Robust Optimization of Score-Based Generative Models with Noisy Samples and Risk Information

核心概念

The core message of this paper is to introduce a risk-sensitive stochastic differential equation (SDE) that can robustly optimize score-based generative models in the presence of noisy samples paired with risk information.

摘要

The paper introduces the problem of optimizing score-based generative models (SGMs) when the observed training samples are noisy and come with associated risk information. It proposes a new type of SDE called "risk-sensitive SDE" that incorporates the risk information into the SDE coefficients to mitigate the negative impact of noisy samples on the optimization of the score-based model.
The key highlights and insights are:

For Gaussian perturbation, the paper proves that there exists a risk-sensitive SDE that can achieve "perturbation stability", where the marginal distribution of noisy samples matches that of clean samples. This allows the score-based model to be optimized using the noisy samples without bias.

For non-Gaussian perturbations, the paper introduces a measure called "perturbation instability" to quantify the discrepancy between the marginal distributions of noisy and clean samples. It then derives the optimal coefficients of the risk-sensitive SDE that minimize this instability measure.

The paper extends two popular SGM variants (VP-SDE and VE-SDE) to their risk-sensitive versions, providing concrete forms of the risk-sensitive SDEs that can be used in practice.

Numerical experiments confirm the effectiveness of the risk-sensitive SDEs in reducing the negative impact of noisy samples on the optimization of score-based models, especially for heavy-tailed noise distributions like Cauchy.

統計資料

The paper does not provide any specific numerical data or metrics to support the key claims. It focuses on the theoretical analysis and derivation of the risk-sensitive SDE formulations.

引述

"The essence of score-based generative models (SGM) is to optimize a score-based model sθ(x, t) towards the score function ∇x ln p(x). However, we show that noisy samples incur another objective function, rather than the one with score function, which will wrongly optimize the model."
"To address this problem, we first consider a new setting where every noisy sample is paired with a risk vector r, indicating the data quality (e.g., noise level). This setting is very common in real-world applications, especially for medical and sensor data."
"We will prove that zero measure: St(r) = 0, is only achievable in the case where noisy samples are caused by Gaussian perturbation. For non-Gaussian cases, we will also provide its optimal coefficients that minimize the misguidance of noisy samples: St(r)."

從以下內容提煉的關鍵洞見

Risk-Sensitive Diffusion for Perturbation-Robust Optimization

by Yangming Li,... 於 arxiv.org 04-08-2024

https://arxiv.org/pdf/2402.02081.pdf

深入探究

How can the proposed risk-sensitive SDE framework be extended to handle more complex noise distributions beyond Gaussian and Cauchy?

The proposed risk-sensitive SDE framework can be extended to handle more complex noise distributions by introducing a more flexible parameterization of the coefficients in the SDE. Instead of assuming specific forms for the drift and diffusion coefficients as in the Gaussian and Cauchy perturbation cases, the risk-sensitive SDE can be generalized to accommodate a wider range of noise distributions. This extension would involve adapting the risk-sensitive coefficients to capture the characteristics of the specific noise distribution.
One approach to handling more complex noise distributions is to introduce additional parameters or functions in the risk-sensitive SDE that can capture the nuances of the noise distribution. For example, for non-Gaussian noise distributions with heavy tails or skewness, the risk-sensitive coefficients can be adjusted to account for these properties. By incorporating more flexible parameterizations and functions in the risk-sensitive SDE, it can effectively model and mitigate the impact of diverse and complex noise distributions on the optimization process.

What are the potential limitations or drawbacks of the risk-sensitive SDE approach compared to alternative techniques like risk-conditional generative models?

While the risk-sensitive SDE approach offers a novel and effective way to optimize generative models in the presence of noisy samples with risk information, it also has some limitations and drawbacks compared to alternative techniques like risk-conditional generative models.
One potential limitation of the risk-sensitive SDE approach is the complexity of determining the optimal risk-sensitive coefficients for different noise distributions. The process of finding the coefficients that minimize the instability measure and achieve perturbation stability can be computationally intensive and may require extensive tuning and experimentation. In contrast, risk-conditional generative models provide a more straightforward way to incorporate risk information into the modeling process by conditioning the generation on the risk vector directly.
Another drawback of the risk-sensitive SDE approach is its reliance on the assumption of continuous noise distributions. In real-world scenarios, noise distributions may not always be continuous or easily modeled, which can limit the applicability of the risk-sensitive SDE framework. Risk-conditional generative models, on the other hand, offer more flexibility in handling discrete or complex noise distributions by conditioning the generation process on the risk information.

Can the risk-sensitive SDE formulation be adapted to other types of generative models beyond score-based methods, such as variational autoencoders or generative adversarial networks?

Yes, the risk-sensitive SDE formulation can be adapted to other types of generative models beyond score-based methods, such as variational autoencoders (VAEs) or generative adversarial networks (GANs). The key idea behind the risk-sensitive SDE framework, which involves incorporating risk information into the optimization process to mitigate the impact of noisy samples, can be applied to a wide range of generative models.
For VAEs, the risk-sensitive SDE approach can be integrated by modifying the latent space representation to include risk information. By conditioning the generation process on the risk vector, VAEs can learn to generate samples that are robust to noisy inputs and maintain the desired data quality. Similarly, for GANs, the risk-sensitive SDE formulation can be adapted by incorporating risk information in the discriminator and generator networks to improve the stability and quality of generated samples in the presence of noise.
Overall, the risk-sensitive SDE framework can be extended and adapted to various generative models beyond score-based methods, providing a versatile and effective approach to optimizing models in the presence of noisy data.