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A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems

arXiv.org Machine Learning

Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional $\mathcal{O}(10^{\ge 2})$ stochastic inputs (e.g., forcing terms, boundary conditions, initial conditions) poses tremendous challenges. The curse of dimensionality can be addressed with suitable unsupervised learning techniques used as a pre-processing tool to encode inputs onto lower-dimensional subspaces while retaining its structural information and meaningful properties. In this work, we review and investigate thirteen dimension reduction methods including linear and nonlinear, spectral, blind source separation, convex and non-convex methods and utilize the resulting embeddings to construct a mapping to quantities of interest via polynomial chaos expansions (PCE). We refer to the general proposed approach as manifold PCE (m-PCE), where manifold corresponds to the latent space resulting from any of the studied dimension reduction methods. To investigate the capabilities and limitations of these methods we conduct numerical tests for three physics-based systems (treated as black-boxes) having high-dimensional stochastic inputs of varying complexity modeled as both Gaussian and non-Gaussian random fields to investigate the effect of the intrinsic dimensionality of input data. We demonstrate both the advantages and limitations of the unsupervised learning methods and we conclude that a suitable m-PCE model provides a cost-effective approach compared to alternative algorithms proposed in the literature, including recently proposed expensive deep neural network-based surrogates and can be readily applied for high-dimensional UQ in stochastic PDEs.


A review of Generative Adversarial Networks (GANs) and its applications in a wide variety of disciplines -- From Medical to Remote Sensing

arXiv.org Artificial Intelligence

We look into Generative Adversarial Network (GAN), its prevalent variants and applications in a number of sectors. GANs combine two neural networks that compete against one another using zero-sum game theory, allowing them to create much crisper and discrete outputs. GANs can be used to perform image processing, video generation and prediction, among other computer vision applications. GANs can also be utilised for a variety of science-related activities, including protein engineering, astronomical data processing, remote sensing image dehazing, and crystal structure synthesis. Other notable fields where GANs have made gains include finance, marketing, fashion design, sports, and music. Therefore in this article we provide a comprehensive overview of the applications of GANs in a wide variety of disciplines. We first cover the theory supporting GAN, GAN variants, and the metrics to evaluate GANs. Then we present how GAN and its variants can be applied in twelve domains, ranging from STEM fields, such as astronomy and biology, to business fields, such as marketing and finance, and to arts, such as music. As a result, researchers from other fields may grasp how GANs work and apply them to their own study. To the best of our knowledge, this article provides the most comprehensive survey of GAN's applications in different fields.


Lexico-semantic and affective modelling of Spanish poetry: A semi-supervised learning approach

arXiv.org Artificial Intelligence

Text classification tasks have improved substantially during the last years by the usage of transformers. However, the majority of researches focus on prose texts, with poetry receiving less attention, specially for Spanish language. In this paper, we propose a semi-supervised learning approach for inferring 21 psychological categories evoked by a corpus of 4572 sonnets, along with 10 affective and lexico-semantic multiclass ones. The subset of poems used for training an evaluation includes 270 sonnets. With our approach, we achieve an AUC beyond 0.7 for 76% of the psychological categories, and an AUC over 0.65 for 60% on the multiclass ones. The sonnets are modelled using transformers, through sentence embeddings, along with lexico-semantic and affective features, obtained by using external lexicons. Consequently, we see that this approach provides an AUC increase of up to 0.12, as opposed to using transformers alone.


A Low Rank Promoting Prior for Unsupervised Contrastive Learning

arXiv.org Artificial Intelligence

Unsupervised learning is just at a tipping point where it could really take off. Among these approaches, contrastive learning has seen tremendous progress and led to state-of-the-art performance. In this paper, we construct a novel probabilistic graphical model that effectively incorporates the low rank promoting prior into the framework of contrastive learning, referred to as LORAC. In contrast to the existing conventional self-supervised approaches that only considers independent learning, our hypothesis explicitly requires that all the samples belonging to the same instance class lie on the same subspace with small dimension. This heuristic poses particular joint learning constraints to reduce the degree of freedom of the problem during the search of the optimal network parameterization. Most importantly, we argue that the low rank prior employed here is not unique, and many different priors can be invoked in a similar probabilistic way, corresponding to different hypotheses about underlying truth behind the contrastive features. Empirical evidences show that the proposed algorithm clearly surpasses the state-of-the-art approaches on multiple benchmarks, including image classification, object detection, instance segmentation and keypoint detection.


Semi-Supervised Learning of Visual Features by Non-Parametrically Predicting View Assignments with Support Samples

arXiv.org Artificial Intelligence

This paper proposes a novel method of learning by predicting view assignments with support samples (PAWS). The method trains a model to minimize a consistency loss, which ensures that different views of the same unlabeled instance are assigned similar pseudo-labels. The pseudo-labels are generated non-parametrically, by comparing the representations of the image views to those of a set of randomly sampled labeled images. The distance between the view representations and labeled representations is used to provide a weighting over class labels, which we interpret as a soft pseudo-label. By non-parametrically incorporating labeled samples in this way, PAWS extends the distance-metric loss used in self-supervised methods such as BYOL and SwAV to the semi-supervised setting. Despite the simplicity of the approach, PAWS outperforms other semi-supervised methods across architectures, setting a new state-of-the-art for a ResNet-50 on ImageNet trained with either 10% or 1% of the labels, reaching 75.5% and 66.5% top-1 respectively. PAWS requires 4x to 12x less training than the previous best methods.


Relieving the Plateau: Active Semi-Supervised Learning for a Better Landscape

arXiv.org Artificial Intelligence

Deep learning (DL) relies on massive amounts of labeled data, and improving its labeled sample-efficiency remains one of the most important problems since its advent. Semi-supervised learning (SSL) leverages unlabeled data that are more accessible than their labeled counterparts. Active learning (AL) selects unlabeled instances to be annotated by a human-in-the-loop in hopes of better performance with less labeled data. Given the accessible pool of unlabeled data in pool-based AL, it seems natural to use SSL when training and AL to update the labeled set; however, algorithms designed for their combination remain limited. In this work, we first prove that convergence of gradient descent on sufficiently wide ReLU networks can be expressed in terms of their Gram matrix' eigen-spectrum. Equipped with a few theoretical insights, we propose convergence rate control (CRC), an AL algorithm that selects unlabeled data to improve the problem conditioning upon inclusion to the labeled set, by formulating an acquisition step in terms of improving training dynamics. Extensive experiments show that SSL algorithms coupled with CRC can achieve high performance using very few labeled data.


Exploring Semi-Supervised Learning for Predicting Listener Backchannels

arXiv.org Artificial Intelligence

Developing human-like conversational agents is a prime area in HCI research and subsumes many tasks. Predicting listener backchannels is one such actively-researched task. While many studies have used different approaches for backchannel prediction, they all have depended on manual annotations for a large dataset. This is a bottleneck impacting the scalability of development. To this end, we propose using semi-supervised techniques to automate the process of identifying backchannels, thereby easing the annotation process. To analyze our identification module's feasibility, we compared the backchannel prediction models trained on (a) manually-annotated and (b) semi-supervised labels. Quantitative analysis revealed that the proposed semi-supervised approach could attain 95% of the former's performance. Our user-study findings revealed that almost 60% of the participants found the backchannel responses predicted by the proposed model more natural. Finally, we also analyzed the impact of personality on the type of backchannel signals and validated our findings in the user-study.


Unsupervised learning of disentangled representations in deep restricted kernel machines with orthogonality constraints

arXiv.org Machine Learning

We introduce Constr-DRKM, a deep kernel method for the unsupervised learning of disentangled data representations. We propose augmenting the original deep restricted kernel machine formulation for kernel PCA by orthogonality constraints on the latent variables to promote disentanglement and to make it possible to carry out optimization without first defining a stabilized objective. After illustrating an end-to-end training procedure based on a quadratic penalty optimization algorithm with warm start, we quantitatively evaluate the proposed method's effectiveness in disentangled feature learning. We demonstrate on four benchmark datasets that this approach performs similarly overall to $\beta$-VAE on a number of disentanglement metrics when few training points are available, while being less sensitive to randomness and hyperparameter selection than $\beta$-VAE. We also present a deterministic initialization of Constr-DRKM's training algorithm that significantly improves the reproducibility of the results. Finally, we empirically evaluate and discuss the role of the number of layers in the proposed methodology, examining the influence of each principal component in every layer and showing that components in lower layers act as local feature detectors capturing the broad trends of the data distribution, while components in deeper layers use the representation learned by previous layers and more accurately reproduce higher-level features.


Self-Supervised Relational Reasoning for Representation Learning

arXiv.org Machine Learning

In self-supervised learning, a system is tasked with achieving a surrogate objective by defining alternative targets on a set of unlabeled data. The aim is to build useful representations that can be used in downstream tasks, without costly manual annotation. In this work, we propose a novel self-supervised formulation of relational reasoning that allows a learner to bootstrap a signal from information implicit in unlabeled data. Training a relation head to discriminate how entities relate to themselves (intra-reasoning) and other entities (inter-reasoning), results in rich and descriptive representations in the underlying neural network backbone, which can be used in downstream tasks such as classification and image retrieval. We evaluate the proposed method following a rigorous experimental procedure, using standard datasets, protocols, and backbones. Self-supervised relational reasoning outperforms the best competitor in all conditions by an average 14% in accuracy, and the most recent state-of-the-art model by 3%. We link the effectiveness of the method to the maximization of a Bernoulli log-likelihood, which can be considered as a proxy for maximizing the mutual information, resulting in a more efficient objective with respect to the commonly used contrastive losses.


Auxiliary Task Reweighting for Minimum-data Learning

arXiv.org Machine Learning

Supervised learning requires a large amount of training data, limiting its application where labeled data is scarce. To compensate for data scarcity, one possible method is to utilize auxiliary tasks to provide additional supervision for the main task. Assigning and optimizing the importance weights for different auxiliary tasks remains an crucial and largely understudied research question. In this work, we propose a method to automatically reweight auxiliary tasks in order to reduce the data requirement on the main task. Specifically, we formulate the weighted likelihood function of auxiliary tasks as a surrogate prior for the main task. By adjusting the auxiliary task weights to minimize the divergence between the surrogate prior and the true prior of the main task, we obtain a more accurate prior estimation, achieving the goal of minimizing the required amount of training data for the main task and avoiding a costly grid search. In multiple experimental settings (e.g. semi-supervised learning, multi-label classification), we demonstrate that our algorithm can effectively utilize limited labeled data of the main task with the benefit of auxiliary tasks compared with previous task reweighting methods. We also show that under extreme cases with only a few extra examples (e.g. few-shot domain adaptation), our algorithm results in significant improvement over the baseline.