Qiuyi Chen

Qiuyi Chen, Cashen Diniz, Mark Fuge

This paper introduces Least Volume (LV)--a simple yet effective regularization method inspired by geometric intuition--that reduces the number of latent dimensions required by an autoencoder without prior knowledge of the dataset's intrinsic dimensionality. We show that its effectiveness depends on the Lipschitz continuity of the decoder, prove that Principal Component Analysis (PCA) is a linear special case, and demonstrate that LV induces a PCA-like importance ordering in nonlinear models. We extend LV to non-Euclidean settings as Generalized Least Volume (GLV), enabling the integration of label information into the latent representation. To support implementation, we also develop an accompanying Dynamic Pruning algorithm. We evaluate LV on several benchmark problems, demonstrating its effectiveness in dimension reduction. Leveraging this, we reveal the role of low-dimensional latent spaces in data sampling and disentangled representation, and use them to probe the varying topological complexity of various datasets. GLV is further applied to labeled datasets, where it induces a contrastive learning effect in representations of discrete labels. On a continuous-label airfoil dataset, it produces representations that lead to smooth changes in aerodynamic performance, thereby stabilizing downstream optimization.

Qiuyi Chen, Panagiotis Tsilifis, Mark Fuge

Solving inverse problems in scientific and engineering fields has long been intriguing and holds great potential for many applications, yet most techniques still struggle to address issues such as high dimensionality, nonlinearity and model uncertainty inherent in these problems. Recently, generative models such as Generative Adversarial Networks (GANs) have shown great potential in approximating complex high dimensional conditional distributions and have paved the way for characterizing posterior densities in Bayesian inverse problems, yet the problems' high dimensionality and high nonlinearity often impedes the model's training. In this paper we show how to tackle these issues with Least Volume--a novel unsupervised nonlinear dimension reduction method--that can learn to represent the given datasets with the minimum number of latent variables while estimating their intrinsic dimensions. Once the low dimensional latent spaces are identified, efficient and accurate training of conditional generative models becomes feasible, resulting in a latent conditional GAN framework for posterior inference. We demonstrate the power of the proposed methodology on a variety of applications including inversion of parameters in systems of ODEs and high dimensional hydraulic conductivities in subsurface flow problems, and reveal the impact of the observables' and unobservables' intrinsic dimensions on inverse problems.

Haiyang Zhang, Qiuyi Chen, Yuanjie Zou et al.

Document set expansion aims to identify relevant documents from a large collection based on a small set of documents that are on a fine-grained topic. Previous work shows that PU learning is a promising method for this task. However, some serious issues remain unresolved, i.e. typical challenges that PU methods suffer such as unknown class prior and imbalanced data, and the need for transductive experimental settings. In this paper, we propose a novel PU learning framework based on density estimation, called puDE, that can handle the above issues. The advantage of puDE is that it neither constrained to the SCAR assumption and nor require any class prior knowledge. We demonstrate the effectiveness of the proposed method using a series of real-world datasets and conclude that our method is a better alternative for the DSE task.