Localized Regression on Principal Manifolds

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Exploring multivariate data structures with local principal curves.

A new approach to find the underlying structure of a multidimensional data cloud is proposed, which is based on a localized version of principal components analysis. More specifically, we calculate a series of local centers of mass and move through the data in directions given by the first local principal axis. One obtains a smooth ``local principal curve'' passing through the "middle" of a multivariate data cloud. The concept adopts to branched curves by considering the second local principal axis. Since the algorithm is based on a simple eigendecomposition, computation is fast and easy

Data compression and regression through local principal curves and surfaces

We consider principal curves and surfaces in the context of multivariate regression modelling. For predictor spaces featuring complex dependency patterns between the involved variables, the intrinsic dimensionality of the data tends to be very small due to the high redundancy induced by the dependencies. In situations of this type, it is useful to approximate the high-dimensional predictor space through a low-dimensional manifold (i.e., a curve or a surface), and use the projections onto the manifold as compressed predictors in the regression problem. In the case that the intrinsic dimensionality of the predictor space equals one, we use the local principal curve algorithm for the the compression step. We provide a novel algorithm which extends this idea to local principal surfaces, thus covering cases of an intrinsic dimensionality equal to two, which is in principle extendible to manifolds of arbitrary dimension. We motivate and apply the novel techniques using astrophysical and oceanographic data examples

Challenging the Need for Transparency, Controllability, and Consistency in Usable Adaptation Design

Adaptive applications constitute the basis for many ubiquitous computing scenarios as they can dynamically adapt to changing contexts. The usability design principles transparency, controllability, and consistency have been recommended for the design of adaptive interfaces. However, designing self-adaptive applications that may act completely autonomous is still a challenging task because there is no set of usability design guidelines. Applying the three principles in the design of the five different adaptations of the mobile adaptive application Meet-U revealed as difficult. Based on an analysis of the design problem space, we elaborate an approach for the design of usable adaptations. Our approach is based on a notification design concept which calculates the attention costs and utility benefits of notified adaptations by varying the design aspects transparency and controllability. We present several designs for the adaptations of Meet‑U. The results of a user study shows that the notification design approach is beneficial for the design of adaptations. Varying transparency and controllability is necessary to adjust an adaptation’s design to the particular context of use. This leads to a partially inconsistent design for adaptations within an application

Retrospective sampling in MCMC with an application to COM-Poisson regression

The normalization constant in the distribution of a discrete random variable may not be available in closed form; in such cases, the calculation of the likelihood can be computationally expensive. Approximations of the likelihood or approximate Bayesian computation methods can be used; but the resulting Markov chain Monte Carlo (MCMC) algorithm may not sample from the target of interest. In certain situations, one can efficiently compute lower and upper bounds on the likelihood. As a result, the target density and the acceptance probability of the Metropolis–Hastings algorithm can be bounded. We propose an efficient and exact MCMC algorithm based on the idea of retrospective sampling. This procedure can be applied to a number of discrete distributions, one of which is the Conway–Maxwell–Poisson distribution. In practice, the bounds on the acceptance probability do not need to be particularly tight in order to accept or reject a move. We demonstrate this method using data on the emergency hospital admissions in Scotland in 2010, where the main interest lies in the estimation of the variability of admissions, as it is considered as a proxy for health inequalities

A dynamic acoustic view of real-time change in word-final liquids in spontaneous Glaswegian

This paper investigates the acoustic evidence for real-time change in word-final liquids (/r/ and /l/) in a small-scale study of older male Glaswegian speakers recorded from the 1970s to the 2000s. A dynamic acoustic analysis of the first three formants across the duration of the rhyme (vowel+liquid sequence) shows significant effects of preceding and following phonetic context on the course and trajectories of the formant tracks. We also find raising of F3 for /r/ in speakers who were born and recorded more recently; F2 is lowering for /l/ in the same speakers. Comparison of F2 across the two word-final liquids suggests that /r/ is clearer than /l/ for this Scottish dialect; interestingly the polarity in resonance between /r/ and /l/ is increasing over time

Efficient Bayesian inference for COM-Poisson regression models

COM-Poisson regression is an increasingly popular model for count data. Its main advantage is that it permits to model separately the mean and the variance of the counts, thus allowing the same covariate to affect in different ways the average level and the variability of the response variable. A key limiting factor to the use of the COM-Poisson distribution is the calculation of the normalisation constant: its accurate evaluation can be time-consuming and is not always feasible. We circumvent this problem, in the context of estimating a Bayesian COM-Poisson regression, by resorting to the exchange algorithm, an MCMC method applicable to situations where the sampling model (likelihood) can only be computed up to a normalisation constant. The algorithm requires to draw from the sampling model, which in the case of the COM-Poisson distribution can be done efficiently using rejection sampling. We illustrate the method and the benefits of using a Bayesian COM-Poisson regression model, through a simulation and two real-world data sets with different levels of dispersion

Model fitting and model selection for 'mixture of experts' models

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