Scalable and Flexible Generative Modeling of Discrete Data with Marginalization Models (MAMs)

Conceptos Básicos

Marginalization Models (MAMs) offer a new approach to generative modeling of discrete data, enabling efficient and scalable approximation of arbitrary marginal probabilities, addressing limitations of existing autoregressive models in both maximum likelihood and energy-based training settings.

Resumen

Bibliographic Information:

Liu, S., Ramadge, P.J., Adams, R.P. (2024). Generative Marginalization Models. Proceedings of the 41st International Conference on Machine Learning, Vienna, Austria. PMLR 235.

Research Objective:

This paper introduces Marginalization Models (MAMs), a novel family of generative models designed to overcome the limitations of existing autoregressive models in efficiently estimating marginal probabilities for high-dimensional discrete data. The research aims to demonstrate the effectiveness of MAMs in both maximum likelihood estimation (MLE) and energy-based training (EB) settings.

Methodology:

The authors propose a novel model architecture that directly models the marginal distribution p(xS) for any subset of variables xS in a discrete data point x. To ensure the validity of the model, they introduce the concept of "marginalization self-consistency," which enforces the sum rule of probability. The authors develop scalable training objectives based on this principle, enabling efficient learning of both marginal and conditional probabilities. They evaluate MAMs on various discrete data distributions, including images, text, physical systems, and molecules, comparing their performance against existing state-of-the-art models in both MLE and EB settings.

Key Findings:

• MAMs achieve competitive performance in terms of negative log-likelihood compared to existing models in MLE tasks.
• MAMs demonstrate significantly faster inference speeds for arbitrary marginal probabilities, achieving up to 4 orders of magnitude speed-up compared to autoregressive models.
• In EB training, MAMs successfully scale to high-dimensional problems where traditional autoregressive models struggle due to memory constraints and slow sampling procedures.
• MAMs maintain high correlation with ground truth marginal probabilities, indicating accurate and consistent estimations.

Main Conclusions:

MAMs present a significant advancement in generative modeling of discrete data by enabling efficient and scalable approximation of arbitrary marginal probabilities. Their ability to handle high-dimensional problems in both MLE and EB settings makes them a powerful tool for various applications, including image generation, text modeling, molecule design, and physical system simulation.

Significance:

This research significantly contributes to the field of generative modeling by introducing a novel model architecture and training procedure that addresses key limitations of existing methods. The proposed MAMs offer a more efficient and scalable approach for learning and inferring complex discrete data distributions, potentially leading to advancements in various domains requiring accurate and efficient probabilistic modeling.

Limitations and Future Research:

While MAMs demonstrate promising results, further research could explore their application to continuous data and investigate the potential benefits of incorporating more sophisticated neural network architectures. Additionally, exploring alternative sampling strategies for the REINFORCE gradient estimator could further improve the model's performance and scalability in energy-based training settings.

Estadísticas

MAMs achieve close to 4 orders of magnitude speed-up in computation time for marginal inference on image data.
On a 30x30 (D=900) Ising model, MAMs achieve a bits-per-dimension (bpd) of 0.835, while other models fail to fit in the GPU memory.
MAMs demonstrate consistent and accurate marginal estimations, achieving Pearson correlation coefficients close to 1.0 when compared to the best-performing models.

Citas

"The ability to directly address such quantities [marginal and conditional probabilities] is critical in applications such as outlier or machine-generated content detection, masked language modeling, image inpainting, and constrained protein/molecule design."
"To enhance scalability and flexibility in the generative modeling of discrete data, we propose a new family of generative models, marginalization models (MAMs), that directly model the marginal distribution p(xS) for any subset of variables xS in x."
"For energy-based training, MAMs are able to scale training of any-order generative models to high-dimensional problems that previous methods fail to achieve."

Ideas clave extraídas de

Generative Marginalization Models

by Sulin Liu, P... a las arxiv.org 10-08-2024

https://arxiv.org/pdf/2310.12920.pdf

Consultas más profundas

How can the concept of "marginalization self-consistency" be extended to other types of generative models beyond those focusing on discrete data?

While the paper focuses on discrete data, the concept of "marginalization self-consistency" can be extended to other generative models for continuous data with some modifications:
1. Continuous Data Adaptation:

Replace Summation with Integration: Instead of summing over discrete values for marginalized variables, we would integrate over their continuous support in the marginalization self-consistency constraint. For a subset of variables xS in a continuous space, the marginalization self-consistency would be expressed as:
p(x_S) = ∫ p(x_S, x_Sc) dx_Sc

Function Approximation: Neural networks can still be used to parameterize the joint and marginal distributions. However, instead of outputting probability masses, they would output parameters of continuous distributions (e.g., mean and variance for Gaussian distributions).
2. Training Adaptations:

Numerical Integration: Evaluating the integral for continuous variables in the self-consistency constraint might not have a closed-form solution. Approaches like Monte Carlo integration or quadrature methods can be used to approximate the integral during training.

Variational Bounds: For intractable integrals, variational bounds can be derived to make the optimization tractable. This would involve introducing auxiliary distributions and optimizing a lower bound on the marginal likelihood.
3. Examples of Extension:

Variational Autoencoders (VAEs): Marginalization self-consistency could be enforced on the latent space of VAEs, encouraging the model to learn a latent representation where marginal distributions over subsets of latent variables are consistent with the joint distribution.

Normalizing Flows: By incorporating the self-consistency constraint during the flow's training, one could potentially improve the flow's ability to capture complex dependencies and generate consistent samples even when conditioning on or marginalizing out subsets of variables.
Challenges:

Computational Complexity: Evaluating integrals for high-dimensional continuous data can be computationally expensive. Efficient approximation techniques and careful model design would be crucial.

Approximation Errors: Numerical integration methods introduce approximation errors, which could affect the accuracy of the learned model.

While MAMs show promise, could their reliance on approximate marginalization lead to unforeseen biases or limitations in specific applications, and how can these be mitigated?

Yes, the reliance on approximate marginalization in MAMs could lead to potential biases or limitations:
1. Bias in Marginal Distributions:

Overfitting to Training Distribution: If the training data is not fully representative of the true data distribution, the approximate marginalization might overfit to the observed marginals, leading to biased estimates for unseen data points or regions with limited training samples.

Sensitivity to Ordering: While MAMs aim for any-order generation, the approximation quality of marginals might still be sensitive to the ordering used during training, potentially introducing biases depending on the chosen orderings.
2. Limitations in Specific Applications:

Applications Requiring Exact Inference: In domains like scientific modeling where exact probabilistic inference is crucial for decision-making, the approximate nature of MAMs might be a limiting factor.

Highly Structured Data: For data with very long-range dependencies or intricate structures, accurately approximating all possible marginals with a single neural network could be challenging, potentially leading to limitations in capturing the full complexity of the data.
Mitigation Strategies:

Diverse Training Data: Using a large and diverse training dataset that adequately covers the underlying data distribution can help reduce bias due to overfitting.

Ordering Strategies: Exploring different ordering strategies during training, such as random orderings or curriculum learning approaches, could help mitigate biases related to specific orderings.

Hybrid Models: Combining MAMs with other generative models that excel in exact inference or capturing specific data structures could leverage the strengths of each approach.

Uncertainty Quantification: Incorporating uncertainty quantification techniques into MAMs could provide insights into the reliability of the approximate marginals and guide decision-making in applications where uncertainty is critical.

If we view the evolution of scientific knowledge as a form of generative modeling, could MAMs be used to model and predict the emergence of new scientific discoveries based on existing knowledge?

The idea of viewing scientific knowledge evolution as generative modeling is intriguing, and MAMs could potentially play a role, though significant challenges exist:
Potential Applications:

Hypothesis Generation: MAMs could be trained on existing scientific literature, representing discoveries as discrete events or concepts. By marginalizing over unexplored areas, the model might suggest plausible new hypotheses or connections between existing concepts.

Predicting Research Trajectories: By modeling the sequential emergence of scientific papers and their relationships, MAMs could potentially predict promising research directions or identify areas ripe for breakthroughs.

Interdisciplinary Discovery: MAMs could be used to represent knowledge from different scientific disciplines. By learning the joint distribution of concepts across disciplines, the model might uncover novel connections and facilitate interdisciplinary discoveries.
Challenges and Considerations:

Representing Scientific Knowledge: Effectively representing complex scientific knowledge in a way suitable for MAMs is a major challenge. It requires careful consideration of ontologies, relationships between concepts, and the dynamic nature of scientific understanding.

Data Sparsity and Bias: Scientific literature is inherently biased towards successful findings and might not fully capture the underlying landscape of scientific exploration. Addressing data sparsity and bias is crucial for building reliable models.

Evaluating Predictions: Evaluating the quality of scientific discovery predictions is inherently difficult. It requires careful consideration of novelty, significance, and the time scales involved in scientific progress.

Ethical Implications: Predicting scientific discoveries raise ethical questions about potential biases, the ownership of knowledge, and the responsible use of such models.
Overall:
While using MAMs to model scientific knowledge evolution is speculative, it presents an exciting research direction. Addressing the challenges and ethical considerations is crucial for realizing the potential of generative models in advancing scientific discovery.