We derive ensembles of decision trees through a nonparametric Bayesian model, allowing us to view such ensembles as samples from a posterior distribution. This insight motivates a class of Bayesian Forest (BF) algorithms that provide small gains in performance and large gains in interpretability. Based on the BF framework, we are able to show that high-level tree hierarchy is stable in large samples. This motivates an empirical Bayesian Forest (EBF) algorithm for building approximate BFs on massive distributed datasets and we show that EBFs outperform sub-sampling based alternatives by a large margin.

This paper presents an observer-based hybrid fuzzy cerebellar model articulation controller (CMAC) neural network control with a supervisory controller for a class of uncertain chaotic systems. This proposed control system is integrating sliding mode control (SMC) theory and CMAC neural network into fuzzy controller design. The total states of the chaotic system are not assumed to be available for measurement. A state observer is used to estimate unmeasured states of the systems. The supervised control is appended to assure that the fuzzy CMAC controller achieve a stable closed-loop system through Lyapunov stability theory. Finally, simulation results show that the effect of the approximation error on the tracking error can be attenuated efficiently by the proposed method.

The maim idea proposed in this paper is integrating sliding mode control (SMC) theory and cerebellar model articulation controller (CMAC) neural network into fuzzy controller design and the fuzzy control rules can be determined systematically by the sliding condition of the SMC. The advantages of using fuzzy model into CMAC are to improve function approximation accuracy in terms of the weighting coefficients of CMAC. The proposed slide-mode-based fuzzy CMAC (SFCMAC), which results from the direct adaptive approach, has the ability to tune the adaptation parameters in the THEN-part of each fuzzy rule during real-time operation. The weight-update law is derived using a Lyapunov stability analysis that guarantees the stability of the closed-loop system. Simulation results show a satisfactory performance of the proposed control scheme.

The basic idea of traditional density estimation is to model the overall point density analytically as the sum of influence functions of data points. However, traditional density estimation techniques only consider the location of a point. Supervised density estimation techniques, on the other hand, additionally consider a variable of interest that is associated with a point. Density in supervised density estimation is measured as the product of an influence function with the variable of interest. Based on this novel idea, a supervised density-based clustering named SCDE is introduced and discussed in detail. The SCDE algorithm forms clusters by associating data points with supervised density attractors which represent maxima and minima of a supervised density function.

Adaptive clustering uses external feedback to improve cluster quality; past experience serves to speed up execution time. An adaptive clustering environment is proposed that uses Q-learning to learn the reward values of successive data clusterings. Adaptive clustering supports the reuse of clusterings by memorizing what worked well in the past. It has the capability of exploring multiple paths in parallel when searching for good clusters. In a case study, we apply adaptive clustering to instance-based learning relying on a distance function modification approach. A distance function adaptation scheme that uses external feedback is proposed and compared with other distance function learning approaches. Experimental results indicate that the use of adaptive clustering leads to significant improvements of instance-based learning techniques, such as k-nearest neighbor classifiers. Moreover, as a by-product a new instance-based learning technique is introduced that classifies examples by solely using cluster representatives; this technique shows high promise in our experimental evaluation.

This paper will address the problem of controlling an unknown MIMO nonlinear affined system. A fuzzy sliding mode controller (FSMC) is used to approximate the equivalent control by using an on-line fuzzy adaptation scheme, and then the hitting control is appended to show that the proposed FSMC can result in a closed-loop system, which is stable. This scheme also provides the designers flexibility to design and to implement fuzzy rule base without domain experts and without mathematical model. The robust adaptive scheme is shown to be able to guarantee that the output tracking error can converge to, a residual set ultimately by a two-dimensional inverted pendulum system.