investigated. The results show that the increase of the damping factor hinders the appearance of SR phenomenon;the larger amplitude and lower frequency of the periodic signal are beneficial to the appearance of SR;the larger stability index of the noise parameter, the more likely SR occurs, and the change of the skew parameter has little effect on the SR. Because the Bandt-Pompe (B-P) algorithm is used in the information-theoretic measure to model the statistical complexity of this system, the robustness of the method is analyzed by changing the embedding dimension and the length of residual time interval sequence in the B-P algorithm. Finally, the mean first passage time of the particle is calculated as a function of the noise intensity and the noise-enhanced stability effect is found.

关键词： Underdamped periodic potential Levy noise statistical complexity Signal-to-noise ratio

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Computational and statistical complexity of Learning in Sequential Models

Computational and Statistical Complexity of Learning in Sequ...

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作者： Mahajan, Gaurav University of California San Diego

学位级别：Ph.D., Doctor of Philosophy

Recent success of machine learning is driven by scaling laws: larger architectures trained using more data and compute lead to more “intelligent” agents. Therefore, even minor enhancements to the sample and compute complexity of these algorithms can have significant scientific and financial implications. In this dissertation, we study these question in the context of sequential models. In particular, we study the following questions. Computational-statistical gaps in reinforcement learning. In this part, we study the computational and statistical complexity of sequential decision-making under the frame-work of reinforcement learning. A fundamental assumption in theory of reinforcement learning is ”RL with linear function approximation”. Under this assumption, the optimal value function (either Q*, or V*, or both) can be obtained as the linear combination of finitely many known basis functions. Even though it was observed as early as 1963 that there are empirical benefits of using linear function approximation, only recently a series of work designed sample efficient algorithms for this setting. These works posed an important open problem: Can we design polynomial time algorithms for this setting? Here, we show progress on this open problem by proving: unless NP=RP, no polynomial time algorithm exists for this settings. Computationally efficient algorithms for learning HMMs. In this part, we study the computational complexity of learning structured distributions over sequences of obser-vations (e.g. DNA sequences, proteins, spoken words and so on). In particular, we are concerned with the computational complexity of learning Hidden Markov Model (HMM). Although HMMs are some of the most widely used tools in sequential and time series modeling, they are cryptographically hard to learn in the standard setting where one has access to i.i.d. samples of observation sequences. Here, we show a positive result: computationally efficient algorithm for learning HMMs when the le

关键词： Machine learning statistical complexity Computationally efficient Decision-making Algorithms

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On the computational and statistical complexity of over-parameterized matrix sensing

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2024年第1期25卷 8006-8052页

作者： Jiacheng Zhuo Jeongyeol Kwon Nhat Ho Constantine Caramanis Department of Computer Science University of Texas Austin TX Wisconsin Institute for Discovery University of Wisconsin-Madison Madison WI Department of Statistics and Data Sciences University of Texas Austin TX Department of Electrical and Computer Engineering University of Texas Austin TX

We consider solving the low-rank matrix sensing problem with the Factorized Gradient Descent (FGD) method when the specified rank is larger than the true rank. We refer to this as over-parameterized matrix sensing. If the ground truth signal X* ∈ ℝd×d is of rank r, but we try to recover it using FF&Tau where F ∈ ℝd×k and k > r, the existing statistical analysis either no longer holds or produces a vacuous statistical error upper bound (infinity) due to the at local curvature of the loss function around the global maxima. By decomposing the factorized matrix F into separate column spaces to capture the impact of using k > r, we show that ||FtFt - X*||2F converges sub-linearly to a statistical error of Õ(kdσ2/n) after $\tilde{\mathcal{O}}(\frac{\sigma_{r}}{\sigma}\sqrt{\frac{n}{d}})$ iterations, where Ft is the output of FGD after t iterations, σ2 is the variance of the observation noise, σr is the r-th largest eigenvalue of X*, and n is the number of samples. With a precise characterization of the convergence behavior and the statistical error, our results, therefore, offer a comprehensive picture of the statistical and computational complexity if we solve the over-parameterized matrix sensing problem with FGD.

关键词： computational complexity statistical complexity over-parameterization matrix sensing matrix regression factorized gradient descent

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Effects of quantum resources and noise on the statistical complexity of quantum circuits

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QUANTUM SCIENCE AND TECHNOLOGY 2023年第2期8卷 025013-025013页

作者： Bu, Kaifeng Koh, Dax Enshan Li, Lu Luo, Qingxian Zhang, Yaobo Harvard Univ Dept Phys Cambridge MA 02138 USA ASTAR Inst High Performance Comp IHPC Agcy Sci Technol & Res 1 Fusionopolis Way 16-16 Connexis Singapore 138632 Singapore Zhejiang Sci Tech Univ Dept Math Hangzhou 310018 Zhejiang Peoples R China Zhejiang Univ Sch Math Sci Hangzhou 310027 Zhejiang Peoples R China Zhejiang Univ Ctr Data Sci Hangzhou 310027 Zhejiang Peoples R China Zhejiang Univ Zhejiang Inst Modern Phys Hangzhou 310027 Zhejiang Peoples R China Zhejiang Univ Dept Phys Hangzhou 310027 Zhejiang Peoples R China Ningxia Univ Sch Phys & Elect Elect Engn Yinchuan 750021 Peoples R China

We investigate how the addition of quantum resources changes the statistical complexity of quantum circuits by utilizing the framework of quantum resource theories. Measures of statistical complexity that we consider include the Rademacher complexity and the Gaussian complexity, which are well-known measures in computational learning theory that quantify the richness of classes of real-valued functions. We derive bounds for the statistical complexities of quantum circuits that have limited access to certain resources and apply our results to two special cases: (a) stabilizer circuits that are supplemented with a limited number of T gates and (b) instantaneous quantum polynomial-time Clifford circuits that are supplemented with a limited number of CCZ gates. We show that the increase in the statistical complexity of a quantum circuit when an additional quantum channel is added to it is upper bounded by the free robustness of the added channel. Moreover, as noise in quantum systems is a major obstacle to implementing many quantum algorithms on large quantum circuits, we also study the effects of noise on the Rademacher complexity of quantum circuits. Finally, we derive bounds for the generalization error associated with learning from training data arising from quantum circuits.

关键词： Rademacher complexity noisy quantum circuits statistical complexity

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Exploration of the Characteristics of Emotion Distribution in Korean TV Series: Common Pattern and statistical complexity

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IEEE ACCESS 2020年 8卷 69438-69447页

作者： Kim, Yunhwan Lee, Sunmi Hankuk Univ Foreign Studies Div Media Commun Seoul 02450 South Korea Kyung Hee Univ Dept Appl Math Yongin 17104 South Korea

The series is one of the most popular formats of television programs, but the emotional aspects of its content have not attracted much attention from researchers. Furthermore, the cinemetric approach, in which move data are quantitively examined, has not been used to analyze affective content in television series. Therefore, this study focused on emotion distribution in Korean television series. In all, 337 episodes from 20 series were divided into shots, then keyframes were selected from the shots. Facial emotions on the keyframes were measured using an online artificial intelligence service. Emotion distributions were obtained from each episode and then were observed for common patterns. In addition, the statistical complexity of the distributions were calculated and compared by the temporal phase of the episode, channel type, genre, ratings, and season. The results show that the emotion distributions of all episodes in all series had the same form: an asymmetric U-shaped distribution biased toward zero. The statistical complexity of emotion distribution was greater in early episodes than in later episodes of a series, and it was higher in episodes with higher ratings. In addition, the complexity of emotion distribution was higher in hard genres and during the summer season. There was no significant difference between terrestrial television channels and cable/general programming channels.

关键词： TV Motion pictures Measurement Films complexity theory Feature extraction Visualization Affective content analysis cinemetrics emotion distribution microsoft azure cognitive services statistical complexity TV series

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statistical complexity in an SU(2) x SU(2) many-fermion environment

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PHYSICA A-statistical MECHANICS AND ITS APPLICATIONS 2019年 517卷 13-20页

作者： Pennini, F. Plastino, A. Apel, V. M. Univ Catolica Norte Dept Fis Av Angamos 0610 Antofagasta Chile Univ Nacl La Pampa CONICET Fac Ciencias Exactas & Nat Dept Fis Av Peru 151 RA-6300 Santa Rosa La Pampa Argentina Univ Nacl La Plata CONICET Inst Fis La Plata RA-1900 La Plata Buenos Aires Argentina Ecole Polytech Fed Lausanne SThAR Lausanne Switzerland

We consider a typical many body problem. In particular, we study an exactly solvable fermion system. We apply to it recently developed statistical quantifiers like the statistical complexity C and the disequilibrium D. The idea consists in trying to ascertain whether statistical quantifiers are able to describe purely dynamic many-body features. Some revealing insights are obtained, specially in what refers to phase transitions. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Disequilibrium statistical complexity Exactly solvable many-body fermion model

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