Abstract: The Hidden Markov Tree (HMT) model, as a statistical model of wavelet transform coefficients, effectively characterizes the statistical correlation and non-Gaussianity of wavelet transform coefficients. When applying the HMT model for fault diagnosis, a crucial issue is the selection of the HMT model structure. The Discriminant Information Criterion (DIC) is a suitable model selection criterion for classification problems; it selects the model least likely to generate data belonging to other categories. Experiments show that, compared to the commonly used Bayesian Information Criterion (BIC), DIC can select HMT models with higher recognition rates. Keywords: DIC BIC HMT model selection fault diagnosis[b][align=center]The Application of HMT Model Selection Based on DIC in fault diagnosis GUI Lin, WU Xiao-yue[/align][/b] Abstract: As a statistical model of wavelet coefficients, hidden Markov tree (HMT) can consider the statistical dependencies and non-Gaussian statistics of wavelet coefficients. When HMT model is applied in fault diagnosis, an important problem is the HMT model topology selection. Discriminative information criterion (DIC) is one kind of model selection criterion fitting for classification problems. DIC selects the model that is the less likely to have generated data belonging to competing classification categories. The experiment indicates that DIC-generated models gets higher recognition rate in comparison with Bayesian information criterion (BIC) - generated models. Key words: DIC; BIC; HMT; model selection; fault diagnosis 0 Introduction Hidden Markov model A Hidden Markov Model (HMM) is a statistical model for time series data. HMM first achieved significant breakthroughs in speech recognition and subsequently found applications in Chinese character recognition and fault diagnosis. A Hidden Markov Tree (HMT) is a wavelet domain HMM model that describes the intrinsic properties of wavelet transforms, characterizing the statistical correlation and non-Gaussianity of wavelet transform coefficients. HMTs have been applied to image denoising, image classification, and mechanical fault diagnosis with good results. The HMT model is determined by its structure and the parameters given the structure, including the number of hidden states and the number of wavelet binary trees. When applying HMT models for fault diagnosis, a crucial issue is model selection. This paper primarily studies the optimization problem of HMT model structure, specifically the optimal HMT model structure to describe the signal. Occam's Razor principle is currently the main principle for model selection, its core idea being to choose the simplest model that best describes the data features. A key theoretical basis of Occam's Razor principle is the Bayesian pattern recognition framework. The main criterion of the Bayesian identification framework is the Bayesian Information Criterion (BIC). BIC has been widely used in various model selections, such as HMM selection. Literature points out that using Occam's razor in classification problems cannot guarantee the best model for classification. This is mainly because BIC focuses on using intra-class features to select the model, without considering inter-class features. Therefore, BIC may not be applicable to classification tasks. For the model selection problem of classification tasks, Alain[10] proposed the Discriminative Information Criterion (DIC). DIC focuses on using inter-class discriminative information to select the model based on BIC. Unlike Occam's razor, which selects the simplest model that can effectively describe the data, DIC selects the least likely data to belong to other categories, and is therefore more suitable for classification tasks. For details, please click: Application of HMT Model Selection Based on DIC in Fault Diagnosis