In supervised learning, the selection of sample points and models is crucial for acquiring a higher level of the generalization capability. So far, the problems of active learning and model selection have been independently studied. If sample points and models are simultaneously optimized, then a higher level of the generalization capability is expected. We call this problem active learning with model selection. However, active learning with model selection can not be generally solved by simply combining existing active learning and model selection techniques because of the active learning/model selection dilemma: the model should be fixed for selecting sample points and conversely the sample points should be fixed for selecting models. In this paper, we show that the dilemma can be dissolved if there is a set of sample points that is optimal for all models in consideration. Based on this idea, we give a practical procedure for active learning with model selection in trigonometric polynomial models. The effectiveness of the proposed procedure is demonstrated through computer simulations.

In this letter, we propose an efficient channel estimation scheme using trigonometric polynomial approximation for OFDM systems with transmit diversity. While the conventional channel estimation scheme has a high computational complexity in given channel delay profiles, the proposed scheme is efficient in the computational complexity. Especially, for channels with smaller rms delay spreads, the proposed scheme has improved BER performance and complexity reduction. In addition, we evaluate the performance of maximum delay spread estimation in unknown channel. The performance of the proposed scheme is evaluated by computer simulation in various multi-path fading environments.

In this paper, we consider the problem of active learning, and give a necessary and sufficient condition of sample points for the optimal generalization capability. By utilizing the properties of pseudo orthogonal bases, we clarify the mechanism of achieving the optimal generalization capability. We also show that the condition does not only provide the optimal generalization capability but also reduces the computational complexity and memory required to calculate learning result functions. Based on the optimality condition, we give design methods of optimal sample points for trigonometric polynomial models. Finally, the effectiveness of the proposed active learning method is demonstrated through computer simulations.

In this paper, subband image coding with symmetric biorthogonal wavelet filters is studied. In order to implement the symmetric biorthogonal wavelet basis, we use the Laplacian Pyramid Model (LPM) and the trigonometric polynomial solution method. These symmetric biorthogonal wavelet basis are used to form filters in each subband. Also coefficients of the filter are optimized with respect to the coding efficiency. From this optimization, we show that the values of a in the LPM generating kernel have the best coding efficiency in the range of 0.7 to 0.75. We also present an optimal bit allocation method based on considerations of the reconstruction filter characteristics. The step size of each subband uniform quantizer is determined by using this bit allocation method. The coding efficiency of the symmetric biorthogonal wavelet filter is compared with those of other filters: QMF, SSKF and Orthonormal wavelet filter. Simulation results demonstrate that the symmetric biorthogonal wavelet filter is useful as a basic means for image analysis/synthesis filters and can give better coding efficiency than other filters.