Inhomogeneous Hidden Markov Research Articles

A novel model based on multi-grained cascade forests with wavelet denoising for indoor occupancy estimation

Reliable occupancy estimation is the key to balancing energy use and comfort as well as promoting energy efficiency in buildings. In this study, a novel occupancy estimation model based on CO2 concentration data was proposed. A wavelet denoising method was applied to remove the random noise of the CO2 sensory data, and then a multi-grained scanning cascade forests (GcForest) method was used to estimate the number of occupants. The GcForest model incorporated three different tree-based classifiers in each level, enabling the estimation performance to be enhanced by exploiting the complementarity among the different learning algorithms. To evaluate the effectiveness of the proposed model, in this study a validation experiment was conducted in a university lab office and its results were compared with the support vector machines (SVM), classification and regression trees (CART), and inhomogeneous hidden Markov (IHMM) algorithms. The experimental results show that the wavelet denoising method could filter the noise and preserve the data features of the CO2 concentration. Moreover, the proposed model could achieve higher estimation accuracy, lower mean absolute error, and higher detection accuracy of the occupant presence/absence. Additionally, this model could capture both the first arrival time and the last departure time. Since the maximum depths of the classifiers affected the GcForest model's performance, the results also show that a proper selection of the maximum depth combination could lead to a significant improvement of the model estimation accuracy.

A Continuous Entropy Rate Estimator for Spike Trains Using a K-Means-Based Context Tree

Entropy rate quantifies the change of information of a stochastic process (Cover & Thomas, 2006). For decades, the temporal dynamics of spike trains generated by neurons has been studied as a stochastic process (Barbieri, Quirk, Frank, Wilson, & Brown, 2001; Brown, Frank, Tang, Quirk, & Wilson, 1998; Kass & Ventura, 2001; Metzner, Koch, Wessel, & Gabbiani, 1998; Zhang, Ginzburg, McNaughton, & Sejnowski, 1998). We propose here to estimate the entropy rate of a spike train from an inhomogeneous hidden Markov model of the spike intervals. The model is constructed by building a context tree structure to lay out the conditional probabilities of various subsequences of the spike train. For each state in the Markov chain, we assume a gamma distribution over the spike intervals, although any appropriate distribution may be employed as circumstances dictate. The entropy and confidence intervals for the entropy are calculated from bootstrapping samples taken from a large raw data sequence. The estimator was first tested on synthetic data generated by multiple-order Markov chains, and it always converged to the theoretical Shannon entropy rate (except in the case of a sixth-order model, where the calculations were terminated before convergence was reached). We also applied the method to experimental data and compare its performance with that of several other methods of entropy estimation.