A grand challenge in machine learning is the development of computational algorithms that match or outperform humans in perceptual inference tasks such as visual object and speech recognition. The key factor complicating such tasks is the presence of numerous nuisance variables, for instance, the unknown object position, orientation, and scale in object recognition or the unknown voice pronunciation, pitch, and speed in speech recognition. Recently, a new breed of deep learning algorithms has emerged for high-nuisance inference tasks; they are constructed from many layers of alternating linear and nonlinear processing units and are trained using large-scale algorithms and massive amounts of training data. The recent success of deep learning systems is impressive— they now routinely yield pattern recognition systems with near or super-human capabilities — but a fundamental question remains: Why do they work? Intuitions abound, but a coherent framework for understanding, analyzing, and synthesizing deep learning architectures has remained elusive.

We answer this question by developing a new probabilistic framework for deep Learning, namely the Deep Rendering Model (DRM), based on a Bayesian generative probabilistic model that explicitly captures variation due to nuisance variables. The graphical structure of the model enables it to be learned from data using classical expectation-maximization techniques. Furthermore, by relaxing the generative model to a discriminative one, we can recover deep convolutional neural networks (DCNs) as well as its variants including the deep residual networks (ResNet) and the densely connected convolutional networks (DenseNet), providing insights into their successes and shortcomings as well as a principled route to their improvement. The DRMM is also 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.