Unsupervised Outlier Detection (UOD) is a critical task in data mining and machine learning, aiming to identify instances that significantly deviate from the majority. Without any label, deep UOD methods struggle with the misalignment between the model's direct optimization goal and the final performance goal of Outlier Detection (OD) task. Through the perspective of training dynamics, this paper proposes an early stopping algorithm to optimize the training of deep UOD models, ensuring they perform optimally in OD rather than overfitting the entire contaminated dataset. Inspired by UOD mechanism and inlier priority phenomenon, where intuitively models fit inliers more quickly than outliers, we propose GradStop, a sampling-based label-free algorithm to estimate model's real-time performance during training. First, a sampling method generates two sets: one likely containing more outliers and the other more inliers, then a metric based on gradient cohesion is applied to probe into current training dynamics, which reflects model's performance on OD task. Experimental results on 4 deep UOD algorithms and 47 real-world datasets and theoretical proofs demonstrate the effectiveness of our proposed early stopping algorithm in enhancing the performance of deep UOD models. Auto Encoder (AE) enhanced by GradStop achieves better performance than itself, other SOTA UOD methods, and even ensemble AEs. Our method provides a robust and effective solution to the problem of performance degradation during training, enabling deep UOD models to achieve better potential in anomaly detection tasks.

Artificial intelligence and machine learning frameworks have served as computationally efficient mapping between inputs and outputs for engineering problems. These mappings have enabled optimization and analysis routines that have warranted superior designs, ingenious material systems and optimized manufacturing processes. A common occurrence in such modeling endeavors is the existence of multiple source of data, each differentiated by fidelity, operating conditions, experimental conditions, and more. Data fusion frameworks have opened the possibility of combining such differentiated sources into single unified models, enabling improved accuracy and knowledge transfer. However, these frameworks encounter limitations when the different sources are heterogeneous in nature, i.e., not sharing the same input parameter space. These heterogeneous input scenarios can occur when the domains differentiated by complexity, scale, and fidelity require different parametrizations. Towards addressing this void, a heterogeneous multi-source data fusion framework is proposed based on input mapping calibration (IMC) and latent variable Gaussian process (LVGP). In the first stage, the IMC algorithm is utilized to transform the heterogeneous input parameter spaces into a unified reference parameter space. In the second stage, a multi-source data fusion model enabled by LVGP is leveraged to build a single source-aware surrogate model on the transformed reference space. The proposed framework is demonstrated and analyzed on three engineering case studies (design of cantilever beam, design of ellipsoidal void and modeling properties of Ti6Al4V alloy). The results indicate that the proposed framework provides improved predictive accuracy over a single source model and transformed but source unaware model.

With the advent of artificial intelligence (AI) and machine learning (ML), various domains of science and engineering communites has leveraged data-driven surrogates to model complex systems from numerous sources of information (data). The proliferation has led to significant reduction in cost and time involved in development of superior systems designed to perform specific functionalities. A high proposition of such surrogates are built extensively fusing multiple sources of data, may it be published papers, patents, open repositories, or other resources. However, not much attention has been paid to the differences in quality and comprehensiveness of the known and unknown underlying physical parameters of the information sources that could have downstream implications during system optimization. Towards resolving this issue, a multi-source data fusion framework based on Latent Variable Gaussian Process (LVGP) is proposed. The individual data sources are tagged as a characteristic categorical variable that are mapped into a physically interpretable latent space, allowing the development of source-aware data fusion modeling. Additionally, a dissimilarity metric based on the latent variables of LVGP is introduced to study and understand the differences in the sources of data. The proposed approach is demonstrated on and analyzed through two mathematical (representative parabola problem, 2D Ackley function) and two materials science (design of FeCrAl and SmCoFe alloys) case studies. From the case studies, it is observed that compared to using single-source and source unaware ML models, the proposed multi-source data fusion framework can provide better predictions for sparse-data problems, interpretability regarding the sources, and enhanced modeling capabilities by taking advantage of the correlations and relationships among different sources.

Predicting stock prices presents a challenging research problem due to the inherent volatility and non-linear nature of the stock market. In recent years, knowledge-enhanced stock price prediction methods have shown groundbreaking results by utilizing external knowledge to understand the stock market. Despite the importance of these methods, there is a scarcity of scholarly works that systematically synthesize previous studies from the perspective of external knowledge types. Specifically, the external knowledge can be modeled in different data structures, which we group into non-graph-based formats and graph-based formats: 1) non-graph-based knowledge captures contextual information and multimedia descriptions specifically associated with an individual stock; 2) graph-based knowledge captures interconnected and interdependent information in the stock market. This survey paper aims to provide a systematic and comprehensive description of methods for acquiring external knowledge from various unstructured data sources and then incorporating it into stock price prediction models. We also explore fusion methods for combining external knowledge with historical price features. Moreover, this paper includes a compilation of relevant datasets and delves into potential future research directions in this domain.

Outlier detection (OD) has received continuous research interests due to its wide applications. With the development of deep learning, increasingly deep OD algorithms are proposed. Despite the availability of numerous deep OD models, existing research has reported that the performance of deep models is extremely sensitive to the configuration of hyperparameters (HPs). However, the selection of HPs for deep OD models remains a notoriously difficult task due to the lack of any labels and long list of HPs. In our study. we shed light on an essential factor, training time, that can introduce significant variation in the performance of deep model. Even the performance is stable across other HPs, training time itself can cause a serious HP sensitivity issue. Motivated by this finding, we are dedicated to formulating a strategy to terminate model training at the optimal iteration. Specifically, we propose a novel metric called loss entropy to internally evaluate the model performance during training while an automated training stopping algorithm is devised. To our knowledge, our approach is the first to enable reliable identification of the optimal training iteration during training without requiring any labels. Our experiments on tabular, image datasets show that our approach can be applied to diverse deep models and datasets. It not only enhances the robustness of deep models to their HPs, but also improves the performance and reduces plenty of training time compared to naive training.

Modern computational methods, involving highly sophisticated mathematical formulations, enable several tasks like modeling complex physical phenomenon, predicting key properties and design optimization. The higher fidelity in these computer models makes it computationally intensive to query them hundreds of times for optimization and one usually relies on a simplified model albeit at the cost of losing predictive accuracy and precision. Towards this, data-driven surrogate modeling methods have shown a lot of promise in emulating the behavior of the expensive computer models. However, a major bottleneck in such methods is the inability to deal with high input dimensionality and the need for relatively large datasets. With such problems, the input and output quantity of interest are tensors of high dimensionality. Commonly used surrogate modeling methods for such problems, suffer from requirements like high number of computational evaluations that precludes one from performing other numerical tasks like uncertainty quantification and statistical analysis. In this work, we propose an end-to-end approach that maps a high-dimensional image like input to an output of high dimensionality or its key statistics. Our approach uses two main framework that perform three steps: a) reduce the input and output from a high-dimensional space to a reduced or low-dimensional space, b) model the input-output relationship in the low-dimensional space, and c) enable the incorporation of domain-specific physical constraints as masks. In order to accomplish the task of reducing input dimensionality we leverage principal component analysis, that is coupled with two surrogate modeling methods namely: a) Bayesian hybrid modeling, and b) DeepHyper's deep neural networks. We demonstrate the applicability of the approach on a problem of a linear elastic stress field data.

A large number of studies on Graph Outlier Detection (GOD) have emerged in recent years due to its wide applications, in which Unsupervised Node Outlier Detection (UNOD) on attributed networks is an important area. UNOD focuses on detecting two kinds of typical outliers in graphs: the structural outlier and the contextual outlier. Most existing works conduct experiments based on datasets with injected outliers. However, we find that the most widely-used outlier injection approach has a serious data leakage issue. By only utilizing such data leakage, a simple approach can achieve state-of-the-art performance in detecting outliers. In addition, we observe that existing algorithms have a performance drop with the mitigated data leakage issue. The other major issue is on balanced detection performance between the two types of outliers, which has not been considered by existing studies. In this paper, we analyze the cause of the data leakage issue in depth since the injection approach is a building block to advance UNOD. Moreover, we devise a novel variance-based model to detect structural outliers, which outperforms existing algorithms significantly and is more robust at kinds of injection settings. On top of this, we propose a new framework, Variance based Graph Outlier Detection (VGOD), which combines our variance-based model and attribute reconstruction model to detect outliers in a balanced way. Finally, we conduct extensive experiments to demonstrate the effectiveness and efficiency of VGOD. The results on 5 real-world datasets validate that VGOD achieves not only the best performance in detecting outliers but also a balanced detection performance between structural and contextual outliers.

GPS technology has revolutionized the way we localize and navigate outdoors. However, the poor reception of GPS signals in buildings makes it unsuitable for indoor localization. WiFi fingerprinting-based indoor localization is one of the most promising ways to meet this demand. Unfortunately, most work in the domain fails to resolve challenges associated with deployability on resource-limited embedded devices. In this work, we propose a compression-aware and high-accuracy deep learning framework called CHISEL that outperforms the best-known works in the area while maintaining localization robustness on embedded devices.

Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems dynamics controls the numerical resolution required to effectively resolve the embedded physics. In practice however, high numerical resolutions is only required in a confined region of the system where fast dynamics or localized material variability are exhibited, whereas a coarser discretization can be sufficient in the rest majority of the system. To this end, a unified computational scheme with uniform spatio-temporal resolutions for uncertainty quantification can be very computationally demanding. Partitioning the complex dynamical system into smaller easier-to-solve problems based of the localized dynamics and material variability can reduce the overall computational cost. However, identifying the region of interest for high-resolution and intensive uncertainty quantification can be a problem dependent. The region of interest can be specified based on the localization features of the solution, user interest, and correlation length of the random material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update our prior knowledge on the localized region of interest using measurements and system response. To address the computational cost of the Bayesian inference, we construct a Gaussian process surrogate for the forward model. Once, the localized region of interest is identified, we use polynomial chaos expansion to propagate the localization uncertainty. We demonstrate our framework through numerical experiments on a three-dimensional elastodynamic problem.

We present a Bayesian approach to identify optimal transformations that map model input points to low dimensional latent variables. The "projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to be inferred jointly with the GP parameters, conditioned on the available training data. The proposed Bayesian inference scheme relies on a two-step iterative algorithm that samples from the marginal posteriors of the GP parameters and the projection matrix respectively, both using Markov Chain Monte Carlo (MCMC) sampling. In order to take into account the orthogonality constraints imposed on the orthonormal projection matrix, a Geodesic Monte Carlo sampling algorithm is employed, that is suitable for exploiting probability measures on manifolds. We extend the proposed framework to multi-fidelity models using GPs including the scenarios of training multiple outputs together. We validate our framework on three synthetic problems with a known lower-dimensional subspace. The benefits of our proposed framework, are illustrated on the computationally challenging three-dimensional aerodynamic optimization of a last-stage blade for an industrial gas turbine, where we study the effect of an 85-dimensional airfoil shape parameterization on two output quantities of interest, specifically on the aerodynamic efficiency and the degree of reaction.