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Oct 31

Uncertainty quantification in a mechanical submodel driven by a Wasserstein-GAN

The analysis of parametric and non-parametric uncertainties of very large dynamical systems requires the construction of a stochastic model of said system. Linear approaches relying on random matrix theory and principal componant analysis can be used when systems undergo low-frequency vibrations. In the case of fast dynamics and wave propagation, we investigate a random generator of boundary conditions for fast submodels by using machine learning. We show that the use of non-linear techniques in machine learning and data-driven methods is highly relevant. Physics-informed neural networks is a possible choice for a data-driven method to replace linear modal analysis. An architecture that support a random component is necessary for the construction of the stochastic model of the physical system for non-parametric uncertainties, since the goal is to learn the underlying probabilistic distribution of uncertainty in the data. Generative Adversarial Networks (GANs) are suited for such applications, where the Wasserstein-GAN with gradient penalty variant offers improved convergence results for our problem. The objective of our approach is to train a GAN on data from a finite element method code (Fenics) so as to extract stochastic boundary conditions for faster finite element predictions on a submodel. The submodel and the training data have both the same geometrical support. It is a zone of interest for uncertainty quantification and relevant to engineering purposes. In the exploitation phase, the framework can be viewed as a randomized and parametrized simulation generator on the submodel, which can be used as a Monte Carlo estimator.

  • 4 authors
·
Oct 26, 2021

Leveraging the Invariant Side of Generative Zero-Shot Learning

Conventional zero-shot learning (ZSL) methods generally learn an embedding, e.g., visual-semantic mapping, to handle the unseen visual samples via an indirect manner. In this paper, we take the advantage of generative adversarial networks (GANs) and propose a novel method, named leveraging invariant side GAN (LisGAN), which can directly generate the unseen features from random noises which are conditioned by the semantic descriptions. Specifically, we train a conditional Wasserstein GANs in which the generator synthesizes fake unseen features from noises and the discriminator distinguishes the fake from real via a minimax game. Considering that one semantic description can correspond to various synthesized visual samples, and the semantic description, figuratively, is the soul of the generated features, we introduce soul samples as the invariant side of generative zero-shot learning in this paper. A soul sample is the meta-representation of one class. It visualizes the most semantically-meaningful aspects of each sample in the same category. We regularize that each generated sample (the varying side of generative ZSL) should be close to at least one soul sample (the invariant side) which has the same class label with it. At the zero-shot recognition stage, we propose to use two classifiers, which are deployed in a cascade way, to achieve a coarse-to-fine result. Experiments on five popular benchmarks verify that our proposed approach can outperform state-of-the-art methods with significant improvements.

  • 6 authors
·
Apr 8, 2019

CTAB-GAN+: Enhancing Tabular Data Synthesis

While data sharing is crucial for knowledge development, privacy concerns and strict regulation (e.g., European General Data Protection Regulation (GDPR)) limit its full effectiveness. Synthetic tabular data emerges as alternative to enable data sharing while fulfilling regulatory and privacy constraints. State-of-the-art tabular data synthesizers draw methodologies from Generative Adversarial Networks (GAN). As GANs improve the synthesized data increasingly resemble the real data risking to leak privacy. Differential privacy (DP) provides theoretical guarantees on privacy loss but degrades data utility. Striking the best trade-off remains yet a challenging research question. We propose CTAB-GAN+ a novel conditional tabular GAN. CTAB-GAN+ improves upon state-of-the-art by (i) adding downstream losses to conditional GANs for higher utility synthetic data in both classification and regression domains; (ii) using Wasserstein loss with gradient penalty for better training convergence; (iii) introducing novel encoders targeting mixed continuous-categorical variables and variables with unbalanced or skewed data; and (iv) training with DP stochastic gradient descent to impose strict privacy guarantees. We extensively evaluate CTAB-GAN+ on data similarity and analysis utility against state-of-the-art tabular GANs. The results show that CTAB-GAN+ synthesizes privacy-preserving data with at least 48.16% higher utility across multiple datasets and learning tasks under different privacy budgets.

  • 4 authors
·
Apr 1, 2022

Wasserstein Dependency Measure for Representation Learning

Mutual information maximization has emerged as a powerful learning objective for unsupervised representation learning obtaining state-of-the-art performance in applications such as object recognition, speech recognition, and reinforcement learning. However, such approaches are fundamentally limited since a tight lower bound of mutual information requires sample size exponential in the mutual information. This limits the applicability of these approaches for prediction tasks with high mutual information, such as in video understanding or reinforcement learning. In these settings, such techniques are prone to overfit, both in theory and in practice, and capture only a few of the relevant factors of variation. This leads to incomplete representations that are not optimal for downstream tasks. In this work, we empirically demonstrate that mutual information-based representation learning approaches do fail to learn complete representations on a number of designed and real-world tasks. To mitigate these problems we introduce the Wasserstein dependency measure, which learns more complete representations by using the Wasserstein distance instead of the KL divergence in the mutual information estimator. We show that a practical approximation to this theoretically motivated solution, constructed using Lipschitz constraint techniques from the GAN literature, achieves substantially improved results on tasks where incomplete representations are a major challenge.

  • 6 authors
·
Mar 27, 2019