Divergence Triangle for Joint Training of Generator Model, Energy-Based Model, and Inferential Model

Abstract

This paper proposes the divergence triangle as a framework for joint training of generator model, energy-based model and inference model. The divergence triangle is a compact and symmetric (anti-symmetric) objective function that seamlessly integrates variational learning, adversarial learning, wake-sleep algorithm, and contrastive divergence in a unified probabilistic formulation. This unification makes the processes of sampling, inference, energy evaluation readily available without the need for costly Markov chain Monte Carlo methods. Our experiments demonstrate that the divergence triangle is capable of learning (1) an energy-based model with well-formed energy landscape, (2) direct sampling in the form of a generator network, and (3) feed-forward inference that faithfully reconstructs observed as well as synthesized data. The divergence triangle is a robust training method that can learn from incomplete data.

Representation Learning: A Statistical Perspective

“…Because of the negative sign in front of the second KL divergence in Equation 22, we need max θ in Equation 22 or min θ in Equation 23, so that the learning becomes adversarial (illustrated in Figure 12). Inspired by (Hinton, 2002), Han et al (2019) called Equation 22 the adversarial contrastive divergence (ACD). It underlies the work of Kim and Bengio (2016); Dai et al (2017).…”

“…3. Π distribution: Π(h, x) = π α (x)q φ (h|x) Han et al (2019) proposed to learn the three models p θ , π α , and q φ by the following divergence triangle…”

A tale of three probabilistic families: Discriminative, descriptive, and generative models

“…For the descriptive model, we use the same structure as the inference net. [36]. The generative model seeks to get close to the data distribution as well as the descriptive model.…”

“…Following the notation of previous subsections, write P data (h, X) = P data (X)ρ φ (h|X), P (h, X) = p θ (X)ρ φ (h|X), and Q(h, X) = q(h)q α (X|h). It has been noticed by the recent work [36] that the variational objective KL(P data Q) and the adversarial objective KL(P data P )− KL(Q P ) can be combined into 12) which is in the form of a triangle formed by P data , P , and Q. See Figure 29 for an illustration.…”

“…See Figure 29 for an illustration. As shown by [36], one can learn the descriptive model, the generative model, and the inference model jointly using the above objective.…”