five action circling

As a complementary to those temporal coding approaches of the current major stream, this paper aims at the Markovian state space temporal models from the perspective of the temporal Bayesian Ying-Yang (BYY) learning with both new insights and new results on not only the discrete state featured Hidden Markov model and extensions but also the continuous state featured linear state spaces and extensions, especially with a new learning mechanism that makes selection of the state number or the dimension of state space either automatically during adaptive learning or subsequently after learning via model selection criteria obtained from this mechanism. Experiments are demonstrated to show how the proposed approach works.

Abstract Both optimization and learning play important roles in a system for intelligent tasks. On one hand, we introduce three types of optimization tasks studied in the machine learning literature, corresponding to the three levels of inverse problems in an intelligent system. Also, we discuss three major roles of convexity in machine learning, either directly towards a convex programming or approximately transferring a difficult problem into a tractable one in help of local convexity and convex duality. No doubly, a good optimization algorithm takes an essential role in a learning process and new developments in the literature of optimization may thrust the advances of machine learning. On the other hand, we also interpret that the key task of learning is not simply optimization, as sometimes misunderstood in the optimization literature. We introduce the key challenges of learning and the current status of efforts towards the challenges. Furthermore, learning versus optimization has also been examined from a unified perspective under the name of Bayesian Ying-Yang learning, with combinatorial optimization made more effectively in help of learning.

Local factor analysis (LFA) is regarded as an efficient approach that implements local feature extraction and dimensionality reduction. A further investigation is made on an automatic BYY harmony data smoothing LFA (LFA-HDS) from the Bayesian Ying-Yang (BYY) harmony learning point of view. On the level of regularization, an data smoothing based regularization technique is adapted into this automatic LFA-HDS learning for problems with small sample sizes, while on the level of model selection, the proposed automatic LFA-HDS algorithm makes parameter learning with automatic determination of both the component number and the factor number in each component. A comparative study has been conducted on simulated data sets and several real problem data sets. The algorithm has been compared with not only a recent approach called Incremental Mixture of Factor Analysers (IMoFA) but also the conventional two-stage implementation of maximum likelihood (ML) plus model selection, namely, using the EM algorithm for parameter learning on a series candidate models, and selecting one best candidate by AIC, CAIC, BIC, and cross-validation (CV). Experiments have shown that IMoFA and ML-BIC, ML-CV outperform ML-AIC or ML-CAIC. Interestingly, the data smoothing BYY harmony learning obtains comparably desired results compared to IMoFA and ML-BIC but with much less computational cost. 1

With uncorrelated Gaussian factors extended to mutually independent factors beyond Gaussian, the conventional factor analysis is extended to what is recently called independent factor analysis. Typically, it is called binary factor analysis (BFA) when the factors are binary and called non-Gaussian factor analysis (NFA) when the factors are from real non-Gaussian distributions. A crucial issue in both BFA and NFA is the determination of the number of factors. In the literature of statistics, there are a number of model selection criteria that can be used for this purpose. Also, the Bayesian Ying-Yang (BYY) harmony learning provides a new principle for this purpose. This paper further investigates BYY harmony learning in comparison with existing typical criteria, including Akaik_s information criterion (AIC), the consistent Akaike_s information criterion (CAIC), the Bayesian inference criterion (BIC), and the cross-validation (CV) criterion on selection of the number of factors. This comparative study is made via experiments on the data sets with different sample sizes, data space dimensions, noise variances, and hidden factors numbers. Experiments have shown that for both BFA and NFA, in most cases BIC outperforms AIC, CAIC, and CV while the BYY criterion is either comparable with or better than BIC. In consideration of the fact that the selection by these criteria has to be implemented at the second stage based on a set of candidate models which have to be obtained at the first stage of parameter learning, while BYY harmony learning can provide not only a new class of criteria implemented in a similar way but also a new family of algorithms that perform parameter learning at the first stage with automated model selection, BYY harmony learning is more preferred since computing costs can be saved significantly.

An investigation of several typical model selection criteria for detecting the number of signals c ○ Higher Education Press and Springer-Verlag Berlin Heidelberg 2011 Abstract Based on the problem of detecting the number of signals, this paper provides a systematic empirical investigation on model selection performances of several classical criteria and recently developed methods (including Akaike’s information criterion (AIC), Schwarz’s Bayesian information criterion, Bozdogan’s consistent AIC, Hannan-Quinn information criterion, Minka’s (MK) principal component analysis (PCA) criterion, Kritchman & Nadler’s hypothesis tests (KN), Perry & Wolfe’s minimax rank estimation thresholding algorithm (MM), and Bayesian Ying-Yang (BYY) harmony learning), by varying signal-to-noise ratio (SNR) and training sample size N. A family of model selection indifference curves is defined by the contour lines of model selection accuracies, such that we can examine the joint effect of N and SNR rather than merely the effect of either of SNR and N with the other fixed as usually done in the literature. The indifference curves visually reveal that all methods demonstrate relative advantages obviously within a region of moderate N and SNR. Moreover, the importance of studying this region is also confirmed by an alternative reference criterion by maximizing the testing likelihood. It has been shown via extensive simulations that AIC and BYY harmony learning, as well as MK, KN, and MM, are relatively more robust than the others against decreasing N and SNR, and BYY is superior for a small sample size.