1,720,998 research outputs found
A probabilistic Taylor expansion with Gaussian processes
No full textWe study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order. The data consist of derivative evaluations at the expansion point and the prior covariance kernel belongs to the class of Taylor kernels, which can be written in a certain power series form. We discuss and prove some results on maximum likelihood estimation of parameters of Taylor kernels. The proposed framework is a special case of Gaussian process regression based on data that is orthogonal in the reproducing kernel Hilbert space of the covariance kernel.</p
A probabilistic Taylor expansion with applications in filtering and differential equations
No full textWe study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order. The data consists of derivative evaluations at the expansion point and the prior covariance kernel belongs to the class of Taylor kernels, which can be written in a certain power series form. This permits statistical modelling of the uncertainty in a variety of algorithms that exploit first and second order Taylor expansions. To demonstrate the utility of this Gaussian process model we introduce new probabilistic versions of the classical extended Kalman filter for non-linear state estimation and the Euler method for solving ordinary differential equations
Modeling the Syntax of the song of the Great Reed Warbler Faculty of Engineering, LTH
Full text linkThe song of many songbirds can be thought of as consisting of variable sequences of a finite set of syllables. A common approach in understanding the structure of these songs is to model the syllable sequences with a Markov Model. The Markov Model can either allow one-to-one (Markov Chain), many-to-many (Hidden Markov Model) or many-to-one (Partially Observed Markov Model) state to syllable mappings. In this project the song of the Great Reed Warbler is being studied in terms of the syllable sequences (strophes) being generated. It is shown that the Markov chain captures a lot of the structure in the song in the sense that it to large degree reproduces the syllable distributions at a specific position in the song that were observed in data. The repetition distribution for some syllable classes was consistent with that of a Markov chain while other syllable classes were better modeled by allowing the self-transition probability to be adapted as the syllable class is repeated more and more. Still some other syllable classes did not have their repetition distributions accurately captured by these two alternatives
Iterative and Geometric Methods for State Estimation in Non-linear Models
No full textMany problems in science and engineering involve estimating a dynamic signal from indirect measurements subject to noise, where points can either evolve in continuous time or in discrete time. These problems are often formalised as inference in probabilistic state-space models, which are also frequently assumed to be Markovian. For inferring the value of the signal at a particular point in time, methods of inference can be divided into different classes, namely prediction, filtering (tracking), and smoothing. In prediction, only past measurements of the signal are used to infer its present value, whereas in filtering both past and present measurements are used, and in smoothing past, present, and future measurements are used. Prediction is useful in situations where decisions need to be made contingent on a future value of the signal before future measurements are made. On the other hand, filtering is useful when the signal needs to be inferred as the measurements arrive, that is on-line. Lastly, smoothing is the preferred choice when none of the aforementioned constraints are present as it allows the use of the entire sequence of measurements to infer the signal.
In this thesis, the filtering and smoothing problems and their applications are examined. In particular, iterative Gaussian filters and smoothers are developed for both inferring continuous and discrete time signals. Furthermore, it is shown that methods for inference in state-space models can be applied to the field of probabilistic numerics. More specifically, estimating the solutions to ordinary differential equations can be formulated as inference in a probabilistic state-space model, hence the solutions can be inferred using either Gaussian filtering methods or sequential Monte Carlo.
Another theme of this thesis is the exploitation of geometry - in a broad sense. Firstly, the geometry of probability densities, namely information geometry, is exploited to approximately infer the signal in filtering. Geometry is also exploited in terms of the geometry of the state-space, the space where the signal takes its values. That is, for tracking a time-varying unit vector, a continuous-time dynamic model is posed that respects the geometry of the unit sphere. Subsequently, a filtering algorithm is developed based on the von Mises-Fisher distribution for inference in this model. The method is demonstrated to have applications in tracking the local gravity and magnetic field vectors using a smartphone. Lastly, the geometry of L_2 spaces is used to approximate a stochastic differential equation with an ordinary differential equation with random coefficients. On this basis filtering and smoothing algorithms are developed
Numerically robust square root implementations of statistical linear regression filters and smoothers
No full textIn this article, square-root formulations of the statistical linear regression filter and smoother are developed. Crucially, the method uses QR decompositions rather than Cholesky downdates. This makes the method inherently more numerically robust than the downdate based methods, which may fail in the face of rounding errors. This increased robustness is demonstrated in an ill-conditioned problem, where it is compared against a reference implementation in both double and single precision arithmetic. The new implementation is found to be more robust, when implemented in lower precision arithmetic as compared to the alternative
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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