Apache Spark is a popular open-source distributed processing framework that enables efficient processing of large amounts of data. Apache Spark has a large number of configuration parameters that are strongly related to performance. Selecting an optimal configuration for Apache Spark application deployed in a cloud environment is a complex task. Making a poor choice may not only result in poor performance but also increases costs. Manually adjusting the Apache Spark configuration parameters can take a lot of time and may not lead to the best outcomes, particularly in a cloud environment where computing resources are allocated dynamically, and workloads can fluctuate significantly. The focus of this thesis project is the development of an auto-tuning approach for Apache Spark configuration parameters. Four machine learning models are formulated and evaluated to predict Apache Spark’s performance. Additionally, two models for Apache Spark configuration parameter search are created and evaluated to identify the most suitable parameters, resulting in the shortest execution time. The obtained results demonstrates that with the developed auto-tuning approach and adjusting Apache Spark configuration parameters, Apache Spark applications can achieve a shorter execution time than when using the default parameters. The developed auto-tuning approach gives an improved cluster utilization and shorter job execution time, with an average performance improvement of 49.98%, 53.84%, and 64.16% for the three different types of Apache Spark applications benchmarked. / Apache Spark är en populär öppen källkodslösning för distribuerad databehandling som möjliggör effektiv bearbetning av stora mängder data. Apache Spark har ett stort antal konfigurationsparametrar som starkt påverkar prestandan. Att välja en optimal konfiguration för en Apache Spark-applikation som distribueras i en molnmiljö är en komplex uppgift. Ett dåligt val kan inte bara leda till dålig prestanda utan också ökade kostnader. Manuell anpassning av Apache Spark-konfigurationsparametrar kan ta mycket tid och leda till suboptimala resultat, särskilt i en molnmiljö där beräkningsresurser tilldelas dynamiskt och arbetsbelastningen kan variera avsevärt. Fokus för detta examensprojekt är att utveckla en automatisk optimeringsmetod för konfigurationsparametrarna i Apache Spark. Fyra maskininlärningsmodeller formuleras och utvärderas för att förutsäga Apache Sparks prestanda. Dessutom skapas och utvärderas två modeller för att söka efter de mest lämpliga konfigurationsparametrarna för Apache Spark, vilket resulterar i kortast möjliga exekveringstid. De erhållna resultaten visar att den utvecklade automatiska optimeringsmetoden, med anpassning av Apache Sparks konfigurationsparameterar, bidrar till att Apache Spark-applikationer kan uppnå kortare exekveringstider än vid användning av standard-parametrar. Den utvecklade metoden för automatisk optimering bidrar till en förbättrad användning av klustret och kortare exekveringstider, med en genomsnittlig prestandaförbättring på 49,98%, 53,84% och 64,16% för de tre olika typerna av Apache Spark-applikationer som testades.

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<div>The rise of artificial intelligence (AI) hinges on the efficient training of modern deep neural networks (DNNs) for non-convex optimization and uncertainty quantification, which boils down to a non-convex Bayesian learning problem. A standard tool to handle the problem is Langevin Monte Carlo, which proposes to approximate the posterior distribution with theoretical guarantees. However, non-convex Bayesian learning in real big data applications can be arbitrarily slow and often fails to capture the uncertainty or informative modes given a limited time. As a result, advanced techniques are still required.</div><div><br></div><div>In this thesis, we start with the replica exchange Langevin Monte Carlo (also known as parallel tempering), which is a Markov jump process that proposes appropriate swaps between exploration and exploitation to achieve accelerations. However, the na\"ive extension of swaps to big data problems leads to a large bias, and the bias-corrected swaps are required. Such a mechanism leads to few effective swaps and insignificant accelerations. To alleviate this issue, we first propose a control variates method to reduce the variance of noisy energy estimators and show a potential to accelerate the exponential convergence. We also present the population-chain replica exchange and propose a generalized deterministic even-odd scheme to track the non-reversibility and obtain an optimal round trip rate. Further approximations are conducted based on stochastic gradient descents, which yield a user-friendly nature for large-scale uncertainty approximation tasks without much tuning costs. </div><div><br></div><div>In the second part of the thesis, we study scalable dynamic importance sampling algorithms based on stochastic approximation. Traditional dynamic importance sampling algorithms have achieved successes in bioinformatics and statistical physics, however, the lack of scalability has greatly limited their extensions to big data applications. To handle this scalability issue, we resolve the vanishing gradient problem and propose two dynamic importance sampling algorithms based on stochastic gradient Langevin dynamics. Theoretically, we establish the stability condition for the underlying ordinary differential equation (ODE) system and guarantee the asymptotic convergence of the latent variable to the desired fixed point. Interestingly, such a result still holds given non-convex energy landscapes. In addition, we also propose a pleasingly parallel version of such algorithms with interacting latent variables. We show that the interacting algorithm can be theoretically more efficient than the single-chain alternative with an equivalent computational budget.</div>