Efficient Uncertainty Quantification and Reduction for Over-Parameterized Neural Networks

Uncertainty quantification (UQ) is important for reliability assessment and enhancement of machine learning models. In deep learning, uncertainties arise not only from data, but also from the training procedure that often injects substantial noises and biases. These hinder the attainment of statistical guarantees and, moreover, impose computational challenges on UQ due to the need for repeated network retraining. Building upon the recent neural tangent kernel theory, we create statistically guaranteed schemes to principally \emph{quantify}, and \emph{remove}, the procedural uncertainty of over-parameterized neural networks with very low computation effort. In particular, our approach, based on what we call a procedural-noise-correcting (PNC) predictor, removes the procedural uncertainty by using only \emph{one} auxiliary network that is trained on a suitably labeled data set, instead of many retrained networks employed in deep ensembles. Moreover, by combining our PNC predictor with suitable light-computation resampling methods, we build several approaches to construct asymptotically exact-coverage confidence intervals using as low as four trained networks without additional overheads

Multi-variate time-series for time constraint adherence prediction in complex job shops

One of the most complex and agile production environments is semiconductor manufacturing, especially wafer fabrication, as products require more than several hundred operations and remain in Work-In-Progress for months leading to complex job shops. Additionally, an increasingly competitive market environment, i.e. owing to Moore’s law, forces semiconductor companies to focus on operational excellence, resiliency and, hence, leads to product quality as a decisive factor. Product-specific time constraints comprising two or more, not necessarily consecutive, operations ensure product quality at an operational level and, thus, are an industry-specific challenge. Time constraint adherence is of utmost importance, since violations typically lead to scrapping entire lots and a deteriorating yield. Dispatching decisions that determine time constraint adherence are as a state of the art performed manually, which is stressful and error-prone. Therefore, this article presents a data-driven approach combining multi-variate time-series with centralized information to predict time constraint adherence probability in wafer fabrication to facilitate dispatching. Real-world data is analyzed and different statistical and machine learning models are evaluated

Neural networks for geospatial data

Analysis of geospatial data has traditionally been model-based, with a mean model, customarily specified as a linear regression on the covariates, and a covariance model, encoding the spatial dependence. We relax the strong assumption of linearity and propose embedding neural networks directly within the traditional geostatistical models to accommodate non-linear mean functions while retaining all other advantages including use of Gaussian Processes to explicitly model the spatial covariance, enabling inference on the covariate effect through the mean and on the spatial dependence through the covariance, and offering predictions at new locations via kriging. We propose NN-GLS, a new neural network estimation algorithm for the non-linear mean in GP models that explicitly accounts for the spatial covariance through generalized least squares (GLS), the same loss used in the linear case. We show that NN-GLS admits a representation as a special type of graph neural network (GNN). This connection facilitates use of standard neural network computational techniques for irregular geospatial data, enabling novel and scalable mini-batching, backpropagation, and kriging schemes. Theoretically, we show that NN-GLS will be consistent for irregularly observed spatially correlated data processes. To our knowledge this is the first asymptotic consistency result for any neural network algorithm for spatial data. We demonstrate the methodology through simulated and real datasets

Computation of risk measures in finance and parallel real-time scheduling

Many application areas employ various risk measures, such as a quantile, to assess risks. For example, in finance, risk managers employ a quantile to help determine appropriate levels of capital needed to be able to absorb (with high probability) large unexpected losses in credit portfolios comprising loans, bonds, and other financial instruments subject to default. This dissertation discusses the computation of risk measures in finance and parallel real-time scheduling. Firstly, two estimation approaches are compared for one risk measure, a quantile, via randomized quasi-Monte Carlo (RQMC) in an asymptotic setting where the number of randomizations for RQMC grows large, but the size of the low-discrepancy point set remains fixed. In the first method, for each randomization, it computes an estimator of the cumulative distribution function (CDF), which is inverted to obtain a quantile estimator, and the overall quantile estimator is the sample average of the quantile estimators across randomizations. The second approach instead computes a single quantile estimator by inverting one CDF estimator across all randomizations. Because quantile estimators are generally biased, the first method leads to an estimator that does not converge to the true quantile as the number of randomizations goes to infinity. In contrast, the second estimator does, and a central limit theorem is established for it. To get an improvement, we use conditional Monte Carlo (CMC) to obtain a smoother estimate of the distribution function, and we combine this with the second RQMC to further reduce the variance. The result is a much more accurate quantile estimator, whose mean square error can converge even faster than the canonical rate of O(1/n). Secondly, another risk measure is estimated, namely economic capital (EC), which is defined as the difference between a quantile and the mean of the loss distribution, given a stochastic model for a portfolio’s loss over a given time horizon. This work applies measure-specific importance sampling to separately estimate the two components of the EC, which can lead to a much smaller variance than when estimating both terms simultaneously. Finally, for parallel real-time tasks, the federated scheduling paradigm, which assigns each parallel task a set of dedicated cores, achieves good theoretical bounds by ensuring exclusive use of processing resources to reduce interferences. However, because cores share the last-level cache and memory bandwidth resources, in practice tasks may still interfere with each other despite executing on dedicated cores. To tackle this issue, this work presents a holistic resource allocation framework for parallel real-time tasks under federated scheduling. Under the proposed framework, in addition to dedicated cores, each parallel task is also assigned with dedicated cache and memory bandwidth resources. This work also shows the study of the characteristics of parallel tasks upon different resource allocations following a measurement-based approach and proposes a technique to handle the challenge of tremendous profiling for all resource allocation combinations under this approach. Further, it proposes a holistic resource allocation algorithm that well balances the allocation between different resources to achieve good schedulability. Additionally, this work provides a full implementation of the framework by extending the federated scheduling system with Intel’s Cache Allocation Technology and MemGuard. It also demonstrates the practicality of the proposed framework via extensive numerical evaluations and empirical experiments using real benchmark programs. In the end, the discussion about the application of risk measures for real-time scheduling is given for future work

HRMobile: A lightweight, local architecture for heart rate measurement

Heart rate and heart rate variability (HRV) are important metrics in the study of numerous physical and psychiatric conditions. Previously, measurement of heart rate was relegated to clinical settings, and was neither convenient nor captured a patient’s typical resting state. In effect, this made gathering heart rate data costly and introduced noise. The current prevalence of mobile phone technology and Internet access has increased the viability of remote health monitoring, thus presenting an opportunity to substantially improve the speed, convenience, and reliability of heart rate readings. Recent attention has focused on different methods for remote, non-contact heart rate measurement. Of these methods, video presents perhaps the best option for optimizing cost and convenience. This thesis introduces a lightweight architecture for estimating heart rate and HRV using a smartphone camera. The system presented here runs locally on a smartphone, requiring only a phone camera and 15s or more of continuous video of a subject’s face. No Internet connection or networking is necessary. Building the system to run locally in this manner means that this software confers benefits such as greater user privacy, offline availability, reliability, cost effectiveness, and speed. However, it also introduces added constraints on computational complexity. With these tradeoffs in mind, the system presented here is implemented within an Android mobile app. The performance of our approach fell short of that of existing state-of-the-art methods in terms of mean absolute error (MAE) of heart rate estimation, achieving MAE during validation that was over $17x$ greater than other existing approaches. There are a number of factors which may contribute to this performance discrepancy, including limitations in the diversity of the data used with respect to gender, age, skin tone, and heart rate intensity. Further, remote photoplethysmographic (rPPG) signal generated by this architecture contains a large number of noise artifacts which are difficult to consistently remove through signal processing. This noise is the primary reason for the underperformance of this architecture, and could potentially be explained by model and feature engineering decisions which were made to address the risk of overfitting on the limited dataset used in this work

Optimization of storage and picking systems in warehouses

La croissance du commerce électronique exige une hausse des performances des systèmes d'entreposage, qui sont maintenant repensés pour faire face à un volume massif de demandes à être satisfait le plus rapidement possible. Le système manuel et le système à robots mobile (SRM) sont parmi les plus utilisés pour ces activités. Le premier est un système centré sur l'humain pour réaliser des opérations complexes que les robots actuels ne peuvent pas effectuer. Cependant, les nouvelles générations de robots autonomes mènent à un remplacement progressif par le dernier pour augmenter la productivité. Quel que soit le système utilisé, plusieurs problèmes interdépendants doivent être résolus pour avoir des processus de stockage et de prélèvement efficaces. Les problèmes de stockage concernent les décisions d'où stocker les produits dans l'entrepôt. Les problèmes de prélèvement incluent le regroupement des commandes à exécuter ensemble et les itinéraires que les cueilleurs et les robots doivent suivre pour récupérer les produits demandés. Dans le système manuel, ces problèmes sont traditionnellement résolus à l'aide de politiques simples que les préparateurs peuvent facilement suivre. Malgré l'utilisation de robots, la même stratégie de solution est répliquée aux problèmes équivalents trouvés dans le SRM. Dans cette recherche, nous étudions les problèmes de stockage et de prélèvement rencontrés lors de la conception du système manuel et du SRM. Nous développons des outils d'optimisation pour aider à la prise de décision pour mettre en place leurs processus, en améliorant les mesures de performance typiques de ces systèmes. Certains problèmes traditionnels sont résolus avec des techniques améliorées, tandis que d'autres sont intégrés pour être résolus ensemble au lieu d'optimiser chaque sous-système de manière indépendante. Nous considérons d'abord un système manuel avec un ensemble connu de commandes et intégrons les décisions de stockage et de routage. Le problème intégré et certaines variantes tenant compte des politiques de routage communes sont modélisés mathématiquement. Une métaheuristique générale de recherche de voisinage variable est présentée pour traiter des instances de taille réelle. Des expériences attestent de l'efficience de la métaheuristique proposée par rapport aux modèles exacts et aux politiques de stockage communes. Lorsque les demandes futures sont incertaines, il est courant d'utiliser une stratégie de zonage qui divise la zone de stockage en zones et attribue les produits les plus demandés aux meilleures zones. Les tailles des zones sont à déterminer. Généralement, des dimensions arbitraires sont choisies, mais elles ignorent les caractéristiques de l'entrepôt et des demandes. Nous abordons le problème de dimensionnement des zones pour déterminer quels facteurs sont pertinents pour choisir de meilleures tailles de zone. Les données générées à partir de simulations exhaustives sont utilisées pour trainer quatre modèles de régression d'apprentissage automatique - moindres carrés ordinaire, arbre de régression, forêt aléatoire et perceptron multicouche - afin de prédire les dimensions optimales des zones en fonction de l'ensemble de facteurs pertinents identifiés. Nous montrons que tous les modèles entraînés suggèrent des dimensions sur mesure des zones qui performent meilleur que les dimensions arbitraires couramment utilisées. Une autre approche pour résoudre les problèmes de stockage pour le système manuel et pour le SRM considère les corrélations entre les produits. L'idée est que les produits régulièrement demandés ensemble doivent être stockés près pour réduire les coûts de routage. Cette politique de stockage peut être modélisée comme une variante du problème d'affectation quadratique (PAQ). Le PAQ est un problème combinatoire traditionnel et l'un des plus difficiles à résoudre. Nous examinons les variantes les plus connues du PAQ et développons une puissante métaheuristique itérative de recherche tabou mémétique en parallèle capable de les résoudre. La métaheuristique proposée s'avère être parmi les plus performantes pour le PAQ et surpasse considérablement l'état de l'art pour ses variantes. Les SRM permettent de repositionner facilement les pods d'inventaire pendant les opérations, ce qui peut conduire à un processus de prélèvement plus économe en énergie. Nous intégrons les décisions de repositionnement des pods à l'attribution des commandes et à la sélection des pods à l'aide d'une stratégie de prélèvement par vague. Les pods sont réorganisés en tenant compte du moment et de l'endroit où ils devraient être demandés au futur. Nous résolvons ce problème en utilisant la programmation stochastique en tenant compte de l'incertitude sur les demandes futures et suggérons une matheuristique de recherche locale pour résoudre des instances de taille réelle. Nous montrons que notre schéma d'approximation moyenne de l'échantillon est efficace pour simuler les demandes futures puisque nos méthodes améliorent les solutions trouvées lorsque les vagues sont planifiées sans tenir compte de l'avenir. Cette thèse est structurée comme suit. Après un chapitre d'introduction, nous présentons une revue de la littérature sur le système manuel et le SRM, et les décisions communes prises pour mettre en place leurs processus de stockage et de prélèvement. Les quatre chapitres suivants détaillent les études pour le problème de stockage et de routage intégré, le problème de dimensionnement des zones, le PAQ et le problème de repositionnement de pod. Nos conclusions sont résumées dans le dernier chapitre.The rising of e-commerce is demanding an increase in the performance of warehousing systems, which are being redesigned to deal with a mass volume of demands to be fulfilled as fast as possible. The manual system and the robotic mobile fulfillment system (RMFS) are among the most commonly used for these activities. The former is a human-centered system that handles complex operations that current robots cannot perform. However, newer generations of autonomous robots are leading to a gradual replacement by the latter to increase productivity. Regardless of the system used, several interdependent problems have to be solved to have efficient storage and picking processes. Storage problems concern decisions on where to store products within the warehouse. Picking problems include the batching of orders to be fulfilled together and the routes the pickers and robots should follow to retrieve the products demanded. In the manual system, these problems are traditionally solved using simple policies that pickers can easily follow. Despite using robots, the same solution strategy is being replicated to the equivalent problems found in the RMFS. In this research, we investigate storage and picking problems faced when designing manual and RMFS warehouses. We develop optimization tools to help in the decision-making process to set up their processes and improve typical performance measures considered in these systems. Some classic problems are solved with improved techniques, while others are integrated to be solved together instead of optimizing each subsystem sequentially. We first consider a manual system with a known set of orders and integrate storage and routing decisions. The integrated problem and some variants considering common routing policies are modeled mathematically. A general variable neighborhood search metaheuristic is presented to deal with real-size instances. Computational experiments attest to the effectiveness of the metaheuristic proposed compared to the exact models and common storage policies. When future demands are uncertain, it is common to use a zoning strategy to divide the storage area into zones and assign the most-demanded products to the best zones. Zone sizes are to be determined. Commonly, arbitrary sizes are chosen, which ignore the characteristics of the warehouse and the demands. We approach the zone sizing problem to determine which factors are relevant to choosing better zone sizes. Data generated from exhaustive simulations are used to train four machine learning regression models - ordinary least squares, regression tree, random forest, and multilayer perceptron - to predict the optimal zone sizes given the set of relevant factors identified. We show that all trained models suggest tailor-made zone sizes with better picking performance than the arbitrary ones commonly used. Another approach to solving storage problems, both in the manual and RMFS, considers the correlations between products. The idea is that products constantly demanded together should be stored closer to reduce routing costs. This storage policy can be modeled as a quadratic assignment problem (QAP) variant. The QAP is a traditional combinatorial problem and one of the hardest to solve. We survey the most traditional QAP variants and develop a powerful parallel memetic iterated tabu search metaheuristic capable of solving them. The proposed metaheuristic is shown to be among the best performing ones for the QAP and significantly outperforms the state-of-the-art for its variants. The RMFS allows easy repositioning of inventory pods during operations that can lead to a more energy-efficient picking process. We integrate pod repositioning decisions with order assignment and pod selection using a wave picking strategy such that pods are parked after being requested considering when and where they are expected to be requested next. We solve this integrated problem using stochastic programming considering the uncertainty about future demands and suggest a local search matheuristic to solve real-size instances. We show that our sample average approximation scheme is effective to simulate future demands since our methods improve solutions found when waves are planned without considering the future demands. This thesis is structured as follows. After an introductory chapter, we present a literature review on the manual and RMFS, and common decisions made to set up their storage and picking processes. The next four chapters detail the studies for the integrated storage and routing problem, the zone sizing problem, the QAP, and the pod repositioning problem. Our findings are summarized in the last chapter

On automated sequential steady-state simulation.

The credibility of the final results from stochastic simulation has had limited discussion in the simulation literature so far. However, it is important that the final results from any simulations be credible. To achieve this, validation, which determines whether the conceptual simulation model is an accurate representation of the system under study, has to be done carefully. Additionally, a proper statistical analysis of simulation output data, including a confidence interval or other assessment of statistical errors, has to be conducted before any valid inferences or conclusions about the performance of simulated dynamic systems, such as for example telecommunication networks, are made. There are many other issues, such as choice of a good pseudo-random number generator, elimination of initialisation bias in steady-state simulations, and consideration of auto correlations in collected observations, which have to be appropriately addressed for the final results to be credible. However, many of these issues are not trivial, particularly for simulation users who may not be experts in these areas. As a consequence, a fully-automated simulation package, which can control all important aspects of stochastic simulation, is needed. This dissertation focuses on the following contributions to such a package for steady-state simulation: properties of confidence intervals (CIs) used in coverage analysis, heuristic rules for improving the coverage of the final CIs in practical applications, automated sequential analysis of mean values by the method of regenerative cycles, automatic detection of the initial transient period for steady-state quantile estimation, and sequential steady-state quantile estimation with the automated detection of the length of initial transient period. One difficulty in obtaining precise estimates of a system using stochastic simulation can be the cost of the computing time needed to collect the large amount of output data required. Indeed there are situations, such as estimation of rare events, where, even assuming an appropriate statistical analysis procedure is available, the cost of collecting the number of observations needed by the analysis procedure can be prohibitively large. Fortunately, inexpensive computer network resources enable computationally intensive simulations by allowing us to run parallel and distributed simulations. Therefore, where possible, we extend the contributions to the distributed stochastic simulation scenario known as the Multiple Replications In Parallel (MRIP), in which multiple processors run their own independent replications of the simulated system but cooperate with central analysers that collect data to estimate the final results