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arXiv 1907.03211cs.LGstat.APstat.ML
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基于卷积字典学习的自然指数族分布自动编码器

Convolutional dictionary learning based auto-encoders for natural exponential-family distributions

Harvard University(哈佛大学);Massachusetts Institute of Technology(麻省理工学院);Brown University(布朗大学)

Bahareh Tolooshams, Andrew H. Song, Simona Temereanca, Demba Ba

摘要:

我们介绍了一类自编码器神经网络,它是为来自自然指数族的数据定制的(例如,计数数据)。这些架构的灵感来自于在具有稀疏约束的卷积生成模型中学习滤波器的问题,通常被称为卷积字典学习(CDL)。我们的工作是第一个结合卷积生成模型和深度学习的想法,用于自然建模的非高斯分布数据(例如,二项式和泊松)。这种观点为我们提供了一个可扩展的和灵活的框架,可以重新用于生成模型上的各种任务和假设。具体而言,用于求解CDL(无监督任务)的迭代优化过程被映射到展开和约束的神经网络,对输入进行迭代调整以考虑生成分布。我们还表明,该框架可以很容易地扩展到判别训练,适合监督任务。我们证明了1)以无监督的方式拟合生成模型来学习神经尖峰数据背后的潜在刺激,与其他基线相比,可以获得更好的拟合优度,2)与最先进的监督泊松图像去噪算法相比,具有竞争力的性能,参数明显较少,以及3)浅二项式自动编码器的梯度动态。

英文摘要:

We introduce a class of auto-encoder neural networks tailored to data from the natural exponential family (e.g., count data). The architectures are inspired by the problem of learning the filters in a convolutional generative model with sparsity constraints, often referred to as convolutional dictionary learning (CDL). Our work is the first to combine ideas from convolutional generative models and deep learning for data that are naturally modeled with a non-Gaussian distribution (e.g., binomial and Poisson). This perspective provides us with a scalable and flexible framework that can be re-purposed for a wide range of tasks and assumptions on the generative model. Specifically, the iterative optimization procedure for solving CDL, an unsupervised task, is mapped to an unfolded and constrained neural network, with iterative adjustments to the inputs to account for the generative distribution. We also show that the framework can easily be extended for discriminative training, appropriate for a supervised task. We demonstrate 1) that fitting the generative model to learn, in an unsupervised fashion, the latent stimulus that underlies neural spiking data leads to better goodness-of-fit compared to other baselines, 2) competitive performance compared to state-of-the-art algorithms for supervised Poisson image denoising, with significantly fewer parameters, and 3) gradient dynamics of shallow binomial auto-encoder.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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