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Register a new userLocally Masked Convolution for Autoregressive Models
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Added by
Ajay Jain
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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High-dimensional generative models have many applications including image compression, multimedia generation, anomaly detection and data completion. State-of-the-art estimators for natural images are autoregressive, decomposing the joint distribution over pixels into a product of conditionals parameterized by a deep neural network, e.g. a convolutional neural network such as the PixelCNN. However, PixelCNNs only model a single decomposition of the joint, and only a single generation order is efficient. For tasks such as image completion, these models are unable to use much of the observed context. To generate data in arbitrary orders, we introduce LMConv: a simple modification to the standard 2D convolution that allows arbitrary masks to be applied to the weights at each location in the image. Using LMConv, we learn an ensemble of distribution estimators that share parameters but differ in generation order, achieving improved performance on whole-image density estimation (2.89 bpd on unconditional CIFAR10), as well as globally coherent image completions. Our code is available at https://ajayjain.github.io/lmconv.
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Conditional autoregressive (CAR) models are commonly used to capture spatial correlation in areal unit data, and are typically specified as a prior distribution for a set of random effects, as part of a hierarchical Bayesian model. The spatial correlation structure induced by these models is determined by geographical adjacency, so that two areas have correlated random effects if they share a common border. However, this correlation structure is too simplistic for real data, which are instead likely to include sub-regions of strong correlation as well as locations at which the response exhibits a step-change. Therefore this paper proposes an extension to CAR priors, which can capture such localised spatial correlation. The proposed approach takes the form of an iterative algorithm, which sequentially updates the spatial correlation structure in the data as well as estimating the remaining model parameters. The efficacy of the approach is assessed by simulation, and its utility is illustrated in a disease mapping context, using data on respiratory disease risk in Greater Glasgow, Scotland.
Stochastic processes generated by non-stationary distributions are difficult to represent with conventional models such as Gaussian processes. This work presents Recurrent Autoregressive Flows as a method toward general stochastic process modeling with normalizing flows. The proposed method defines a conditional distribution for each variable in a sequential process by conditioning the parameters of a normalizing flow with recurrent neural connections. Complex conditional relationships are learned through the recurrent network parameters. In this work, we present an initial design for a recurrent flow cell and a method to train the model to match observed empirical distributions. We demonstrate the effectiveness of this class of models through a series of experiments in which models are trained on three complex stochastic processes. We highlight the shortcomings of our current formulation and suggest some potential solutions.
Autoregressive models are widely used for tasks such as image and audio generation. The sampling process of these models, however, does not allow interruptions and cannot adapt to real-time computational resources. This challenge impedes the deployment of powerful autoregressive models, which involve a slow sampling process that is sequential in nature and typically scales linearly with respect to the data dimension. To address this difficulty, we propose a new family of autoregressive models that enables anytime sampling. Inspired by Principal Component Analysis, we learn a structured representation space where dimensions are ordered based on their importance with respect to reconstruction. Using an autoregressive model in this latent space, we trade off sample quality for computational efficiency by truncating the generation process before decoding into the original data space. Experimentally, we demonstrate in several image and audio generation tasks that sample quality degrades gracefully as we reduce the computational budget for sampling. The approach suffers almost no loss in sample quality (measured by FID) using only 60% to 80% of all latent dimensions for image data. Code is available at https://github.com/Newbeeer/Anytime-Auto-Regressive-Model .
Machine learning is gaining popularity in a broad range of areas working with geographic data, such as ecology or atmospheric sciences. Here, data often exhibit spatial effects, which can be difficult to learn for neural networks. In this study, we propose SXL, a method for embedding information on the autoregressive nature of spatial data directly into the learning process using auxiliary tasks. We utilize the local Morans I, a popular measure of local spatial autocorrelation, to nudge the model to learn the direction and magnitude of local spatial effects, complementing the learning of the primary task. We further introduce a novel expansion of Morans I to multiple resolutions, thus capturing spatial interactions over longer and shorter distances simultaneously. The novel multi-resolution Morans I can be constructed easily and as a multi-dimensional tensor offers seamless integration into existing machine learning frameworks. Throughout a range of experiments using real-world data, we highlight how our method consistently improves the training of neural networks in unsupervised and supervised learning tasks. In generative spatial modeling experiments, we propose a novel loss for auxiliary task GANs utilizing task uncertainty weights. Our proposed method outperforms domain-specific spatial interpolation benchmarks, highlighting its potential for downstream applications. This study bridges expertise from geographic information science and machine learning, showing how this integration of disciplines can help to address domain-specific challenges. The code for our experiments is available on Github: https://github.com/konstantinklemmer/sxl.
Winograds minimal filtering algorithm has been widely used in Convolutional Neural Networks (CNNs) to reduce the number of multiplications for faster processing. However, it is only effective on convolutions with kernel size as 3x3 and stride as 1, because it suffers from significantly increased FLOPs and numerical accuracy problem for kernel size larger than 3x3 and fails on convolution with stride larger than 1. In this paper, we propose a novel Decomposable Winograd Method (DWM), which breaks through the limitation of original Winograds minimal filtering algorithm to a wide and general convolutions. DWM decomposes kernels with large size or large stride to several small kernels with stride as 1 for further applying Winograd method, so that DWM can reduce the number of multiplications while keeping the numerical accuracy. It enables the fast exploring of larger kernel size and larger stride value in CNNs for high performance and accuracy and even the potential for new CNNs. Comparing against the original Winograd, the proposed DWM is able to support all kinds of convolutions with a speedup of ~2, without affecting the numerical accuracy.
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