Slack More, Predict Better: Proximal Relaxation for Probabilistic Latent Variable Model-based Soft Sensors
arXiv:2603.11473v1 Announce Type: new Abstract: Nonlinear Probabilistic Latent Variable Models (NPLVMs) are a cornerstone of soft sensor modeling due to their capacity for uncertainty delineation. However, conventional NPLVMs are trained using amortized variational inference, where neural networks parameterize the variational posterior. While facilitating model implementation, this parameterization converts the distributional optimization problem within an infinite-dimensional function space to parameter optimization within a finite-dimensional parameter space, which introduces an approximation error gap, thereby degrading soft sensor modeling accuracy. To alleviate this issue, we introduce KProxNPLVM, a novel NPLVM that pivots to relaxing the objective itself and improving the NPLVM's performance. Specifically, we first prove the approximation error induced by the conventional approach. Based on this, we design the Wasserstein distance as the proximal operator to relax the learning o
arXiv:2603.11473v1 Announce Type: new Abstract: Nonlinear Probabilistic Latent Variable Models (NPLVMs) are a cornerstone of soft sensor modeling due to their capacity for uncertainty delineation. However, conventional NPLVMs are trained using amortized variational inference, where neural networks parameterize the variational posterior. While facilitating model implementation, this parameterization converts the distributional optimization problem within an infinite-dimensional function space to parameter optimization within a finite-dimensional parameter space, which introduces an approximation error gap, thereby degrading soft sensor modeling accuracy. To alleviate this issue, we introduce KProxNPLVM, a novel NPLVM that pivots to relaxing the objective itself and improving the NPLVM's performance. Specifically, we first prove the approximation error induced by the conventional approach. Based on this, we design the Wasserstein distance as the proximal operator to relax the learning objective, yielding a new variational inference strategy derived from solving this relaxed optimization problem. Based on this foundation, we provide a rigorous derivation of KProxNPLVM's optimization implementation, prove the convergence of our algorithm can finally sidestep the approximation error, and propose the KProxNPLVM by summarizing the abovementioned content. Finally, extensive experiments on synthetic and real-world industrial datasets are conducted to demonstrate the efficacy of the proposed KProxNPLVM.
Executive Summary
This article introduces KProxNPLVM, a novel Probabilistic Latent Variable Model (PLVM) designed to improve the accuracy of soft sensor modeling in the presence of approximation errors. The authors identify the root cause of these errors in conventional PLVMs and propose a new variational inference strategy that relaxes the learning objective using the Wasserstein distance as a proximal operator. Through rigorous mathematical derivation and extensive experimentation, the authors demonstrate the efficacy of KProxNPLVM on both synthetic and real-world industrial datasets. The proposed approach has significant implications for the development of more accurate and reliable soft sensors in various fields, including process control and monitoring.
Key Points
- ▸ Introduction of KProxNPLVM, a novel PLVM designed to alleviate approximation errors in soft sensor modeling
- ▸ Relaxation of the learning objective using the Wasserstein distance as a proximal operator
- ▸ Rigorous mathematical derivation of KProxNPLVM's optimization implementation and convergence proof
Merits
Methodological Innovation
The authors propose a novel and innovative approach to addressing the approximation errors in conventional PLVMs, which is a significant methodological contribution to the field of soft sensor modeling.
Theoretical Foundation
The authors provide a rigorous mathematical derivation of KProxNPLVM's optimization implementation, which provides a solid theoretical foundation for the proposed approach.
Experimental Validation
The authors conduct extensive experimentation on both synthetic and real-world industrial datasets, which provides strong evidence for the efficacy of KProxNPLVM.
Demerits
Limited Generalizability
The authors focus primarily on the industrial control and monitoring applications, which may limit the generalizability of the proposed approach to other domains.
Computational Complexity
The proposed approach involves the computation of the Wasserstein distance, which may be computationally intensive and require significant computational resources.
Expert Commentary
This article makes a significant contribution to the field of soft sensor modeling by proposing a novel and innovative approach to addressing the approximation errors in conventional PLVMs. The authors' rigorous mathematical derivation and extensive experimentation provide strong evidence for the efficacy of KProxNPLVM. However, the limited generalizability of the proposed approach and computational complexity of the Wasserstein distance computation are notable limitations. Nevertheless, the authors' work has significant implications for process control and monitoring, and their proposed approach may lead to more accurate and reliable soft sensors.
Recommendations
- ✓ Future research should focus on extending the proposed approach to other domains and applications to improve its generalizability.
- ✓ Investigating more efficient algorithms for computing the Wasserstein distance may be necessary to reduce the computational complexity of the proposed approach.