论文标题
深层生成网络的分析概率分布和学习
Analytical Probability Distributions and EM-Learning for Deep Generative Networks
论文作者
论文摘要
目前，通过各种自动编码器（VAE）对其产量和潜在空间进行概率建模的深层生成网络（DGN）。在没有已知的后部和可能性期望的已知分析形式的情况下，VAES诉诸近似值，包括（摊销）变异推理（AVI）和蒙特卡洛（MC）采样。我们利用现代DGN的连续分段仿射（CPA）属性来得出其后部和边缘分布以及后者的第一时刻。这些发现使我们能够得出一种分析期望最大化（EM）算法，从而实现无梯度DNG学习。我们从经验上证明，与VAE培训相比，对DGN的EM培训产生的可能性更大。我们的发现将指导新的VAE AVI的设计，以更好地近似真正的后部和开放途径，以应用标准的统计工具进行模型比较，异常检测和缺少数据插补。
Deep Generative Networks (DGNs) with probabilistic modeling of their output and latent space are currently trained via Variational Autoencoders (VAEs). In the absence of a known analytical form for the posterior and likelihood expectation, VAEs resort to approximations, including (Amortized) Variational Inference (AVI) and Monte-Carlo (MC) sampling. We exploit the Continuous Piecewise Affine (CPA) property of modern DGNs to derive their posterior and marginal distributions as well as the latter's first moments. These findings enable us to derive an analytical Expectation-Maximization (EM) algorithm that enables gradient-free DGN learning. We demonstrate empirically that EM training of DGNs produces greater likelihood than VAE training. Our findings will guide the design of new VAE AVI that better approximate the true posterior and open avenues to apply standard statistical tools for model comparison, anomaly detection, and missing data imputation.
