Tree of Latent Mixtures for Bayesian Modelling and Classification of High Dimensional Data
Many domains of interest to machine learning, such as audio and video, computational biology, climate modelling, and quantitative finance, involve very high dimensional data. Such data are often characterized by statistical structure that includes correlations on multiple scales. Attempts to model those high dimensional data raise problems that are much less significant in low dimensions. This paper presents a novel approach to modelling and classification in high dimensions. The approach is based on a graphical model with a tree structure, which performs density estimation on multiple spatial scales. Exact inference in this model is computationally intractable; two algorithms for approximate inference using variational techniques are derived and analyzed. We discuss learning and classification using these algorithms, and demonstrate their performance on a handwritten digit recognition task.