The gamma belief network (GBN), often regarded as a deep topic model, has demonstrated its potential for uncovering multi-layer interpretable latent representations in text data. Its notable capability to acquire interpretable latent factors is partially attributed to sparse and non-negative gamma-distributed latent variables. However, the existing GBN and its variations are constrained by the linear generative model, thereby limiting their expressiveness and applicability. To address this limitation, we introduce the generalized gamma belief network (Generalized GBN) in this paper, which extends the original linear generative model to a more expressive non-linear generative model. Since the parameters of the Generalized GBN no longer possess an analytic conditional posterior, we further propose an upward-downward Weibull inference network to approximate the posterior distribution of the latent variables. The parameters of both the generative model and the inference network are jointly trained within the variational inference framework. Finally, we conduct comprehensive experiments on both expressivity and disentangled representation learning tasks to evaluate the performance of the Generalized GBN against state-of-the-art Gaussian variational autoencoders serving as baselines.

翻译：伽马信念网络（GBN）常被视为一种深度主题模型，其在揭示文本数据中多层可解释潜在表征方面已展现出潜力。其获取可解释潜在因子的显著能力，部分归功于稀疏且非负的伽马分布潜在变量。然而，现有的GBN及其变体受限于线性生成模型，从而制约了其表达能力和适用性。为克服这一局限，本文提出了广义伽马信念网络（Generalized GBN），将原有的线性生成模型扩展为更具表达力的非线性生成模型。由于广义GBN的参数不再具备解析条件后验，我们进一步提出了一种上下行威布尔推断网络，以近似潜在变量的后验分布。生成模型与推断网络的参数均在变分推断框架下进行联合训练。最后，我们在表达能力和解耦表征学习任务上开展了全面的实验，以评估广义GBN相对于作为基准的先进高斯变分自编码器的性能。