How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case. Our contributions is two-fold. First, we show that a reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods. Second, we show that for i.i.d. datasets with continuous latent variables per datapoint, posterior inference can be made especially efficient by fitting an approximate inference model (also called a recognition model) to the intractable posterior using the proposed lower bound estimator. Theoretical advantages are reflected in experimental results.

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Auto-Encoding Variational Bayes

计量经济分析 = Econometric analysis

Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Machine Learning : A Probabilistic Perspective

“Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”の学習報告

We develop stochastic variational inference, a scalable algorithm for approximating posterior distributions. We develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models, latent Dirichlet allocation and the hierarchical Dirichlet process topic model. Using stochastic variational inference, we analyze several large collections of documents: 300K articles from Nature, 1.8M articles from The New York Times, and 3.8M articles from Wikipedia. Stochastic inference can easily handle data sets of this size and outperforms traditional variational inference, which can only handle a smaller subset. (We also show that the Bayesian nonparametric topic model outperforms its parametric counterpart.) Stochastic variational inference lets us apply complex Bayesian models to massive data sets.

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Stochastic variational inference

We propose a new deep network architecture for removing rain streaks from individual images based on the deep convolutional neural network (CNN). Inspired by the deep residual network (ResNet) that simplifies the learning process by changing the mapping form, we propose a deep detail network to directly reduce the mapping range from input to output, which makes the learning process easier. To further improve the de-rained result, we use a priori image domain knowledge by focusing on high frequency detail during training, which removes background interference and focuses the model on the structure of rain in images. This demonstrates that a deep architecture not only has benefits for high-level vision tasks but also can be used to solve low-level imaging problems. Though we train the network on synthetic data, we find that the learned network generalizes well to real-world test images. Experiments show that the proposed method significantly outperforms state-of-the-art methods on both synthetic and real-world images in terms of both qualitative and quantitative measures. We discuss applications of this structure to denoising and JPEG artifact reduction at the end of the paper.

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Removing Rain from Single Images via a Deep Detail Network

We introduce a deep network architecture called DerainNet for removing rain streaks from an image. Based on the deep convolutional neural network (CNN), we directly learn the mapping relationship between rainy and clean image detail layers from data. Because we do not possess the ground truth corresponding to real-world rainy images, we synthesize images with rain for training. In contrast to other common strategies that increase depth or breadth of the network, we use image processing domain knowledge to modify the objective function and improve deraining with a modestly sized CNN. Specifically, we train our DerainNet on the detail (high-pass) layer rather than in the image domain. Though DerainNet is trained on synthetic data, we find that the learned network translates very effectively to real-world images for testing. Moreover, we augment the CNN framework with image enhancement to improve the visual results. Compared with the state-of-the-art single image de-raining methods, our method has improved rain removal and much faster computation time after network training.

Clearing the Skies: A Deep Network Architecture for Single-Image Rain Removal

We propose a deep network architecture for the pan-sharpening problem called PanNet. We incorporate domain-specific knowledge to design our PanNet architecture by focusing on the two aims of the pan-sharpening problem: spectral and spatial preservation. For spectral preservation, we add up-sampled multispectral images to the network output, which directly propagates the spectral information to the reconstructed image. To preserve spatial structure, we train our network parameters in the high-pass filtering domain rather than the image domain. We show that the trained network generalizes well to images from different satellites without needing retraining. Experiments show significant improvement over state-of-the-art methods visually and in terms of standard quality metrics.

John Paisley

Papers

Stochastic variational inference

Removing Rain from Single Images via a Deep Detail Network

Clearing the Skies: A Deep Network Architecture for Single-Image Rain Removal

PanNet: A Deep Network Architecture for Pan-Sharpening

A fusion-based enhancing method for weakly illuminated images