Learning in Implicit Generative Models (1610.03483v4)

Abstract: Generative adversarial networks (GANs) provide an algorithmic framework for constructing generative models with several appealing properties: they do not require a likelihood function to be specified, only a generating procedure; they provide samples that are sharp and compelling; and they allow us to harness our knowledge of building highly accurate neural network classifiers. Here, we develop our understanding of GANs with the aim of forming a rich view of this growing area of machine learning---to build connections to the diverse set of statistical thinking on this topic, of which much can be gained by a mutual exchange of ideas. We frame GANs within the wider landscape of algorithms for learning in implicit generative models--models that only specify a stochastic procedure with which to generate data--and relate these ideas to modelling problems in related fields, such as econometrics and approximate Bayesian computation. We develop likelihood-free inference methods and highlight hypothesis testing as a principle for learning in implicit generative models, using which we are able to derive the objective function used by GANs, and many other related objectives. The testing viewpoint directs our focus to the general problem of density ratio estimation. There are four approaches for density ratio estimation, one of which is a solution using classifiers to distinguish real from generated data. Other approaches such as divergence minimisation and moment matching have also been explored in the GAN literature, and we synthesise these views to form an understanding in terms of the relationships between them and the wider literature, highlighting avenues for future exploration and cross-pollination.

Essay on "Learning in Implicit Generative Models"

The paper "Learning in Implicit Generative Models" by Shakir Mohamed and Balaji Lakshminarayanan offers an in-depth examination of the methodologies associated with learning in implicit generative models, specifically through the lens of generative adversarial networks (GANs). By situating GANs within the broader landscape of implicit model learning, the authors aim to establish connections to various statistical principles and related fields like econometrics and approximate Bayesian computation (ABC).

Key Contributions

The primary contributions of this paper can be summarized as follows:

1. Implicit vs. Prescribed Models: It distinguishes between implicit and prescribed probabilistic models. While prescribed models explicitly define a distribution with a likelihood function, implicit models do not. Implicit models specify a stochastic process for data generation, making them more applicable to complex systems where mechanistic simulation is available, such as in climate science or epidemiology.
2. Likelihood-Free Inference and Density Estimation by Comparison: The authors develop a framework for likelihood-free inference, essentially driven by hypothesis testing. This approach forefronts density ratio and density difference estimation as methods for learning in implicit generative models.
3. Approaches for Density Comparison: The paper explores four principal strategies for density comparison:
   • Class-Probability Estimation: Involving classifiers, such as those utilized in GANs, to distinguish between real and generated data.
   • Divergence Minimisation: Utilizes divergences like the f-divergence to quantify and minimize the difference between the true and generated data distributions.
   • Ratio Matching: Directly minimizes the error between the true density ratio and an estimated density ratio.
   • Moment Matching: Aligns the moments of the real and generated distributions, often using kernel methods.
4. Algorithmic Implementations: The authors deduce that many methods like GANs, NCE (Noise Contrastive Estimation), and strategies within ABC can be seen through a unified lens of density estimation by comparison.

Implications and Future Directions

The work advances the theoretical understanding of implicit generative models and provides a structured overview of strategies applicable to these models. Practically, it opens up promising pathways for leveraging implicit models in domains traditionally reliant on prescribed models, facilitated by discussions on the advantages of non-maximum likelihood methods especially under model misspecifications.

Furthermore, the interplay between implicit models and Bayesian inference is highlighted, indicating fruitful research avenues in probabilistic modeling where uncertainty representation is crucial. The paper also inspires new directions for research in non-differentiable models, suggesting the use of gradient-free optimization approaches in such contexts.

Speculation on AI Developments

As machine learning systems increasingly deal with high-dimensional data and complex environments, models that accommodate the structural and simulation-based aspects without explicit probability computations become invaluable. As suggested in this paper, future development in AI may increasingly rely on implicit generative models for settings where complex dynamics are best captured by stochastic processes rather than explicit likelihoods.

Conclusion

The paper succeeds in synthesizing existing methodologies with fresh perspectives on implicit model learning. By establishing a comprehensive framework based on hypothesis testing, it underscores the robustness and potential of these models for diverse applications. Such insights pave the way for more effective and theoretically grounded generative model applications in fields demanding sophisticated and principled data simulation strategies.