Competitive regression.

This thesis is about investigating the predictive complexity of online regression. In essence, supervised learning from a data sequence consisting of n-dimensional input and the corresponding output is considered. In this work online learning scenario considered consists of sequential arrival of data, without making any stochastic assumptions on the nature of the arriving data. At each trial, the learner receives the input, it produces a prediction. Then as a second step, the true output is observed, and the learner suffers a loss which is consequently used to learn. The goal of online learning regression in this thesis, is to minimise the regret suffered when considering the loss of the minimum of the sum of squares. In the present work, three novel algorithms (Online Shrinkage via Limit of Gibbs sampler (OSLOG), Competitive Iterated Ridge Regression (CIRR) and Competitive Normalised Least Squares (CNLS)) are derived and analysed. The development of these algorithms is driven by Kolmogorov complexity (known also as “competitive analysis”). OSLOG appraises the Bayesian approach, CIRR relies on game theory, whereas CNLS makes use of gradient descent methods. The analysis of the algorithms investigates two aspects: (1) formulating the upper bound on the cumulative square loss and (2) identifying the precise conditions under which they perform better than other algorithms. In fact, the theoretical results indicate that they have a better guarantee than the state-of-the-art algorithms. The empirical study conducted on real-world datasets show also that the performance of the proposed algorithms is better than the state-of-the-art algorithms and close to the minimum of the sum of squares

Anomalous phase separation dynamics in a correlated electron system: machine-learning enabled large-scale kinetic Monte Carlo simulations

Phase separation plays a central role in the emergence of novel functionalities of correlated electron materials. The structure of the mixed-phase states depends strongly on the nonequilibrium phase-separation dynamics, which has so far yet to be systematically investigated, especially on the theoretical side. With the aid of modern machine learning methods, we demonstrate the first-ever large-scale kinetic Monte Carlo simulations of the phase separation process for the Falicov-Kimball model, which is one of the canonical strongly correlated electron systems. We uncover an unusual phase-separation scenario where domain coarsening occurs simultaneously at two different scales: the growth of checkerboard clusters at smaller length scales and the expansion of super-clusters, which are aggregates of the checkerboard clusters of the same sign, at a larger scale. We show that the emergence of super-clusters is due to a hidden dynamical breaking of the sublattice symmetry. Arrested growth of the checkerboard patterns and of the super-clusters is shown to result from a correlation-induced self-trapping mechanism. Glassy behaviors similar to the one reported in this work could be generic for other correlated electron systems.Comment: 11 pages, 11 figure

Applying Secure Multi-party Computation in Practice

In this work, we present solutions for technical difficulties in deploying secure multi-party computation in real-world applications. We will first give a brief overview of the current state of the art, bring out several shortcomings and address them. The main contribution of this work is an end-to-end process description of deploying secure multi-party computation for the first large-scale registry-based statistical study on linked databases. Involving large stakeholders like government institutions introduces also some non-technical requirements like signing contracts and negotiating with the Data Protection Agency

Fuzzy Sets, Fuzzy Logic and Their Applications 2020

The present book contains the 24 total articles accepted and published in the Special Issue “Fuzzy Sets, Fuzzy Logic and Their Applications, 2020” of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity

Turvalise ühisarvutuse rakendamine

Andmetest on kasu vaid siis kui neid saab kasutada. Eriti suur lisandväärtus tekib siis, kui ühendada andmed erinevatest allikatest. Näiteks, liites kokku maksu- ja haridusandmed, saab riik läbi viia kõrghariduse erialade tasuvusanalüüse. Sama kehtib ka erasektoris - ühendades pankade maksekohustuste andmebaasid, saab efektiivsemalt tuvastada kõrge krediidiriskiga kliente. Selline andmekogude ühendamine on aga tihti konfidentsiaalsus- või privaatsusnõuete tõttu keelatud. Õigustatult, sest suuremahulised ühendatud andmekogud on atraktiivsed sihtmärgid nii häkkeritele kui ka ametnikele ja andmebaaside administraatoritele, kes oma õigusi kuritarvitada võivad. Seda sorti rünnete vastus aitab turvalise ühisarvutuse tehnoloogia kasutamine, mis võimaldab mitmed osapoolel andmeid ühiselt analüüsida, ilma et keegi neist pääseks ligi üksikutele kirjetele. Oma esimesest rakendamisest praktikas 2008. aastal on turvalise ühisarvutuse tehnoloogia praeguseks jõudnud seisu, kus seda juurutatakse hajusates rakendustes üle interneti ning seda pakutakse ka osana teistest teenustest. Käesolevas töös keskendume turvalise ühisarvutuse praktikas rakendamise tehnilistele küsimustele. Alustuseks tutvustame esimesi selle tehnoloogia rakendusi, tuvastame veel lahendamata probleeme ning pakume töö käigus välja lahendusi. Töö põhitulemus on samm-sammuline ülevaade sellise juurutuse elutsüklist, kasutades näitena esimest turvalise ühisarvutuse abil läbi viidud suuremahulisi registriandmeid hõlmavat uuringut. Sealhulgas anname ülevaate ka mittetehnilistest toimingutest nagu lepingute sõlmimine ja Andmekaitse Inspektsiooniga suhtlemine, mis tulenevad suurte organisatsioonide kaasamisest nagu seda on riigiasutused. Tulevikku vaadates pakume välja lahenduse, mis ühendab endas födereeritud andmevahetusplatvormi ja turvalise ühisarvutuse tehnoloogiat. Konkreetse lahendusena pakume Eesti riigi andmevahetuskihi X-tee täiustamist turvalise ühisarvutuse teenusega Sharemind. Selline arhitektuur võimaldaks mitmeid olemasolevaid andmekogusid uuringuteks liita efektiivselt ja turvaliselt, ilma üksikisikute privaatsust rikkumata.Data is useful only when used. This is especially true if one is able to combine several data sets. For example, combining income and educational data, it is possible for a government to get a return of investment overview of educational investments. The same is true in private sector. Combining data sets of financial obligations of their customers, banks could issue loans with lower credit risks. However, this kind of data sharing is often forbidden as citizens and customers have their privacy expectations. Moreover, such a combined database becomes an interesting target for both hackers as well as nosy officials and administrators taking advantage of their position. Secure multi-party computation is a technology that allows several parties to collaboratively analyse data without seeing any individual values. This technology is suitable for the above mentioned scenarios protecting user privacy from both insider and outsider attacks. With first practical applications using secure multi-party computation developed in 2000s, the technology is now mature enough to be used in distributed deployments and even offered as part of a service. In this work, we present solutions for technical difficulties in deploying secure multi-party computation in real-world applications. We will first give a brief overview of the current state of the art, bring out several shortcomings and address them. The main contribution of this work is an end-to-end process description of deploying secure multi-party computation for the first large-scale registry-based statistical study on linked databases. Involving large stakeholders like government institutions introduces also some non-technical requirements like signing contracts and negotiating with the Data Protection Agency. Looking into the future, we propose to deploy secure multi-party computation technology as a service on a federated data exchange infrastructure. This allows privacy-preserving analysis to be carried out faster and more conveniently, thus promoting a more informed government