We develop a probabilistic framework for deep learning based on the Deep Rendering Mixture Model (DRMM), a new generative probabilistic model that explicitly capture variations in data due to latent task nuisance variables. We demonstrate that max-sum inference in the DRMM yields an algorithm that exactly reproduces the operations in deep convolutional neural networks (DCNs), providing a first principles derivation. Our framework provides new insights into the successes and shortcomings of DCNs as well as a principled route to their improvement. DRMM training via the Expectation-Maximization (EM) algorithm is a powerful alternative to DCN back-propagation, and initial training results are promising. Classification based on the DRMM and other variants outperforms DCNs in supervised digit classification, training 2-3x faster while achieving similar accuracy. Moreover, the DRMM is applicable to semi-supervised and unsupervised learning tasks, achieving results that are state-of-the-art in several categories on the MNIST benchmark and comparable to state of the art on the CIFAR10 benchmark.
Hierarchical Generative Models. The DRMM is closely related to several hierarchical models, including the Deep Mixture of Factor Analyzers @cite_7 and the Deep Gaussian Mixture Model @cite_8 .
@cite_7 @cite_8
2148464528 1636244751 2129414564 1994205671
Generative models can be seen as the swiss army knives of machine learning, as many problems can be written probabilistically in terms of the distribution of the data, including prediction, reconstruction, imputation and simulation. One of the most promising directions for unsupervised learning may lie in Deep Learning methods, given their success in supervised learning. However, one of the current problems with deep unsupervised learning methods, is that they often are harder to scale. As a result there are some easier, more scalable shallow methods, such as the Gaussian Mixture Model and the Student-t Mixture Model, that remain surprisingly competitive. In this paper we propose a new scalable deep generative model for images, called the Deep Gaussian Mixture Model, that is a straightforward but powerful generalization of GMMs to multiple layers. The parametrization of a Deep GMM allows it to efficiently capture products of variations in natural images. We propose a new EM-based algorithm that scales well to large datasets, and we show that both the Expectation and the Maximization steps can easily be distributed over multiple machines. In our density estimation experiments we show that deeper GMM architectures generalize better than more shallow ones, with results in the same ballpark as the state of the art. We introduce, analyze and demonstrate a recursive hierarchical generalization of the widely used hidden Markov models, which we name Hierarchical Hidden Markov Models (HHMM). Our model is motivated by the complex multi-scale structure which appears in many natural sequences, particularly in language, handwriting and speech. We seek a systematic unsupervised approach to the modeling of such structures. By extending the standard Baum-Welch (forward-backward) algorithm, we derive an efficient procedure for estimating the model parameters from unlabeled data. We then use the trained model for automatic hierarchical parsing of observation sequences. We describe two applications of our model and its parameter estimation procedure. In the first application we show how to construct hierarchical models of natural English text. In these models different levels of the hierarchy correspond to structures on different length scales in the text. In the second application we demonstrate how HHMMs can be used to automatically identify repeated strokes that represent combination of letters in cursive handwriting. We propose probabilistic generative models, called parametric mixture models (PMMs), for multiclass, multi-labeled text categorization problem. Conventionally, the binary classification approach has been employed, in which whether or not text belongs to a category is judged by the binary classifier for every category. In contrast, our approach can simultaneously detect multiple categories of text using PMMs. We derive efficient learning and prediction algorithms for PMMs. We also empirically show that our method could significantly outperform the conventional binary methods when applied to multi-labeled text categorization using real World Wide Web pages. This paper illustrates a hierarchical generative model for representing and recognizing compositional object categories with large intra-category variance. In this model, objects are broken into their constituent parts and the variability of configurations and relationships between these parts are modeled by stochastic attribute graph grammars, which are embedded in an And-Or graph for each compositional object category. It combines the power of a stochastic context free grammar (SCFG) to express the variability of part configurations, and a Markov random field (MRF) to represent the pictorial spatial relationships between these parts. As a generative model, different object instances of a category can be realized as a traversal through the And-Or graph to arrive at a valid configuration (like a valid sentence in language, by analogy). The inference recognition procedure is intimately tied to the structure of the model and follows a probabilistic formulation consisting of bottom-up detection steps for the parts, which in turn recursively activate the grammar rules for top-down verification and searches for missing parts. We present experiments comparing our results to state of art methods and demonstrate the potential of our proposed framework on compositional objects with cluttered backgrounds using training and testing data from the public Lotus Hill and Caltech datasets.