Jun-ichiro Hirayama

Learning a common dictionary for subject-transfer decoding with resting calibration.

Brain signals measured over a series of experiments have inherent variability because of different physical and mental conditions among multiple subjects and sessions. Such variability complicates the analysis of data from multiple subjects and sessions in a consistent way, and degrades the performance of subject-transfer decoding in a brain-machine interface (BMI). To accommodate the variability in brain signals, we propose 1) a method for extracting spatial bases (or a dictionary) shared by multiple subjects, by employing a signal-processing technique of dictionary learning modified to compensate for variations between subjects and sessions, and 2) an approach to subject-transfer decoding that uses the resting-state activity of a previously unseen target subject as calibration data for compensating for variations, eliminating the need for a standard calibration based on task sessions. Applying our methodology to a dataset of electroencephalography (EEG) recordings during a selective visual-spatial attention task from multiple subjects and sessions, where the variability compensation was essential for reducing the redundancy of the dictionary, we found that the extracted common brain activities were reasonable in the light of neuroscience knowledge. The applicability to subject-transfer decoding was confirmed by improved performance over existing decoding methods. These results suggest that analyzing multisubject brain activities on common bases by the proposed method enables information sharing across subjects with low-burden resting calibration, and is effective for practical use of BMI in variable environments.

Markov and Semi-Markov Switching of Source Appearances for Nonstationary Independent Component Analysis

Independent component analysis (ICA) is currently the most popularly used approach to blind source separation (BSS), the problem of recovering unknown source signals when their mixtures are observed but the actual mixing process is unknown. Many ICA algorithms assume that a fixed set of source signals consistently exists in mixtures throughout the time-series to be examined. However, real-world signals often have such difficult nonstationarity that each source signal abruptly appears or disappears, thus the set of active sources dynamically changes with time. In this paper, we propose switching ICA (SwICA), which focuses on such situations. The proposed approach is based on the noisy ICA formulated as a generative model. We employ a special type of hidden Markov model (HMM) to represent such prior knowledge that the source may abruptly appear or disappear with time. The special HMM setting then provides an effect of variable selection in a dynamic way. We use the variational Bayes (VB) method to derive an effective approximation of Bayesian inference for this model. In simulation experiments using artificial and realistic source signals, the proposed method exhibited performance superior to existing methods, especially in the presence of noise. The compared methods include the natural-gradient ICA with a nonholonomic constraint, and the existing ICA method incorporating an HMM source model, which aims to deal with general nonstationarities that may exist in source signals. In addition, the proposed method could successfully recover the source signals even when the total number of true sources was overestimated or was larger than that of mixtures. We also propose a modification of the basic Markov model into a semi-Markov model, and show that the semi-Markov one is more effective for robust estimation of the source appearance.

Dynamic Exponential Family Matrix Factorization

We propose a new approach to modeling time-varying relational data such as e-mail transactions based on a dynamic extension of matrix factorization. To estimate effectively the true relationships behind a sequence of noise-corrupted relational matrices, their dynamic evolutions are modeled in a space of low-rank matrices. The observed matrices are assumed as to be sampled from an exponential family distribution that has the low-rank matrix as natural parameters. We apply the sequential Bayesian framework to track the variations of true parameters. In the experiments using both artificial and real-world datasets, we demonstrate our method can appropriately estimate time-varying true relations based on noisy observations, more effectively than existing methods.

Balancing plasticity and stability of on-line learning based on hierarchical Bayesian adaptation of forgetting factors

Abstract An important character of on-line learning is its potential to adapt to changing environments by properly adjusting meta-parameters that control the balance between plasticity and stability of the learning model. In our previous study, we proposed a learning scheme to address changing environments in the framework of an on-line variational Bayes (VB), which is an effective on-line learning scheme based on Bayesian inference. The motivation of that work was, however, its implications for animal learning, and the formulation of the learning model was heuristic and not theoretically justified. In this article, we propose a new approach that balances the plasticity and stability of on-line VB learning in a more theoretically justifiable manner by employing the principle of hierarchical Bayesian inference. We present a new interpretation of on-line VB as a special case of incremental Bayes that allows the hierarchical Bayesian setting to balance the plasticity and stability as well as yielding a simple learning rule compared to standard on-line VB. This dynamic on-line VB scheme is applied to probabilistic PCA as an example of probabilistic models involving latent variables. In computer simulations using artificial data sets, the new on-line VB learning shows robust performance to regulate the balance between plasticity and stability, thus adapting to changing environments.

Characterizing variability of modular brain connectivity with constrained principal component analysis

Characterizing the variability of resting-state functional brain connectivity across subjects and/or over time has recently attracted much attention. Principal component analysis (PCA) serves as a fundamental statistical technique for such analyses. However, performing PCA on high-dimensional connectivity matrices yields complicated “eigenconnectivity” patterns, for which systematic interpretation is a challenging issue. Here, we overcome this issue with a novel constrained PCA method for connectivity matrices by extending the idea of the previously proposed orthogonal connectivity factorization method. Our new method, modular connectivity factorization (MCF), explicitly introduces the modularity of brain networks as a parametric constraint on eigenconnectivity matrices. In particular, MCF analyzes the variability in both intra- and inter-module connectivities, simultaneously finding network modules in a principled, data-driven manner. The parametric constraint provides a compact module-based visualization scheme with which the result can be intuitively interpreted. We develop an optimization algorithm to solve the constrained PCA problem and validate our method in simulation studies and with a resting-state functional connectivity MRI dataset of 986 subjects. The results show that the proposed MCF method successfully reveals the underlying modular eigenconnectivity patterns in more general situations and is a promising alternative to existing methods.

Sparse and low-rank matrix regularization for learning time-varying Markov networks

Statistical dependencies observed in real-world phenomena often change drastically with time. Graphical dependency models, such as the Markov networks (MNs), must deal with this temporal heterogeneity in order to draw meaningful conclusions about the transient nature of the target phenomena. However, in practice, the estimation of time-varying dependency graphs can be inefficient due to the potentially large number of parameters of interest. To overcome this problem, we propose such a novel approach to learning time-varying MNs that effectively reduces the number of parameters by constraining the rank of the parameter matrix. The underlying idea is that the effective dimensionality of the parameter space is relatively low in many realistic situations. Temporal smoothness and sparsity of the network are also incorporated as in previous studies. The proposed method is formulated as a convex minimization of a smoothed empirical loss with both the

Simultaneous blind separation and clustering of coactivated EEG/MEG sources for analyzing spontaneous brain activity

\ell _1

Orthogonal connectivity factorization: Interpretable decomposition of variability in correlation matrices

ℓ1- and the nuclear-norm regularization terms. This non-smooth optimization problem is numerically solved by the alternating direction method of multipliers. We take the Ising model as a fundamental example of an MN, and we show in several simulation studies that the rank-reducing effect from the nuclear norm can improve the estimation performance of time-varying dependency graphs. We also demonstrate the utility of the method for analyzing real-world datasets for improving the interpretability and predictability of the obtained networks.