Yohei Nakada

Bayesian on-line learning: a sequential Monte Carlo with importance resampling

A Bayesian online learning scheme with sequential Monte Carlo incorporating importance resampling is proposed. The proposed scheme adjusts not only parameters for data fitting but also adjusts hyperparameters online so that the scheme attempts to avoid overfitting in an adaptive manner. One of the advantages of the scheme is the fact that it can adapt to environmental changes, i.e., it can perform learning, even when the underlying input-output relationship varies over time. The scheme is tested against simple examples and is shown to be functional.

Gibbsboost: a Boosting Algorithm using a Sequential Monte Carlo Approach

This study proposes a novel boosting algorithm, GibbsBoost. A Gibbs distribution of a weaklearner sequence with a specific loss (energy) function is used in this algorithm as the posterior distribution in Bayesian learning. Weaklearner sequence samples are recursively drawn from the distribution via sequential Monte Carlo. The predictions are derived from a combination of the weaklearner sequence samples. The proposed algorithm is demonstrated by using a numerical example.

Online Bayesian learning for dynamical classification problem using natural sequential prior

Classification problems in dynamical environments are in many fields,including signal processing and pattern recognition. In this paper, we propose a novel Bayesian approach to classification in a dynamical environment. The proposed approach employs natural sequential prior to improve online learning for an online classifier model. By using the natural sequential prior,the proposed approach describes the dynamical changes in the classifier modelpsilas parameters in a more natural manner. For comparison,the proposed approach and a conventional approach are validated by means of several numerical experiments.

A Hierarchical Bayesian Hidden Markov Model for Multi-Dimensional Discrete Data

1.1 Motivation A fundamental problem encountered in many fields is to model data t o given a discrete time-series data sequence ( ) T o o : y , ,L 1 = . This problem is found in diverse fields, such as control systems, robotics, event detection (Motoi et al., 2007), handwriting recognition (Yasuda et al., 2000 ; Funada et al., 2005), and protein structure prediction (Krogh et al., 2001 ; Tusnady & Simon, 1998 ; Kaburagi et al., 2007). The data t o can often be a multidimensional variable exhibiting stochastic activity. A powerful tool for solving such problems is multi-dimensional discrete Hidden Markov Models (HMMs), and the effectiveness of this approach has been demonstrated in numerous studies (Motoi et al., 2007 ; Yasuda et al., 2000 ; Funada et al., 2005 ; Kaburagi et al., 2007). The hidden states of the HMMs are treated as hidden factors for emission of the observed data t o . However, if redundant components having low dependencies on the hidden states are contained in the data t o , these components often have a negative impact on the HMM performance. Overcoming this problem requires a method of quantifying the redundancy (state independence) of these components and/or reducing their influence. In this chapter, we describe an extension of the HMM for these kinds of data sequences within the framework of a hierarchical Bayesian scheme. In this extended model, we introduce commonality hyperparameters to describe the degree of commonality of the emission probabilities among different hidden states (that is, hidden factors of the data t o ). Additionally, there is a one-to-one relationship between each hyperparameter and a component of the data t o . This allows us to identify low-dependency components and to minimize their negative impact. Like other Bayesian HMMs, the extended model requires complicated integrations in the learning and prediction processes, usually involving a posterior distribution. Analytic solutions of these integrations are often intractable or non-trivial due to their inherent

On-line Bayesian change detection scheme for unknown nonlinear systems via sequential Monte Carlo

An attempt is made to perform on-line change detection given sequential data from an unknown nonlinear system. The algorithm sequentially estimates the probability of occurrence of a change within a Bayesian framework. The implementation is done via sequential Monte Carlo (SMC). The proposed scheme is tested against two specific examples.

Bayesian MCMC nonlinear time series prediction

A MCMC (Markov chain Monte Carlo) algorithm is proposed for nonlinear time series prediction with a hierarchical Bayesian framework. The algorithm computes predictive mean and error bar by drawing samples from predictive distributions. The algorithm is tested against time series generated by a (chaotic) Rossler system and it outperforms quadratic approximations previously proposed by the authors.

An On-Line Change Detection Scheme for Nonlinear Time Series Data from Unknown Dynamical Systems: A Bayesian Appraoch Using Sequential Monte Carlo

This paper attempts to perform on-line change detection given time series data from unknown nonlinear dynamical systems. In the algorithm, the probability of occurrence of an abrupt change is estimated within a Bayesian framework. The implementation is done via sequential Monte Carlo (SMC). The proposed scheme is tested against two examples with nonlinear dynamical systems

Sequential Monte Carlo learning with hyperparameter adjustments

Sequential Monte Carlo scheme is proposed for online Bayesian learning. The proposed scheme adjusts not only parameters for data fitting but adjust hyperparameters online so that the scheme attempts to avoid over fitting in an adaptive manner. The scheme is tested against simple examples and is shown to be functional.