Federated learning faces a challenge when dealing with highly heterogeneous data and it can sometimes be inadequate to adopt an approach where a single model is trained for usage at all nodes in the network. Different approaches have been investigated to succumb this issue such as adapting the trained model to each node and clustering the nodes in the network and train a different model for each cluster where the data is less heterogeneous. In this work we study the possibilities to improve the local model performance utilizing the hierarchical setup that comes with clustering the participating clients in the network. Experiments are carried out featuring a Long Short-Term Memory network to perform time series forecasting to evaluate different approaches utilizing the hierarchical setup and comparing them to standard federated learning approaches. The experiments are done using a dataset collected by Ericsson AB consisting of handovers recorded at base stations in an European city. The hierarchical approaches didn’t show any benefit over common two-level approaches. / Federated Learning står inför en utmaning när det gäller att hantera data med en hög grad av heterogenitet och det kan i vissa fall vara olämpligt att använda sig av en approach där en och samma modell är tränad för att användas av alla noder i nätverket. Olika approacher för att hantera detta problem har undersökts som att anpassa den tränade modellen till varje nod och att klustra noderna i nätverket och träna en egen modell för varje kluster inom vilket datan är mindre heterogen. I detta arbete studeras möjligheterna att förbättra prestandan hos de lokala modellerna genom att dra nytta av den hierarkiska anordning som uppstår när de deltagande noderna i nätverket grupperas i kluster. Experiment är utförda med ett Long Short-Term Memory-nätverk för att utföra tidsserieprognoser för att utvärdera olika approacher som drar nytta av den hierarkiska anordningen och jämför dem med vanliga federated learning-approacher. Experimenten är utförda med ett dataset insamlat av Ericsson AB. Det består av "handoversfrån basstationer i en europeisk stad. De hierarkiska approacherna visade inga fördelar jämfört med de vanliga två-nivåapproacherna.

Prädiktive Modelle sind hilfreiche Mittel zur quantitativen Entscheidungsunterstützung von modernen Unternehmen. Jedoch gibt es in vielen Fällen statistische Probleme in den genutzten Daten, die eine wirkungsvolle Anwendung prädiktiver Modelle zur Entscheidungsunterstützung verhindern. In dieser Doktorarbeit werden solche häufig auftretenden statistischen Probleme analysiert und statistische Methoden werden vorgestellt, mit denen man diese Probleme überwinden und damit prädiktive Modellierung und Entscheidungsunterstützung wirkungsvoll machen kann. Der erste Teil der Arbeit behandelt das Problem von "Concept Drift" in Google Trends Zeitreihen. Die Doktorarbeit bietet eine empirische Analyse des Problems und einen Ansatz um die Daten zu bereinigen. Für den speziellen Anwendungsfall der Tourismusnachfragevorhersage in Deutschland demonstriert die Arbeit empirisch den Nutzen der Bereinigungsmethode. Der zweite Teil der Arbeit setzt sich mit Experimenten und Modellen zur Schätzung von heterogenen Behandlungseffekten von Individuen auseinander. In solchen Anwendungen stellt Rauschen (Noise) in den Daten eine statistische Herausforderung dar, die zu einer hohen benötigten Fallzahl im Experiment und unerwarteten negativen Folgen bei der anschließenden selektiven Vergabe der Behandlung führen kann. Um diese Probleme zu überwinden entwickelt die Arbeit Methoden um Experimente mit einer kleineren Fallzahl durchzuführen, ohne Einbußen in der Qualität der Ergebnisse zu erleiden. Darüber hinaus analysiert die Arbeit die potenziell negativen Folgen von Noise auf die selektive Behandlungsvergabe und schlägt Ideen vor, wie man diese verhindern kann. / Predictive models are useful methods for quantitative decision support in contemporary business. However, often there are statistical problems in the data sets, hindering effective predictive modeling and decision support. This thesis analyzes such frequently occurring statistical problems and provides statistical approaches to overcome them and thereby enable efficient predictive modeling and decision support. The first part of the thesis focuses on concept drift in Google Trends time series data. The thesis provides an empirical analysis of the problem and an approach to sanitize the data. For the specific use case of tourism demand forecasting in Germany, the thesis demonstrates the usefulness of the statistical approach. The second part of the thesis focuses on experiments and models to estimate heterogeneous treatment effects of individuals. In such applications, noise in the data poses a statistical challenge, leading to high requirements in the sample size for randomized experiments and potentially leading to unexpected negative results in the treatment allocation process. To overcome this problem, the thesis proposes methods to conduct experiments with a limited number of individuals, without impairing the decision support. Moreover, the thesis analyzes the potential adverse effects of noise on the treatment allocation process and provides ideas on how to prevent them.

Cette thèse envisage un ensemble de méthodes permettant aux algorithmes d'apprentissage statistique de mieux traiter la nature séquentielle des problèmes de gestion de portefeuilles financiers. Nous débutons par une considération du problème général de la composition d'algorithmes d'apprentissage devant gérer des tâches séquentielles, en particulier celui de la mise-à-jour efficace des ensembles d'apprentissage dans un cadre de validation séquentielle. Nous énumérons les desiderata que des primitives de composition doivent satisfaire, et faisons ressortir la difficulté de les atteindre de façon rigoureuse et efficace. Nous poursuivons en présentant un ensemble d'algorithmes qui atteignent ces objectifs et présentons une étude de cas d'un système complexe de prise de décision financière utilisant ces techniques. Nous décrivons ensuite une méthode générale permettant de transformer un problème de décision séquentielle non-Markovien en un problème d'apprentissage supervisé en employant un algorithme de recherche basé sur les K meilleurs chemins. Nous traitons d'une application en gestion de portefeuille où nous entraînons un algorithme d'apprentissage à optimiser directement un ratio de Sharpe (ou autre critère non-additif incorporant une aversion au risque). Nous illustrons l'approche par une étude expérimentale approfondie, proposant une architecture de réseaux de neurones spécialisée à la gestion de portefeuille et la comparant à plusieurs alternatives. Finalement, nous introduisons une représentation fonctionnelle de séries chronologiques permettant à des prévisions d'être effectuées sur un horizon variable, tout en utilisant un ensemble informationnel révélé de manière progressive. L'approche est basée sur l'utilisation des processus Gaussiens, lesquels fournissent une matrice de covariance complète entre tous les points pour lesquels une prévision est demandée. Cette information est utilisée à bon escient par un algorithme qui transige activement des écarts de cours (price spreads) entre des contrats à terme sur commodités. L'approche proposée produit, hors échantillon, un rendement ajusté pour le risque significatif, après frais de transactions, sur un portefeuille de 30 actifs. / This thesis considers a number of approaches to make machine learning algorithms better suited to the sequential nature of financial portfolio management tasks. We start by considering the problem of the general composition of learning algorithms that must handle temporal learning tasks, in particular that of creating and efficiently updating the training sets in a sequential simulation framework. We enumerate the desiderata that composition primitives should satisfy, and underscore the difficulty of rigorously and efficiently reaching them. We follow by introducing a set of algorithms that accomplish the desired objectives, presenting a case-study of a real-world complex learning system for financial decision-making that uses those techniques. We then describe a general method to transform a non-Markovian sequential decision problem into a supervised learning problem using a K-best paths search algorithm. We consider an application in financial portfolio management where we train a learning algorithm to directly optimize a Sharpe Ratio (or other risk-averse non-additive) utility function. We illustrate the approach by demonstrating extensive experimental results using a neural network architecture specialized for portfolio management and compare against well-known alternatives. Finally, we introduce a functional representation of time series which allows forecasts to be performed over an unspecified horizon with progressively-revealed information sets. By virtue of using Gaussian processes, a complete covariance matrix between forecasts at several time-steps is available. This information is put to use in an application to actively trade price spreads between commodity futures contracts. The approach delivers impressive out-of-sample risk-adjusted returns after transaction costs on a portfolio of 30 spreads.

Predicting the behavior of financial markets is largely an unsolved problem. The problem hasbeen approached with many different methods ranging from binary logic, statisticalcalculations and genetic algorithms. In this thesis, the problem is approached with a machinelearning method, namely the Long Short-Term Memory (LSTM) variant of Recurrent NeuralNetworks (RNNs). Recurrent neural networks are artificial neural networks (ANNs)—amachine learning algorithm mimicking the neural processing of the mammalian nervoussystem—specifically designed for time series sequences. The thesis investigates the capabilityof the LSTM in modeling financial market behavior as well as compare it to the traditionalRNN, evaluating their performances using various measures. / Prediktion av den finansiella marknadens beteende är i stort ett olöst problem. Problemet hartagits an på flera sätt med olika metoder så som binär logik, statistiska uträkningar ochgenetiska algoritmer. I den här uppsatsen kommer problemet undersökas medmaskininlärning, mer specifikt Long Short-Term Memory (LSTM), en variant av rekurrentaneurala nätverk (RNN). Rekurrenta neurala nätverk är en typ av artificiellt neuralt nätverk(ANN), en maskininlärningsalgoritm som ska efterlikna de neurala processerna hos däggdjursnervsystem, specifikt utformat för tidsserier. I uppsatsen undersöks kapaciteten hos ett LSTMatt modellera finansmarknadens beteenden och jämförs den mot ett traditionellt RNN, merspecifikt mäts deras effektivitet på olika vis.

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Abstracts in English, Afrikaans and Northern Sotho / More time series forecasting methods were researched and made available in recent years. This is mainly due to the emergence of machine learning methods which also found applicability in time series forecasting. The emergence of a variety of methods and their variants presents a challenge when choosing appropriate forecasting methods. This study explored the performance of four advanced forecasting methods: autoregressive integrated moving averages (ARIMA); artificial neural networks (ANN); support vector machines (SVM) and regression models with ARIMA errors. To improve their performance, bagging was also applied. The performance of the different methods was illustrated using South African air passenger data collected for planning purposes by the Airports Company South Africa (ACSA). The dissertation discussed the different forecasting methods at length. Characteristics such as strengths and weaknesses and the applicability of the methods were explored. Some of the most popular forecast accuracy measures were discussed in order to understand how they could be used in the performance evaluation of the methods. It was found that the regression model with ARIMA errors outperformed all the other methods, followed by the ARIMA model. These findings are in line with the general findings in the literature. The ANN method is prone to overfitting and this was evident from the results of the training and the test data sets. The bagged models showed mixed results with marginal improvement on some of the methods for some performance measures. It could be concluded that the traditional statistical forecasting methods (ARIMA and the regression model with ARIMA errors) performed better than the machine learning methods (ANN and SVM) on this data set, based on the measures of accuracy used. This calls for more research regarding the applicability of the machine learning methods to time series forecasting which will assist in understanding and improving their performance against the traditional statistical methods / Die afgelope tyd is verskeie tydreeksvooruitskattingsmetodes ondersoek as gevolg van die ontwikkeling van masjienleermetodes met toepassings in die vooruitskatting van tydreekse. Die nuwe metodes en hulle variante laat ʼn groot keuse tussen vooruitskattingsmetodes. Hierdie studie ondersoek die werkverrigting van vier gevorderde vooruitskattingsmetodes: outoregressiewe, geïntegreerde bewegende gemiddeldes (ARIMA), kunsmatige neurale netwerke (ANN), steunvektormasjiene (SVM) en regressiemodelle met ARIMA-foute. Skoenlussaamvoeging is gebruik om die prestasie van die metodes te verbeter. Die prestasie van die vier metodes is vergelyk deur hulle toe te pas op Suid-Afrikaanse lugpassasiersdata wat deur die Suid-Afrikaanse Lughawensmaatskappy (ACSA) vir beplanning ingesamel is. Hierdie verhandeling beskryf die verskillende vooruitskattingsmetodes omvattend. Sowel die positiewe as die negatiewe eienskappe en die toepasbaarheid van die metodes is uitgelig. Bekende prestasiemaatstawwe is ondersoek om die prestasie van die metodes te evalueer. Die regressiemodel met ARIMA-foute en die ARIMA-model het die beste van die vier metodes gevaar. Hierdie bevinding strook met dié in die literatuur. Dat die ANN-metode na oormatige passing neig, is deur die resultate van die opleidings- en toetsdatastelle bevestig. Die skoenlussamevoegingsmodelle het gemengde resultate opgelewer en in sommige prestasiemaatstawwe vir party metodes marginaal verbeter. Op grond van die waardes van die prestasiemaatstawwe wat in hierdie studie gebruik is, kan die gevolgtrekking gemaak word dat die tradisionele statistiese vooruitskattingsmetodes (ARIMA en regressie met ARIMA-foute) op die gekose datastel beter as die masjienleermetodes (ANN en SVM) presteer het. Dit dui op die behoefte aan verdere navorsing oor die toepaslikheid van tydreeksvooruitskatting met masjienleermetodes om hul prestasie vergeleke met dié van die tradisionele metodes te verbeter. / Go nyakišišitšwe ka ga mekgwa ye mentši ya go akanya ka ga molokoloko wa dinako le go dirwa gore e hwetšagale mo mengwageng ye e sa tšwago go feta. Se k e k a le b a k a la g o t šwelela ga mekgwa ya go ithuta ya go diriša metšhene yeo le yona e ilego ya dirišwa ka kakanyong ya molokolokong wa dinako. Go t šwelela ga mehutahuta ya mekgwa le go fapafapana ga yona go tšweletša tlhohlo ge go kgethwa mekgwa ya maleba ya go akanya. Dinyakišišo tše di lekodišišitše go šoma ga mekgwa ye mene ya go akanya yeo e gatetšego pele e lego: ditekanyotshepelo tšeo di kopantšwego tša poelomorago ya maitirišo (ARIMA); dinetweke tša maitirelo tša nyurale (ANN); metšhene ya bekthara ya thekgo (SVM); le mekgwa ya poelomorago yeo e nago le diphošo tša ARIMA. Go kaonafatša go šoma ga yona, nepagalo ya go ithuta ka metšhene le yona e dirišitšwe. Go šoma ga mekgwa ye e fepafapanego go laeditšwe ka go šomiša tshedimošo ya banamedi ba difofane ba Afrika Borwa yeo e kgobokeditšwego mabakeng a dipeakanyo ke Khamphani ya Maemafofane ya Afrika Borwa (ACSA). Sengwalwanyaki šišo se ahlaahlile mekgwa ya kakanyo ye e fapafapanego ka bophara. Dipharologanyi tša go swana le maatla le bofokodi le go dirišega ga mekgwa di ile tša šomišwa. Magato a mangwe ao a tumilego kudu a kakanyo ye e nepagetšego a ile a ahlaahlwa ka nepo ya go kwešiša ka fao a ka šomišwago ka gona ka tshekatshekong ya go šoma ga mekgwa ye. Go hweditšwe gore mokgwa wa poelomorago wa go ba le diphošo tša ARIMA o phadile mekgwa ye mengwe ka moka, gwa latela mokgwa wa ARIMA. Dikutollo tše di sepelelana le dikutollo ka kakaretšo ka dingwaleng. Mo k gwa wa ANN o ka fela o fetišiša gomme se se bonagetše go dipoelo tša tlhahlo le dihlo pha t ša teko ya tshedimošo. Mekgwa ya nepagalo ya go ithuta ka metšhene e bontšhitše dipoelo tšeo di hlakantšwego tšeo di nago le kaonafalo ye kgolo go ye mengwe mekgwa ya go ela go phethagatšwa ga mešomo. Go ka phethwa ka gore mekgwa ya setlwaedi ya go akanya dipalopalo (ARIMA le mokgwa wa poelomorago wa go ba le diphošo tša ARIMA) e šomile bokaone go phala mekgwa ya go ithuta ka metšhene (ANN le SVM) ka mo go sehlopha se sa tshedimošo, go eya ka magato a nepagalo ya magato ao a šomišitšwego. Se se nyaka gore go dirwe dinyakišišo tše dingwe mabapi le go dirišega ga mekgwa ya go ithuta ka metšhene mabapi le go akanya molokoloko wa dinako, e lego seo se tlago thuša go kwešiša le go kaonafatša go šoma ga yona kgahlanong le mekgwa ya setlwaedi ya dipalopalo. / Decision Sciences / M. Sc. (Operations Research)