Human in the Loop: Interactive Passive Automata Learning via Evidence-Driven State-Merging Algorithms

We present an interactive version of an evidence-driven state-merging (EDSM) algorithm for learning variants of finite state automata. Learning these automata often amounts to recovering or reverse engineering the model generating the data despite noisy, incomplete, or imperfectly sampled data sources rather than optimizing a purely numeric target function. Domain expertise and human knowledge about the target domain can guide this process, and typically is captured in parameter settings. Often, domain expertise is subconscious and not expressed explicitly. Directly interacting with the learning algorithm makes it easier to utilize this knowledge effectively.Comment: 4 pages, presented at the Human in the Loop workshop at ICML 201

Optimal Spectral-Norm Approximate Minimization of Weighted Finite Automata

We address the approximate minimization problem for weighted finite automata (WFAs) over a one-letter alphabet: to compute the best possible approximation of a WFA given a bound on the number of states. This work is grounded in Adamyan-Arov-Krein Approximation theory, a remarkable collection of results on the approximation of Hankel operators. In addition to its intrinsic mathematical relevance, this theory has proven to be very effective for model reduction. We adapt these results to the framework of weighted automata over a one-letter alphabet. We provide theoretical guarantees and bounds on the quality of the approximation in the spectral and $\ell^2$ norm. We develop an algorithm that, based on the properties of Hankel operators, returns the optimal approximation in the spectral norm.Comment: 24 pages, authors appear in alphabetical order; minor correction in Theorem 3.2 and consequently updated notation in Section 3, the validity of the result is not affecte

Optimal Approximate Minimization of One-Letter Weighted Finite Automata

In this paper, we study the approximate minimization problem of weighted finite automata (WFAs): to compute the best possible approximation of a WFA given a bound on the number of states. By reformulating the problem in terms of Hankel matrices, we leverage classical results on the approximation of Hankel operators, namely the celebrated Adamyan-Arov-Krein (AAK) theory. We solve the optimal spectral-norm approximate minimization problem for irredundant WFAs with real weights, defined over a one-letter alphabet. We present a theoretical analysis based on AAK theory, and bounds on the quality of the approximation in the spectral norm and $\ell^2$ norm. Moreover, we provide a closed-form solution, and an algorithm, to compute the optimal approximation of a given size in polynomial time.Comment: 32 pages. arXiv admin note: substantial text overlap with arXiv:2102.0686

Bisimulation Metrics for Weighted Automata

We develop a new bisimulation (pseudo)metric for weighted finite automata (WFA) that generalizes Boreale\u27s linear bisimulation relation. Our metrics are induced by seminorms on the state space of WFA. Our development is based on spectral properties of sets of linear operators. In particular, the joint spectral radius of the transition matrices of WFA plays a central role. We also study continuity properties of the bisimulation pseudometric, establish an undecidability result for computing the metric, and give a preliminary account of applications to spectral learning of weighted automata

Learning Deterministic Finite Automata from Confidence Oracles

We discuss the problem of learning a deterministic finite automaton (DFA) from a confidence oracle. That is, we are given access to an oracle $Q$ with incomplete knowledge of some target language $L$ over an alphabet $\Sigma$; the oracle maps a string $x\in\Sigma^*$ to a score in the interval $[-1,1]$ indicating its confidence that the string is in the language. The interpretation is that the sign of the score signifies whether $x\in L$, while the magnitude $|Q(x)|$ represents the oracle's confidence. Our goal is to learn a DFA representation of the oracle that preserves the information that it is confident in. The learned DFA should closely match the oracle wherever it is highly confident, but it need not do this when the oracle is less sure of itself

Linnade laienemine Eestis: seire, analüüs ja modelleerimine

Väitekirja elektrooniline versioon ei sisalda publikatsiooneLinnade laienemine, mida iseloomustab vähese tihedusega, ruumiliselt ebaühtlane ja hajutatud areng linna piiridest välja. Kuna linnade laienemine muudab põllumajandus- ja metsamaid ning väikesed muutused linnapiirkondades võivad pikaajaliselt mõjutada elurikkust ja maastikku, on hädavajalik seirata linnade ruumilist laienemist ning modelleerida tulevikku, saamaks ülevaadet suundumustest ja tagajärgedest pikemas perspektiivis. Eestis võeti pärast taasiseseisvumist 1991. aastal vastu maareformi seadus ning algas “maa” üleandmine riigilt eraomandisse. Sellest ajast peale on Eestis toimunud elamupiirkondade detsentraliseerimine, mis on mõjutanud Tallinna ümbruse põllumajandus- ja tööstuspiirkondade muutumist, inimeste elustiili muutusi ning jõukate inimeste elama asumist ühepereelamutesse Tallinna, Tartu ja Pärnu lähiümbruse. Selle aja jooksul on Eesti rahvaarv vähenenud 15,31%. Käesoleva doktoritöö eesmärgiks on "jälgida, analüüsida ja modelleerida Eesti linnade laienemist viimase 30 aasta jooksul ning modelleerida selle tulevikku", kasutades paljusid modelleerimismeetodeid, sealhulgas logistilist regressiooni, mitmekihilisi pertseptronnärvivõrke, rakkautomaate, Markovi ahelate analüüsi, mitme kriteeriumi. hindamist ja analüütilise hierarhia protsesse. Töö põhineb neljal originaalartiklil, milles uuriti linnade laienemist Eestis. Tegu on esimese põhjaliku uuringuga Eesti linnade laienemise modelleerimisel, kasutades erinevaid kaugseireandmeid, mõjutegureid, parameetreid ning modelleerimismeetodeid. Kokkuvõtteks võib öelda, et uusehitiste hajumismustrid laienevad jätkuvalt suuremate linnade ja olemasolevate elamupiirkondade läheduses ning põhimaanteede ümber.Urban expansion is characterized by the low–density, spatially discontinued, and scattered development of urban-related constructions beyond the city boundaries. Since urban expansion changes the agricultural and forest lands, and slight changes in urban areas can affect biodiversity and landscape on a regional scale in the long-term, spatiotemporal monitoring of urban expansion and modeling of the future are essential to provide insights into the long-term trends and consequences. In Estonia, after the regaining independence in 1991, the Land Reform Act was passed, and the transfer of “land” from the state to private ownership began. Since then, Estonia has experienced the decentralization of residential areas affecting the transformation of agricultural and industrial regions around Tallinn, changes in people's lifestyles, and the settling of wealthy people in single-family houses in the suburbs of Tallinn, Tartu, and Pärnu. During this period, Estonia's population has declined dramatically by 15.31%. Therefore, this dissertation aims to "monitor, analyze and model Estonian urban expansion over the last 30 years and simulate its future" using many modeling approaches including logistic regression, multi-layer perceptron neural networks, cellular automata, Markov chain Analysis, multi-criteria evaluation, and analytic hierarchy process. The thesis comprises four original research articles that studied urban expansion in Estonia. So far, this is the first comprehensive study of modeling Estonian urban expansion utilizing various sets of remotely sensed data, driving forces and predictors, and modeling approaches. The scattering patterns of new constructions are expected to continue as the infilling form, proximate to main cities and existing residential areas and taking advantage of main roads in future.https://www.ester.ee/record=b550782