arXiv subjects

Masahiro Yukawa

Publications and source records attributed to Masahiro Yukawa.

At least 19 recordsLinked to original sources

arXiv2026

Theoretical Validation of the Latent Optimally Partitioned-$\ell_2/\ell_1$ Penalty with Application to Angular Power Spectrum Estimation

This paper demonstrates that, in both theory and practice, the latent optimally partitioned (LOP)-$\ell_2/\ell_1$ penalty is effective for exploiting block-sparsity without knowledge of the concrete block structure. More precisely, we first present a novel theoretical result showing that the optimized block partition in the LOP-$\ell_2/\ell_1$ penalty satisfies a condition required for accurate recovery of block-sparse signals. Motivated by this result, we present a new application of the LOP-$\ell_2/\ell_1$ penalty to estimation of angular power spectrum, which is block-sparse with unknown block partition, in MIMO communication systems. Numerical simulations show that the proposed use of block-sparsity with the LOP-$\ell_2/\ell_1$ penalty significantly improves the estimation accuracy of the angular power spectrum.

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arXiv2026

Nonconvex Latent Optimally Partitioned Block-Sparse Recovery via Log-Sum and Minimax Concave Penalties

We propose two nonconvex regularization methods, LogLOP-l2/l1 and AdaLOP-l2/l1, for recovering block-sparse signals with unknown block partitions. These methods address the underestimation bias of existing convex approaches by extending log-sum penalty and the Minimax Concave Penalty (MCP) to the block-sparse domain via novel variational formulations. Unlike Generalized Moreau Enhancement (GME) and Bayesian methods dependent on the squared-error data fidelity term, our proposed methods are compatible with a broad range of data fidelity terms. We develop efficient Alternating Direction Method of Multipliers (ADMM)-based algorithms for these formulations that exhibit stable empirical convergence. Numerical experiments on synthetic data, angular power spectrum estimation, and denoising of nanopore currents demonstrate that our methods outperform state-of-the-art baselines in estimation accuracy.

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arXiv2025

Plugging Weight-tying Nonnegative Neural Network into Proximal Splitting Method: Architecture for Guaranteeing Convergence to Optimal Point

We propose a novel multi-layer neural network architecture that gives a promising neural network empowered optimization approach to the image restoration problem. The proposed architecture is motivated by the recent study of monotone Lipschitz-gradient (MoL-Grad) denoiser (Yukawa and Yamada, 2025) which establishes an ``explainable'' plug-and-play (PnP) framework in the sense of disclosing the objective minimized. The architecture is derived from the gradient of a superposition of functions associated with each layer, having the weights in the encoder and decoder tied with each other. Convexity of the potential, and thus monotonicity of its gradient (denoiser), is ensured by restricting ourselves to nonnegative weights. Unlike the previous PnP approaches with theoretical guarantees, the denoiser is free from constraints on the Lipschitz constant of the denoiser. Our PnP algorithm employing the weight-tying nonnegative neural network converges to a minimizer of the objective involving an ``implicit'' weakly convex regularizer induced by the denoiser. The convergence analysis relies on an efficient technique to preserve the overall convexity even in the ill-conditioned case where the loss function is not strongly convex. The simulation study shows the advantages of the Lipschitz-constraint-free nature of the proposed denoiser in training time as well as deblurring performance.

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arXiv2025

Monotone Lipschitz-Gradient Denoiser: Explainability of Operator Regularization Approaches Free From Lipschitz Constant Control

This paper addresses explainability of the operator-regularization approach under the use of monotone Lipschitz-gradient (MoL-Grad) denoiser -- an operator that can be expressed as the Lipschitz continuous gradient of a differentiable convex function. We prove that an operator is a MoL-Grad denoiser if and only if it is the ``single-valued'' proximity operator of a weakly convex function. An extension of Moreau's decomposition is also shown with respect to a weakly convex function and the conjugate of its convexified function. Under these arguments, two specific algorithms, the forward-backward splitting algorithm and the primal-dual splitting algorithm, are considered, both employing MoL-Grad denoisers. These algorithms generate a sequence of vectors converging weakly, under conditions, to a minimizer of a certain cost function which involves an ``implicit regularizer'' induced by the denoiser. Unlike the previous studies of operator regularization, our framework requires no control of the Lipschitz constant in learning the denoiser. The theoretical findings are supported by simulations.

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arXiv2025

Continuous Relaxation of Discontinuous Shrinkage Operator: Proximal Inclusion and Conversion

We present a principled way of deriving a continuous relaxation of a given discontinuous shrinkage operator, which is based on two fundamental results, proximal inclusion and conversion. Using our results, the discontinuous operator is converted, via double inversion, to a continuous operator; more precisely, the associated ``set-valued'' operator is converted to a ``single-valued'' Lipschitz continuous operator. The first illustrative example is the firm shrinkage operator which can be derived as a continuous relaxation of the hard shrinkage operator. We also derive a new operator as a continuous relaxation of the discontinuous shrinkage operator associated with the so-called reversely ordered weighted L1 (ROWL) penalty. Numerical examples demonstrate potential advantages of the continuous relaxation.

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arXiv2025

Federated Smoothing ADMM for Localization

This paper addresses the challenge of localization in federated settings, which are characterized by distributed data, non-convexity, and non-smoothness. To tackle the scalability and outlier issues inherent in such environments, we propose a robust algorithm that employs an $\ell_1$-norm formulation within a novel federated ADMM framework. This approach addresses the problem by integrating an iterative smooth approximation for the total variation consensus term and employing a Moreau envelope approximation for the convex function that appears in a subtracted form. This transformation ensures that the problem is smooth and weakly convex in each iteration, which results in enhanced computational efficiency and improved estimation accuracy. The proposed algorithm supports asynchronous updates and multiple client updates per iteration, which ensures its adaptability to real-world federated systems. To validate the reliability of the proposed algorithm, we show that the method converges to a stationary point, and numerical simulations highlight its superior performance in convergence speed and outlier resilience compared to existing state-of-the-art localization methods.

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arXiv2023

Distributed Convex Optimization "Over-the-Air" in Dynamic Environments

This paper presents a decentralized algorithm for solving distributed convex optimization problems in dynamic networks with time-varying objectives. The unique feature of the algorithm lies in its ability to accommodate a wide range of communication systems, including previously unsupported ones, by abstractly modeling the information exchange in the network. Specifically, it supports a novel communication protocol based on the "over-the-air" function computation (OTA-C) technology, that is designed for an efficient and truly decentralized implementation of the consensus step of the algorithm. Unlike existing OTA-C protocols, the proposed protocol does not require the knowledge of network graph structure or channel state information, making it particularly suitable for decentralized implementation over ultra-dense wireless networks with time-varying topologies and fading channels. Furthermore, the proposed algorithm synergizes with the "superiorization" methodology, allowing the development of new distributed algorithms with enhanced performance for the intended applications. The theoretical analysis establishes sufficient conditions for almost sure convergence of the algorithm to a common time-invariant solution for all agents, assuming such a solution exists. Our algorithm is applied to a real-world distributed random field estimation problem, showcasing its efficacy in terms of convergence speed, scalability, and spectral efficiency. Furthermore, we present a superiorized version of our algorithm that achieves faster convergence with significantly reduced energy consumption compared to the unsuperiorized algorithm.

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arXiv2023

Linearly-involved Moreau-Enhanced-over-Subspace Model: Debiased Sparse Modeling and Stable Outlier-Robust Regression

We present an efficient mathematical framework based on the linearly-involved Moreau-enhanced-over-subspace (LiMES) model. Two concrete applications are considered: sparse modeling and robust regression. The popular minimax concave (MC) penalty for sparse modeling subtracts, from the $\ell_1$ norm, its Moreau envelope, inducing nearly unbiased estimates and thus yielding remarkable performance enhancements. To extend it to underdetermined linear systems, we propose the projective minimax concave penalty using the projection onto the input subspace, where the Moreau-enhancement effect is restricted to the subspace for preserving the overall convexity. We also present a novel concept of stable outlier-robust regression which distinguishes noise and outlier explicitly. The LiMES model encompasses those two specific examples as well as two other applications: stable principal component pursuit and robust classification. The LiMES function involved in the model is an ``additively nonseparable'' weakly convex function but is defined with the Moreau envelope returning the minimum of a ``separable'' convex function. This mixed nature of separability and nonseparability allows an application of the LiMES model to the underdetermined case with an efficient algorithmic implementation. Two linear/affine operators play key roles in the model: one corresponds to the projection mentioned above and the other takes care of robust regression/classification. A necessary and sufficient condition for convexity of the smooth part of the objective function is studied. Numerical examples show the efficacy of LiMES in applications to sparse modeling and robust regression.

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arXiv2021

Learning Sparse Graph with Minimax Concave Penalty under Gaussian Markov Random Fields

This paper presents a convex-analytic framework to learn sparse graphs from data. While our problem formulation is inspired by an extension of the graphical lasso using the so-called combinatorial graph Laplacian framework, a key difference is the use of a nonconvex alternative to the $\ell_1$ norm to attain graphs with better interpretability. Specifically, we use the weakly-convex minimax concave penalty (the difference between the $\ell_1$ norm and the Huber function) which is known to yield sparse solutions with lower estimation bias than $\ell_1$ for regression problems. In our framework, the graph Laplacian is replaced in the optimization by a linear transform of the vector corresponding to its upper triangular part. Via a reformulation relying on Moreau's decomposition, we show that overall convexity is guaranteed by introducing a quadratic function to our cost function. The problem can be solved efficiently by the primal-dual splitting method, of which the admissible conditions for provable convergence are presented. Numerical examples show that the proposed method significantly outperforms the existing graph learning methods with reasonable CPU time.

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arXiv2021

Relaxed Zero-Forcing Beamformer under Temporally-Correlated Interference

The relaxed zero-forcing (RZF) beamformer is a quadratically-and-linearly constrained minimum variance beamformer. The central question addressed in this paper is whether RZF performs better than the widely-used minimum variance distortionless response and zero-forcing beamformers under temporally-correlated interference. First, RZF is rederived by imposing an ellipsoidal constraint that bounds the amount of interference leakage for mitigating the intrinsic gap between the output variance and the mean squared error (MSE) which stems from the temporal correlations. Second, an analysis of RZF is presented for the single-interference case, showing how the MSE is affected by the spatio-temporal correlations between the desired and interfering sources as well as by the signal and noise powers. Third, numerical studies are presented for the multiple-interference case, showing the remarkable advantages of RZF in its basic performance as well as in its application to brain activity reconstruction from EEG data. The analytical and experimental results clarify that the RZF beamformer gives near-optimal performance in some situations.

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arXiv2019

Kernel-Based Adaptive Online Reconstruction of Coverage Maps With Side Information

In this paper, we address the problem of reconstructing coverage maps from path-loss measurements in cellular networks. We propose and evaluate two kernel-based adaptive online algorithms as an alternative to typical offline methods. The proposed algorithms are application-tailored extensions of powerful iterative methods such as the adaptive projected subgradient method and a state-of-the-art adaptive multikernel method. Assuming that the moving trajectories of users are available, it is shown how side information can be incorporated in the algorithms to improve their convergence performance and the quality of the estimation. The complexity is significantly reduced by imposing sparsity-awareness in the sense that the algorithms exploit the compressibility of the measurement data to reduce the amount of data which is saved and processed. Finally, we present extensive simulations based on realistic data to show that our algorithms provide fast, robust estimates of coverage maps in real-world scenarios. Envisioned applications include path-loss prediction along trajectories of mobile users as a building block for anticipatory buffering or traffic offloading.

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arXiv2019

Convolutional-Sparse-Coded Dynamic Mode Decomposition and Its Application to River State Estimation

This work proposes convolutional-sparse-coded dynamic mode decomposition (CSC-DMD) by unifying extended dynamic mode decomposition (EDMD) and convolutional sparse coding. EDMD is a data driven analysis method for describing a nonlinear dynamical system with a linear time-evolution equation. Compared with existing EDMD methods, CSC-DMD has an advantage of reflecting spatial structure of the target. As an example, the proposed method is applied to river bed shape estimation from the water surface observation. The estimation problem is reduced to sparsity-aware restoration with a hard constraint, which is given by the CSC-DMD prediction, where the algorithm is derived by the primal-dual splitting method. A time series set of water surface and bed shape measured through an experimental river setup is used to train and test the system. From the result, the significance of the proposed method is verified.

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arXiv2018

Continuous-time Value Function Approximation in Reproducing Kernel Hilbert Spaces

Motivated by the success of reinforcement learning (RL) for discrete-time tasks such as AlphaGo and Atari games, there has been a recent surge of interest in using RL for continuous-time control of physical systems (cf. many challenging tasks in OpenAI Gym and DeepMind Control Suite). Since discretization of time is susceptible to error, it is methodologically more desirable to handle the system dynamics directly in continuous time. However, very few techniques exist for continuous-time RL and they lack flexibility in value function approximation. In this paper, we propose a novel framework for model-based continuous-time value function approximation in reproducing kernel Hilbert spaces. The resulting framework is so flexible that it can accommodate any kind of kernel-based approach, such as Gaussian processes and kernel adaptive filters, and it allows us to handle uncertainties and nonstationarity without prior knowledge about the environment or what basis functions to employ. We demonstrate the validity of the presented framework through experiments.

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arXiv2018

Online Nonlinear Estimation via Iterative L2-Space Projections: Reproducing Kernel of Subspace

We propose a novel online learning paradigm for nonlinear-function estimation tasks based on the iterative projections in the L2 space with probability measure reflecting the stochastic property of input signals. The proposed learning algorithm exploits the reproducing kernel of the so-called dictionary subspace, based on the fact that any finite-dimensional space of functions has a reproducing kernel characterized by the Gram matrix. The L2-space geometry provides the best decorrelation property in principle. The proposed learning paradigm is significantly different from the conventional kernel-based learning paradigm in two senses: (i) the whole space is not a reproducing kernel Hilbert space and (ii) the minimum mean squared error estimator gives the best approximation of the desired nonlinear function in the dictionary subspace. It preserves efficiency in computing the inner product as well as in updating the Gram matrix when the dictionary grows. Monotone approximation, asymptotic optimality, and convergence of the proposed algorithm are analyzed based on the variable-metric version of adaptive projected subgradient method. Numerical examples show the efficacy of the proposed algorithm for real data over a variety of methods including the extended Kalman filter and many batch machine-learning methods such as the multilayer perceptron.

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arXiv2018

Distributed Adaptive Learning with Multiple Kernels in Diffusion Networks

We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion stage to achieve consensus on the estimates over the whole network. Multiple kernels are incorporated to enhance the approximation of functions with several high and low frequency components common in practical scenarios. We provide a thorough convergence analysis of the proposed scheme based on the metric of the Cartesian product of multiple reproducing kernel Hilbert spaces. To this end, we introduce a modified consensus matrix considering this specific metric and prove its equivalence to the ordinary consensus matrix. Besides, the use of hyperslabs enables a significant reduction of the computational demand with only a minor loss in the performance. Numerical evaluations with synthetic and real data are conducted showing the efficacy of the proposed algorithm compared to the state of the art schemes.

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arXiv2018

Detection for 5G-NOMA: An Online Adaptive Machine Learning Approach

Non-orthogonal multiple access (NOMA) has emerged as a promising radio access technique for enabling the performance enhancements promised by the fifth-generation (5G) networks in terms of connectivity, low latency, and high spectrum efficiency. In the NOMA uplink, successive interference cancellation (SIC) based detection with device clustering has been suggested. In the case of multiple receive antennas, SIC can be combined with the minimum mean-squared error (MMSE) beamforming. However, there exists a tradeoff between the NOMA cluster size and the incurred SIC error. Larger clusters lead to larger errors but they are desirable from the spectrum efficiency and connectivity point of view. We propose a novel online learning based detection for the NOMA uplink. In particular, we design an online adaptive filter in the sum space of linear and Gaussian reproducing kernel Hilbert spaces (RKHSs). Such a sum space design is robust against variations of a dynamic wireless network that can deteriorate the performance of a purely nonlinear adaptive filter. We demonstrate by simulations that the proposed method outperforms the MMSE-SIC based detection for large cluster sizes.

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arXiv2014

Adaptive Learning in Cartesian Product of Reproducing Kernel Hilbert Spaces

We propose a novel adaptive learning algorithm based on iterative orthogonal projections in the Cartesian product of multiple reproducing kernel Hilbert spaces (RKHSs). The task is estimating/tracking nonlinear functions which are supposed to contain multiple components such as (i) linear and nonlinear components, (ii) high- and low- frequency components etc. In this case, the use of multiple RKHSs permits a compact representation of multicomponent functions. The proposed algorithm is where two different methods of the author meet: multikernel adaptive filtering and the algorithm of hyperplane projection along affine subspace (HYPASS). In a certain particular case, the sum space of the RKHSs is isomorphic to the product space and hence the proposed algorithm can also be regarded as an iterative projection method in the sum space. The efficacy of the proposed algorithm is shown by numerical examples.

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arXiv2014

A stochastic behavior analysis of stochastic restricted-gradient descent algorithm in reproducing kernel Hilbert spaces

This paper presents a stochastic behavior analysis of a kernel-based stochastic restricted-gradient descent method. The restricted gradient gives a steepest ascent direction within the so-called dictionary subspace. The analysis provides the transient and steady state performance in the mean squared error criterion. It also includes stability conditions in the mean and mean-square sense. The present study is based on the analysis of the kernel normalized least mean square (KNLMS) algorithm initially proposed by Chen et al. Simulation results validate the analysis.

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