The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, autoencoders, manifold learning, and deep networks. This motivates longer term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation, and manifold learning.

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Representation Learning: A Review and New Perspectives

Probabilistic generative models can be used for compression, denoising, inpainting, texture synthesis, semi-supervised learning, unsupervised feature learning, and other tasks. Given this wide range of applications, it is not surprising that a lot of heterogeneity exists in the way these models are formulated, trained, and evaluated. As a consequence, direct comparison between models is often difficult. This article reviews mostly known but often underappreciated properties relating to the evaluation and interpretation of generative models with a focus on image models. In particular, we show that three of the currently most commonly used criteria---average log-likelihood, Parzen window estimates, and visual fidelity of samples---are largely independent of each other when the data is high-dimensional. Good performance with respect to one criterion therefore need not imply good performance with respect to the other criteria. Our results show that extrapolation from one criterion to another is not warranted and generative models need to be evaluated directly with respect to the application(s) they were intended for. In addition, we provide examples demonstrating that Parzen window estimates should generally be avoided.

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A note on the evaluation of generative models

We propose a deep learning framework for modeling complex high-dimensional densities called Non-linear Independent Component Estimation (NICE). It is based on the idea that a good representation is one in which the data has a distribution that is easy to model. For this purpose, a non-linear deterministic transformation of the data is learned that maps it to a latent space so as to make the transformed data conform to a factorized distribution, i.e., resulting in independent latent variables. We parametrize this transformation so that computing the Jacobian determinant and inverse transform is trivial, yet we maintain the ability to learn complex non-linear transformations, via a composition of simple building blocks, each based on a deep neural network. The training criterion is simply the exact log-likelihood, which is tractable. Unbiased ancestral sampling is also easy. We show that this approach yields good generative models on four image datasets and can be used for inpainting.

NICE: Non-linear Independent Components Estimation

Due to the storage and retrieval efficiency, hashing has been widely deployed to approximate nearest neighbor search for large-scale multimedia retrieval. Supervised hashing, which improves the quality of hash coding by exploiting the semantic similarity on data pairs, has received increasing attention recently. For most existing supervised hashing methods for image retrieval, an image is first represented as a vector of hand-crafted or machine-learned features, followed by another separate quantization step that generates binary codes. However, suboptimal hash coding may be produced, because the quantization error is not statistically minimized and the feature representation is not optimally compatible with the binary coding. In this paper, we propose a novel Deep Hashing Network (DHN) architecture for supervised hashing, in which we jointly learn good image representation tailored to hash coding and formally control the quantization error. The DHN model constitutes four key components: (1) a subnetwork with multiple convolution-pooling layers to capture image representations; (2) a fully-connected hashing layer to generate compact binary hash codes; (3) a pairwise cross-entropy loss layer for similarity-preserving learning; and (4) a pairwise quantization loss for controlling hashing quality. Extensive experiments on standard image retrieval datasets show the proposed DHN model yields substantial boosts over latest state-of-the-art hashing methods.

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Deep Hashing Network for efficient similarity retrieval

One of the most successful frameworks in computational neuroscience is modeling visual processing using the statistical structure of natural images. In this framework, the visual system of the brain constructs a model of the statistical regularities of the incoming visual data. This enables the visual system to perform efficient probabilistic inference. The same framework is also very useful in engineering applications such as image processing and computer vision. This book is the first comprehensive introduction to the multidisciplinary field of natural image statistics. The book starts with a review of background material in signal processing and neuroscience, which makes it accessible to a wide audience. The book then explains both the basic theory and the most recent advances in a coherent and user-friendly manner. This structure, together with the included exercises and computer assignments, also make it an excellent textbook. "Natural Image Statistics" is a timely and valuable resource for advanced students and researchers in any discipline related to vision, such as neuroscience, computer science, psychology, electrical engineering, cognitive science or statistics.

Jarmo Hurri

Papers

Natural Image Statistics: A Probabilistic Approach to Early Computational Vision.