Interpretable Categorization of Heterogeneous Time Series Data

Understanding heterogeneous multivariate time series data is important in many applications ranging from smart homes to aviation. Learning models of heterogeneous multivariate time series that are also human-interpretable is challenging and not adequately addressed by the existing literature. We propose grammar-based decision trees (GBDTs) and an algorithm for learning them. GBDTs extend decision trees with a grammar framework. Logical expressions derived from a context-free grammar are used for branching in place of simple thresholds on attributes. The added expressivity enables support for a wide range of data types while retaining the interpretability of decision trees. In particular, when a grammar based on temporal logic is used, we show that GBDTs can be used for the interpretable classi cation of high-dimensional and heterogeneous time series data. Furthermore, we show how GBDTs can also be used for categorization, which is a combination of clustering and generating interpretable explanations for each cluster. We apply GBDTs to analyze the classic Australian Sign Language dataset as well as data on near mid-air collisions (NMACs). The NMAC data comes from aircraft simulations used in the development of the next-generation Airborne Collision Avoidance System (ACAS X).Comment: 9 pages, 5 figures, 2 tables, SIAM International Conference on Data Mining (SDM) 201

Colored operads, series on colored operads, and combinatorial generating systems

We introduce bud generating systems, which are used for combinatorial generation. They specify sets of various kinds of combinatorial objects, called languages. They can emulate context-free grammars, regular tree grammars, and synchronous grammars, allowing us to work with all these generating systems in a unified way. The theory of bud generating systems uses colored operads. Indeed, an object is generated by a bud generating system if it satisfies a certain equation in a colored operad. To compute the generating series of the languages of bud generating systems, we introduce formal power series on colored operads and several operations on these. Series on colored operads are crucial to express the languages specified by bud generating systems and allow us to enumerate combinatorial objects with respect to some statistics. Some examples of bud generating systems are constructed; in particular to specify some sorts of balanced trees and to obtain recursive formulas enumerating these.Comment: 48 page

The Magnus expansion, trees and Knuth's rotation correspondence

W. Magnus introduced a particular differential equation characterizing the logarithm of the solution of linear initial value problems for linear operators. The recursive solution of this differential equation leads to a peculiar Lie series, which is known as Magnus expansion, and involves Bernoulli numbers, iterated Lie brackets and integrals. This paper aims at obtaining further insights into the fine structure of the Magnus expansion. By using basic combinatorics on planar rooted trees we prove a closed formula for the Magnus expansion in the context of free dendriform algebra. From this, by using a well-known dendriform algebra structure on the vector space generated by the disjoint union of the symmetric groups, we derive the Mielnik-Pleba\'nski-Strichartz formula for the continuous Baker-Campbell-Hausdorff series

Permafrost biases climate signals in δ18Otree-ring series from a sub-alpine tree stand in Val Bever/Switzerland

During recent decades, stable oxygen isotopes derived from tree-ring cellulose (δ18OTRC) have been frequently utilised as the baseline for palaeoclimatic reconstructions. In this context, numerous studies take advantage of the high sensitivity of trees close to their ecological distribution limit (high elevation or high latitudes). However, this increases the chance that indirect climatic forces such as cold ground induced by permafrost can distort the climate-proxy relationship. In this study, a tree stand of sub-alpine larch trees (Larix decidua Mill.) located in an inner alpine dry valley (Val Bever), Switzerland, was analysed for its δ18OTRC variations during the last 180 years. A total of eight L. decidua trees were analysed on an individual base, half of which are located on verified sporadic permafrost lenses approximately 500 m below the expected lower limit of discontinuous permafrost. The derived isotope time series are strongly dependent on variations in summer temperature, precipitation and large-scale circulation patterns (geopotential height fields). The results demonstrate that trees growing outside of the permafrost distribution provide a significantly stronger and more consistent climate-proxy relationship over time than permafrost-affected tree stands. The climate sensitivity of permafrost-affected trees is analogical to the permafrost-free tree stands (positive and negative correlations with temperature and precipitation, respectively) but attenuated partly leading to a complete loss of significance. In particular, decadal summer temperature variations are well reflected in δ18OTRC from permafrost-free sites (r = 0.62, p 0.05). Since both tree stands are located just a few meters away from one another and are subject to the same climatic influences, discrepancies in the isotope time series can only be attributed to variations in the trees’ source water that constraints the climatic fingerprints on δ18OTRC. If the two individual time series are merged to one local mean chronology, the climatic sensitivity reflects an intermediate between the permafrost-free and –affected δ18OTRC time series. It can be deduced, that a significant loss of information on past climate variations arises by simply averaging both tree stands without prior knowledge of differing subsurface conditions

Arabic parsing using grammar transforms

We investigate Arabic Context Free Grammar parsing with dependency annotation comparing lexicalised and unlexicalised parsers. We study how morphosyntactic as well as function tag information percolation in the form of grammar transforms (Johnson, 1998, Kulick et al., 2006) affects the performance of a parser and helps dependency assignment. We focus on the three most frequent functional tags in the Arabic Penn Treebank: subjects, direct objects and predicates . We merge these functional tags with their phrasal categories and (where appropriate) percolate case information to the non-terminal (POS) category to train the parsers. We then automatically enrich the output of these parsers with full dependency information in order to annotate trees with Lexical Functional Grammar (LFG) f-structure equations with produce f-structures, i.e. attribute-value matrices approximating to basic predicate-argument-adjunct structure representations. We present a series of experiments evaluating how well lexicalized, history-based, generative (Bikel) as well as latent variable PCFG (Berkeley) parsers cope with the enriched Arabic data. We measure quality and coverage of both the output trees and the generated LFG f-structures. We show that joint functional and morphological information percolation improves both the recovery of trees as well as dependency results in the form of LFG f-structures

Automaták , fixpontok, és logika = Automata, fixed points, and logic

Megmutattuk, hogy a véges automaták (faautomaták, súlyozott automaták, stb.) viselkedése végesen leírható a fixpont művelet általános tulajdonságainak felhasználásával. Teljes axiomatizálást adtunk a véges automaták viselkedését leíró racionális hatványsorokra és fasorokra, ill. a véges automaták biszimuláció alapú viselkedésére. Megmutattuk, hogy az automaták elméletének alapvető Kleene tétele és általánosításai a fixpont művelet azonosságainak következménye. Algebrai eszközökkel vizsgáltuk az elágazó idejű temporális logikák és a monadikus másodrendű logika frágmenseinek kifejező erejét fákon. Fő eredményünk egy olyan kölcsönösen egyértelmű kapcsolat kimutatása, amely ezen logikák kifejező erejének vizsgálatát visszavezeti véges algebrák és preklónok bizonyos pszeudovarietásainak vizsgálatára. Jellemeztük a reguláris és környezetfüggetlen nyelvek lexikografikus rendezéseit, végtelen szavakra általánosítottuk a környezetfüggetlen nyelv fogalmát, és tisztáztuk ezek számos algoritmikus tulajdonságát. | We have proved that the the bahavior of finite automata (tree automata, weighted automata, etc.) has a finite description with respect to the general properties of fixed point operations. We have obtained complete axiomatizations of rational power series and tree series, and the bisimulation based behavior of finite automata. As an intermediate step of the completeness proofs, we have shown that Kleene's fundamental theorem and its generalizations follow from the equational properties of fixed point operations. We have developed an algebraic framework for describing the expressive power of branching time temporal logics and fragments of monadic second-order logic on trees. Our main results establish a bijective correspondence between these logics and certain pseudo-varieties of finite algebras and/or finitary preclones. We have characterized the lexicographic orderings of the regular and context-free languages and generalized the notion of context-free languages to infinite words and established several of their algorithmic properties