LEARNING TO REGULARIZE WITH A VARIATIONAL AUTOENCODER FOR HYDROGEOLOGIC INVERSE ANALYSIS

<p><strong>Deep generative models have greatly advanced the field of artificial intelligence by learning the distribution of unlabelled datasets. In this thesis, we aim to develop a novel variational autoencoder (VAE)-based deep generative model that learns meaningful representations for effective unsupervised clustering in the latent space of high-dimensional datasets.</strong></p><p>Existing VAE-based deep clustering algorithms assume a mixture distribution either for the variational posterior over the latent variables or for the prior, to approximate the distribution of unlabelled datasets. The proposed mixtures variational autoencoders (MVAE) model assumes a mixture distribution for both the prior and variational posterior over the latent variables within the VAE framework.</p><p>We apply the variational inference to construct the evidence lower bound (ELBO) of the marginal log-likelihood function for our proposed MVAE model and then derive the analytical form for the clustering assignment estimate, also called the posterior probability estimate. This estimate is associated with each component of the VAE framework and enables the optimization of two distinct ELBO functions based on soft and hard assignment approaches. The training procedure for MVAE involves the joint optimization of both clustering assignment probabilities and model parameters. We evaluate the clustering performance on the latent embeddings of a dataset using both the posterior probability estimate and the Gaussian mixture model (GMM) methods.</p><p>We proposed two variants of the expectation-maximization (EM) algorithm to optimize the parameters for the MVAE model. The MVAE (EM) algorithm provides two distinct, numerically stable solutions for the posterior probability estimate: MVAE(EM-V1), where the estimate is associated with only the prior distribution, and MVAE(EM-V2), where the estimate incorporates both the variational posterior and the prior distribution. Among the proposed models, MVAE(EM-V2) requires less computation time for training. Additionally, this model achieves superior clustering performance on most datasets compared to the baseline models.</p><p>We modified the MVAE(EM-V2) algorithm by including a coefficient (β) with the regularizer term. The trained regularized mixtures VAE model with a small regularization coefficient (β < 1) achieves good unsupervised clustering performance on the test datasets. We further propose a variant of the regularized mixtures VAE model in which the regularization coefficient follows an annealing schedule from β > 1 to β < 1. The scheduled regularized model demonstrates superior clustering accuracy across most benchmark datasets compared to state-of-the-art deep clustering algorithms.</p><p>In this thesis, we point out that assuming a mixture distribution for both the prior and variational posterior components over the latent variables within the VAE framework enhances unsupervised clustering in the latent space. Our proposed models outperform state-of-the-art deep clustering algorithms, including VADE and k-DVAE, as well as the standard VAE model, in cluster analysis of latent representations across most benchmark datasets. Additionally, the proposed models demonstrate reasonable reconstruction performance and generate realistic examples from the latent space.</p>

One of the main challenges that the industry faces when dealing with massive data for failure diagnosis is high dimensionality of such data. This can be tackled by dimensionality reduction method such as principal components analysis, which usually results in an improved fault diagnosis. Other available techniques include auto-encoders and its variants denoising auto-encoders and sparse auto-encoders. Most recently, variational auto-encoders are one of the most promising techniques for unsupervised learning with successful applications in image processing and speech recognition. Differently from other auto-encoder methods, variational auto-encoders use variational inference to generate a latent representation of the data and impose a distribution over the latent variables and the data itself. In this article, we propose a fully unsupervised deep variational auto-encoder-based approach for dimensionality reduction in fault diagnosis and explore the variational auto-encoder capabilities for such a task. This is achieved by comparing the latent representations provided by variational auto-encoders to the ones from principal components analysis as well as when no reduction is performed in ball bearings’ fault classification using vibration signals. To tackle massive sensor data, we propose different architectures for the variational auto-encoder’s encoder and decoder that are based on deep neural networks and deep convolutional neural networks. Experiments are also carried out by varying the data preprocessing methods for generating spectrograms and hand-engineering features as well as the use of raw vibration data, the architecture of the neural networks fault classifiers operating on the latent representations from variational auto-encoder and principal components analysis, the degree of data dimension reduction, and the size of the available labeled data used for training the fault classifiers. The results show that variational auto-encoders are a competent and promising tool for dimensionality reduction for use in fault diagnosis and worth further exploring their capabilities beyond vibration signals of ball bearing elements.

Variational autoencoder: An unsupervised model for encoding and decoding fMRI activity in visual cortex

Purpose:There has been burgeoning interest in applying machine learning methods for predicting radiotherapy outcomes. However, the imbalanced ratio of a large number of variables to a limited sample size in radiation oncology constitutes a major challenge. Therefore, dimensionality reduction methods can be a key to success. The study investigates and contrasts the application of traditional machine learning methods and deep learning approaches for outcome modeling in radiotherapy. In particular, new joint architectures based on variational autoencoder (VAE) for dimensionality reduction are presented and their application is demonstrated for the prediction of lung radiation pneumonitis (RP) from a large-scale heterogeneous dataset.Methods:A large-scale heterogeneous dataset containing a pool of 230 variables including clinical factors (e.g., dose, KPS, stage) and biomarkers (e.g., single nucleotide polymorphisms (SNPs), cytokines and micro-RNAs) in a population of 106 non-small cell lung cancer (NSCLC) patients who received radiotherapy was used for modeling RP. 22 patients had grade 2 or higher RP. Four methods were investigated, including feature selection (case A) and feature extraction (case B) with traditional machine learning methods, a VAE-MLP joint architecture (case C) with deep learning and lastly, the combination of feature selection and joint-architecture (case D). For feature selection, Random forest (RF), Support Vector Machine (SVM) and multi-layer perceptron (MLP) were implemented to select relevant features. Specifically, each method was run for multiple times to rank features within several cross-validated (CV) resampled sets. A collection of ranking lists were then aggregated by top 5% and Kemeny graph methods to identify the final ranking for prediction. A synthetic minority oversampling technique (SMOTE) was applied to correct for class imbalance during this process. For deep learning, a VAE-MLP joint architecture where a VAE aimed for dimensionality reduction and an MLP aimed for classification was developed. In this architecture, reconstruction loss and prediction loss were combined into a single loss function to realize simultaneous training and weights were assigned to different classes to mitigate class imbalance. To evaluate the prediction performance and conduct comparisons, the area under receiver operating characteristic (ROC) curves (AUCs) were performed for nested CVs for both handcrafted feature selections and the deep learning approach. The significance of differences in AUCs was assessed using the DeLong test of U-statistics.Results:An MLP-based method using weight pruning (WP) feature selection yielded the best performance among the different hand-crafted feature selection methods (case A), reaching an AUC of 0.804 (95% CI: 0.761–0.823) with 29 top features. A VAE-MLP joint architecture (case C) achieved a comparable but slightly lower AUC of 0.781 (95% CI: 0.737–0.808) with the size of latent dimension being 2. The combination of handcrafted features (case A) and latent representation (case D) achieved a significant AUC improvement of 0.831 (95% CI: 0.805–0.863) with 22 features (p-value = 0.000642 compared with handcrafted features only (Case A) and p-value=0.000453 compared to VAE alone (Case C)) with an MLP classifier.Conclusion:The potential for combination of traditional machine learning methods and deep learning VAE techniques has been demonstrated for dealing with limited datasets in modeling radiotherapy toxicities. Specifically, latent variables from a VAE-MLP joint architecture are able to complement handcrafted features for the prediction of RP and improve prediction over either method alone.

Latent variables and reconstruction error generated from auto encoder are the common means for anomaly detection dealing with high dimensional signals. They are exclusively typical representations of the original input, and a plenty of methods utilizing them for anomaly detection have achieved good results. In this paper, we propose a new method combining these two features together to generate proper scores for anomaly detection. As both these two features contain useful information contributing to anomaly detection, good results can be expected by fusion of those two. The architecture proposed in this paper comprises of two networks, and we only use normal data for training. To compress and rebuild an input, a deep auto encoder (AE) is utilized where low dimensional latent variables and reconstruction error can be obtained, and compactness loss is introduced on latent variables to maintain a low intra-variance. Meanwhile, multi-layer perceptron (MLP) network which takes the generated latent variables as input is established aiming at predicting its corresponding reconstruction error. By introducing MLP network, anomalies sharing similar reconstruction error yet different distribution of latent variables to normal data or vice versa can be separated. These two networks, AE and MLP are trained jointly in our model and the prediction error form MLP network is used as the final score for anomaly detection. Experiments on several benchmarks including image and multivariable datasets demonstrate the effectiveness and practicability of this new approach when comparing with several up-to-data algorithms.

A multi-scale reconstruction method for the anomaly detection in stochastic dynamic networks

The convergence of free-energy calculations based on importance sampling depends heavily on the choice of collective variables (CVs), which in principle, should include the slow degrees of freedom of the biological processes to be investigated. Autoencoders (AEs), as emerging data-driven dimension reduction tools, have been utilised for discovering CVs. AEs, however, are often treated as black boxes, and what AEs actually encode during training, and whether the latent variables from encoders are suitable as CVs for further free-energy calculations remains unknown. In this contribution, we review AEs and their time-series-based variants, including time-lagged AEs (TAEs) and modified TAEs, as well as the closely related model variational approach for Markov processes networks (VAMPnets). We then show through numerical examples that AEs learn the high-variance modes instead of the slow modes. In stark contrast, time series-based models are able to capture the slow modes. Moreover, both modified TAEs with extensions from slow feature analysis and the state-free reversible VAMPnets (SRVs) can yield orthogonal multidimensional CVs. As an illustration, we employ SRVs to discover the CVs of the isomerizations of N-acetyl-N′-methylalanylamide and trialanine by iterative learning with trajectories from biased simulations. Last, through numerical experiments with anisotropic diffusion, we investigate the potential relationship of time-series-based models and committor probabilities.

VAE (Variational Autoencoder) and CVAE (Conditional V AE) encode the sentence with the latent variable to generate response in Dialogue. However, studies have shown that the latent variables obtained are more inclined to remember the first words and the length of the sentence, and only represents limited local features. In order to alleviate this problem, we propose to involve contrastive learning to generate positive and negative samples for training process, which enriches the latent variables representation with the global information of sentence and generates more relevant response. On the other hand, those generative models do not consider emotional information of dialogue, a sentiment discrimination module is introduced in our model to maintain the emotional consistency. Experiments on two public datasets - DailyDialog and PERSONA-CHAT demonstrate the effectiveness of our method, the evaluation results of BLEU and Rouge are both improved. The sentiment discrimination network also forces the model to generating emotional consistency response with share embedding.

This research attempts to construct a network that can convert online and offline handwritten characters to each other. The proposed network consists of two Variational Auto-Encoders (VAEs) with a shared latent space. The VAEs are trained to generate online and offline handwritten Latin characters simultaneously. In this way, we create a cross-modal VAE (Cross-VAE). During training, the proposed Cross-VAE is trained to minimize the reconstruction loss of the two modalities, the distribution loss of the two VAEs, and a novel third loss called the space sharing loss. This third, space sharing loss is used to encourage the modalities to share the same latent space by calculating the distance between the latent variables. Through the proposed method mutual conversion of online and offline handwritten characters is possible. In this paper, we demonstrate the performance of the Cross-VAE through qualitative and quantitative analysis.

The recently developed variational autoencoders (VAEs) have proved to be an effective confluence of the rich representational power of neural networks with Bayesian methods. However, most work on VAEs use a rather simple prior over the latent variables such as standard normal distribution, thereby restricting its applications to relatively simple phenomena. In this work, we propose hierarchical non-parametric variational autoencoders, which combines tree-structured Bayesian nonparametric priors with VAEs, to enable infinite flexibility of the latent representation space. Both the neural parameters and Bayesian priors are learned jointly using tailored variational inference. The resulting model induces a hierarchical structure of latent semantic concepts underlying the data corpus, and infers accurate representations of data instances. We apply our model in video representation learning. Our method is able to discover highly interpretable activity hierarchies, and obtain improved clustering accuracy and generalization capacity based on the learned rich representations.

Variational Autoencoder (VAE) is widely used as a generative model to approximate a model's posterior on latent variables by combining the amortized variational inference and deep neural networks. However, when paired with strong autoregressive decoders, VAE often converges to a degenerated local optimum known as "posterior collapse". Previous approaches consider the Kullback–Leibler divergence (KL) individual for each datapoint. We propose to let the KL follow a distribution across the whole dataset, and analyze that it is sufficient to prevent posterior collapse by keeping the expectation of the KL's distribution positive. Then we propose Batch Normalized-VAE (BN-VAE), a simple but effective approach to set a lower bound of the expectation by regularizing the distribution of the approximate posterior's parameters. Without introducing any new model component or modifying the objective, our approach can avoid the posterior collapse effectively and efficiently. We further show that the proposed BN-VAE can be extended to conditional VAE (CVAE). Empirically, our approach surpasses strong autoregressive baselines on language modeling, text classification and dialogue generation, and rivals more complex approaches while keeping almost the same training time as VAE.

Addressing posterior collapse by splitting decoders in variational recurrent autoencoders

Purpose This study aims to propose a systematic reinforcement strategy in large, thin-walled panels with an image-based optimization framework that maximizes stiffness gains while minimizing added mass. By leveraging image-based inputs and generative modeling techniques, specifically variational autoencoders (VAEs), the approach enables efficient exploration and optimization of high-dimensional design spaces. The goal is to identify the optimal placement and configuration of local directed energy deposition (DED) reinforcements, fulfilling industrial demands for lightweight, yet rigid, structures through an automated design pipeline. Design/methodology/approach A path-optimization framework integrating a VAE with pretrained convolutional neural networks (CNNs) was developed to enhance thin-walled structure stiffness in large-sized parts. Latent variables of VAEs serve as continuous design parameters; the decoder generates candidate reinforcement-path images; and CNNs evaluate to compute stiffness and mass objectives. An optimization loop adjusts the latent codes to minimize mass under stiffness constraints, enabling nonparametric discovery of optimal local reinforcement geometries. Findings The VAE-based method achieved a 43.48% increase in panel stiffness with only a 2.81% increase in mass. Beyond straight-line reinforcements, the VAE generated curved paths, internal voids, and mid-panel start/end points, novel geometries not present in the training data, superior material utilization and structural performance. These results demonstrate that VAEs are highly effective at modeling complex design spaces and hold strong potential for generative design applications. Originality/value This work pioneers combining generative deep learning with an additive manufacturing process freedom to optimize structural reinforcements. Unlike traditional parametric or rule-based methods, the VAE uncovers creative reinforcement designs tailored to complex constraints, leveraging DED’s local deposition capabilities. Additionally, representing the design space through the continuous latent dimensions offered by VAEs enables the exploration of a significantly larger and more diverse design space compared to previous studies. The result is a flexible, efficient design tool for automotive, aerospace and defense applications seeking innovative, lightweight, high-performance, thin-walled components.

Key performance indicator (KPI) anomaly detection is the underlying core technology in Artificial Intelligence for IT operations (AIOps). It has an important impact on subsequent anomaly location and root cause analysis. Variational auto-encoder (VAE) is a symmetry network structure composed of encoder and decoder, which has attracted extensive attention because of its ability to capture complex KPI data features and better detection results. However, VAE is not well applied to the modeling of KPI time series data and it is often necessary to set the threshold to obtain more accurate results. In response to these problems, this paper proposes a novel hybrid method for KPI anomaly detection based on VAE and support vector data description (SVDD). This method consists of two modules: a VAE reconstructor and SVDD anomaly detector. In the VAE reconstruction module, firstly, bi-directional long short-term memory (BiLSTM) is used to replace the traditional feedforward neural network in VAE to capture the time correlation of sequences; then, batch normalization is used at the output of the encoder to prevent the disappearance of KL (Kullback–Leibler) divergence, which prevents ignoring latent variables to reconstruct data directly. Finally, exponentially weighted moving average (EWMA) is used to smooth the reconstruction error, which reduces false positives and false negatives during the detection process. In the SVDD anomaly detection module, smoothed reconstruction errors are introduced into the SVDD for training to determine the threshold of adaptively anomaly detection. Experimental results on the public dataset show that this method has a better detection effect than baseline methods.

<abstract><p>In this paper, an inverse problem of determining the space-dependent volatility from the observed market prices of options with different strikes is studied. Being different from other inverse volatility problem with classical parabolic equations, we apply the linearization method and introduce some variable substitutions to convert the original problem into an inverse source problem in a degenerate parabolic equation in a bounded area, from which an unknown volatility can be recovered and deficiencies caused by artificial truncation can be solved. Based on the optimal control framework, the problem is transformed into an optimization problem and the existence of the minimizer is established. After the necessary conditions are deduced, the uniqueness and stability of the minimizer are proved. Then, the Landweber iterative method is used to obtain a stable numerical solution of the inverse problem and some numerical experiments are also performed. The numerical results show that the algorithm which we proposed is robust and the unknown coefficient is recovered quite well.</p></abstract>