Integrating Domain Knowledge into Learning Probabilistic Circuits for Improved Generalization and Robustness

Core Concepts

A unified framework that can effectively integrate diverse types of probabilistic domain knowledge into the parameter learning of Probabilistic Circuits, enabling improved generalization and robustness in data-scarce and noisy settings.

Abstract

The paper proposes a unified framework for integrating diverse types of domain knowledge into the parameter learning of Probabilistic Circuits (PCs). PCs are an efficient framework for representing and learning complex probability distributions, but they often struggle with limited and noisy data, similar to deep generative models.
The key contributions are:

Developing a unified mathematical framework that allows encoding different types of domain knowledge as probabilistic constraints, including generalization, monotonicity, context-specific independence, class imbalance, synergy, and privileged information.

Formulating the knowledge-intensive parameter learning of PCs as a constrained optimization problem, where the domain constraints are seamlessly incorporated into the maximum likelihood objective.

Empirically validating the effectiveness of the proposed approach on several benchmark and real-world datasets, demonstrating that incorporating domain knowledge can significantly improve the generalization performance and robustness of PCs, especially in data-scarce and noisy settings.

The experiments show that the framework can faithfully integrate diverse forms of domain knowledge, leading to superior performance compared to purely data-driven approaches. The approach is also shown to be robust to noisy or redundant advice from domain experts.

Stats

"The dataset sizes range from 100 to 10,000 data points."
"The real-world nuMoM2b dataset contains 3,657 subjects with 7 risk factors for Gestational Diabetes Mellitus."

Quotes

"Incorporating domain constraints enables the model to exploit the symmetries present in the dataset and generalize to unseen symmetric regions while requiring only a small amount of samples from the domain set of the constraint."
"The model's performance remains relatively stable even with up to 40% noise in the constraints, suggesting that the framework is robust as data can compensate for some level of noise in the knowledge."

Key Insights Distilled From

A Unified Framework for Human-Allied Learning of Probabilistic Circuits

by Athresh Kara... at arxiv.org 05-07-2024

https://arxiv.org/pdf/2405.02413.pdf

Deeper Inquiries

How can the proposed framework be extended to also learn the structure of Probabilistic Circuits in a Bayesian manner, rather than just the parameters?

The extension of the proposed framework to learn the structure of Probabilistic Circuits in a Bayesian manner involves incorporating Bayesian principles into the learning process. This can be achieved by introducing prior distributions over the structure of the Probabilistic Circuits and updating these priors based on the data and domain knowledge constraints.

Bayesian Structural Learning: By treating the structure of the Probabilistic Circuits as a random variable, Bayesian structural learning can be employed to infer the most probable structure given the data and constraints. This involves defining prior distributions over possible structures and updating these priors using Bayesian inference techniques.

Bayesian Model Averaging: Another approach is to consider multiple possible structures for the Probabilistic Circuits and use Bayesian model averaging to combine the predictions from different structures based on their posterior probabilities. This allows for uncertainty in the structure to be accounted for in the final predictions.

Bayesian Optimization: Bayesian optimization techniques can be used to search for the optimal structure of the Probabilistic Circuits by iteratively evaluating different structures based on their performance on the data and constraints. This allows for an efficient search in the space of possible structures.

By incorporating Bayesian methods into the learning of Probabilistic Circuit structures, the framework can provide more principled and uncertainty-aware modeling, leading to improved performance and robustness in real-world applications.

How can the insights gained from this work on incorporating domain knowledge into Probabilistic Circuits be applied to improve the robustness and generalization of other types of deep generative models?

The insights gained from incorporating domain knowledge into Probabilistic Circuits can be applied to improve the robustness and generalization of other types of deep generative models in the following ways:

Constraint Integration: Similar to Probabilistic Circuits, other deep generative models can benefit from integrating domain knowledge as constraints during training. By encoding domain-specific constraints, such as monotonicity, independence, or synergistic relationships, into the learning process, models can better capture the underlying structure of the data and improve generalization.

Knowledge-Intensive Learning: Adopting a knowledge-intensive learning approach, where domain knowledge is leveraged to guide the learning process, can enhance the performance of deep generative models. By incorporating expert insights and constraints, models can learn more effectively from limited data and adapt to specific domain requirements.

Bayesian Framework: Extending the Bayesian framework to other deep generative models can enable the incorporation of uncertainty and prior knowledge into the modeling process. Bayesian methods allow for principled integration of domain knowledge, leading to more robust and generalizable models.

Ablation Studies: Conducting ablation studies to analyze the sensitivity of deep generative models to domain knowledge and constraints can help identify the most impactful forms of knowledge integration. This can guide the development of more robust models that are less sensitive to noisy or redundant advice.

By applying the principles of knowledge-intensive learning, Bayesian modeling, and constraint integration to other deep generative models, researchers can enhance their robustness, generalization capabilities, and applicability to real-world scenarios.