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Researcher profile

Toshiyasu Matsushima

Toshiyasu Matsushima contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningInformation Theorymath.ITComputer Visioneess.SP

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Published work

7 published item(s)

preprint2026arXiv

A Mixture Autoregressive Image Generative Model on Quadtree Regions for Gaussian Noise Removal via Variational Bayes and Gradient Methods

This paper addresses the problem of image denoising for grayscale images. We propose a probabilistic image generative model that combines a quadtree region-partitioning model with a mixture autoregressive model, and propose a framework that reduces MAP (maximum a posteriori)-estimation-based denoising to the maximization of a variational lower bound. To maximize this lower bound, we develop an algorithm that alternately applies variational Bayes and gradient methods. We particularly demonstrate that the gradient-based update rule can be computed analytically without numerical computation or approximation. We carried out some experiments to verify that the proposed algorithm actually removes image noise and to identify directions for future improvement.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Soft Bayesian Context Tree Models for Real-Valued Time Series

This paper proposes the soft Bayesian context tree model (Soft-BCT), which is a novel BCT model for real-valued time series. The Soft-BCT considers soft (probabilistic) splits of the context space, instead of hard (deterministic) splits of the context space as in the previous BCT for real-valued time series. A learning algorithm of the Soft-BCT is proposed based on the variational inference. For some real-world datasets, the Soft-BCT demonstrates almost the same or superior performance to the previous BCT.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A Generalization of the Stratonovich's Value of Information and Application to Privacy-Utility Trade-off

The Stratonovich's value of information (VoI) is quantity that measure how much inferential gain is obtained from a perturbed sample under information leakage constraint. In this paper, we introduce a generalized VoI for a general loss function and general information leakage. Then we derive an upper bound of the generalized VoI. Moreover, for a classical loss function, we provide a achievable condition of the upper bound which is weaker than that of in previous studies. Since VoI can be viewed as a formulation of a privacy-utility trade-off (PUT) problem, we provide an interpretation of the achievable condition in the PUT context.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

An Algorithm for Computing the Stratonovich's Value of Information

We propose an algorithm for computing Stratonovich's value of information (VoI) that can be regarded as an analogue of the distortion-rate function. We construct an alternating optimization algorithm for VoI under a general information leakage constraint and derive a convergence condition. Furthermore, we discuss algorithms for computing VoI under specific information leakage constraints, such as Shannon's mutual information (MI), $f$-leakage, Arimoto's MI, Sibson's MI, and Csiszar's MI.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Probability Distribution on Rooted Trees

The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical expressive capability causes a problem in tree selection to avoid overfitting. One unified approach to solve this is a Bayesian approach, on which the rooted tree is regarded as a random variable and a direct loss function can be assumed on the selected model or the predicted value for a new data point. However, all the previous studies on this approach are based on the probability distribution on full trees, to the best of our knowledge. In this paper, we propose a generalized probability distribution for any rooted trees in which only the maximum number of child nodes and the maximum depth are fixed. Furthermore, we derive recursive methods to evaluate the characteristics of the probability distribution without any approximations.

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preprint2022arXiv

Stochastic 2D Signal Generative Model with Wavelet Packets Basis Regarded as a Random Variable and Bayes Optimal Processing

This study deals with two-dimensional (2D) signal processing using the wavelet packet transform. When the basis is unknown the candidate of basis increases in exponential order with respect to the signal size. Previous studies do not consider the basis as a random vaiables. Therefore, the cost function needs to be used to select a basis. However, this method is often a heuristic and a greedy search because it is impossible to search all the candidates for a huge number of bases. Therefore, it is difficult to evaluate the entire signal processing under a criterion and also it does not always gurantee the optimality of the entire signal processing. In this study, we propose a stochastic generative model in which the basis is regarded as a random variable. This makes it possible to evaluate entire signal processing under a unified criterion i.e. Bayes criterion. Moreover we can derive an optimal signal processing scheme that achieves the theoretical limit. This derived scheme shows that all the bases should be combined according to the posterior in stead of selecting a single basis. Although exponential order calculations is required for this scheme, we have derived a recursive algorithm for this scheme, which successfully reduces the computational complexity from the exponential order to the polynomial order.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Information Spectrum Approach to Overflow Probability of Variable-Length Codes with Conditional Cost Function

Lossless variable-length source coding with unequal cost function is considered for general sources. In this problem, the codeword cost instead of codeword length is important. The infimum of average codeword cost has already been determined for general sources. We consider the overflow probability of codeword cost and determine the infimum of achievable overflow threshold. Our analysis is on the basis of information-spectrum methods and hence valid through the general source.

0 citations0 reviewsNo code linkedOpen access