论文标题
概率数字卷积神经网络
Probabilistic Numeric Convolutional Neural Networks
论文作者
论文摘要
连续的输入信号（如图像和时间序列）不规则地采样或缺少值对现有的深度学习方法具有挑战性。连贯定义的特征表示必须取决于输入未观察到的区域中的值。从概率数字中的工作中借鉴，我们提出了代表特征为高斯过程（GPS）的概率数字卷积神经网络，从而提供了离散误差的概率描述。然后，我们将卷积层定义为在此GP上定义的PDE的演变，其次是非线性。这种方法自然还可以承认在例如旋转组。在实验中，我们表明我们的方法产生了$ 3 \ times $ $减少了以前的超级像素 - 纳斯特数据集中最新技术的错误，并且在医疗时间序列数据集Physionet2012上的竞争性能和竞争性能。
Continuous input signals like images and time series that are irregularly sampled or have missing values are challenging for existing deep learning methods. Coherently defined feature representations must depend on the values in unobserved regions of the input. Drawing from the work in probabilistic numerics, we propose Probabilistic Numeric Convolutional Neural Networks which represent features as Gaussian processes (GPs), providing a probabilistic description of discretization error. We then define a convolutional layer as the evolution of a PDE defined on this GP, followed by a nonlinearity. This approach also naturally admits steerable equivariant convolutions under e.g. the rotation group. In experiments we show that our approach yields a $3\times$ reduction of error from the previous state of the art on the SuperPixel-MNIST dataset and competitive performance on the medical time series dataset PhysioNet2012.
