2,833 research outputs found
Minimizing Negative Transfer of Knowledge in Multivariate Gaussian Processes: A Scalable and Regularized Approach
Recently there has been an increasing interest in the multivariate Gaussian
process (MGP) which extends the Gaussian process (GP) to deal with multiple
outputs. One approach to construct the MGP and account for non-trivial
commonalities amongst outputs employs a convolution process (CP). The CP is
based on the idea of sharing latent functions across several convolutions.
Despite the elegance of the CP construction, it provides new challenges that
need yet to be tackled. First, even with a moderate number of outputs, model
building is extremely prohibitive due to the huge increase in computational
demands and number of parameters to be estimated. Second, the negative transfer
of knowledge may occur when some outputs do not share commonalities. In this
paper we address these issues. We propose a regularized pairwise modeling
approach for the MGP established using CP. The key feature of our approach is
to distribute the estimation of the full multivariate model into a group of
bivariate GPs which are individually built. Interestingly pairwise modeling
turns out to possess unique characteristics, which allows us to tackle the
challenge of negative transfer through penalizing the latent function that
facilitates information sharing in each bivariate model. Predictions are then
made through combining predictions from the bivariate models within a Bayesian
framework. The proposed method has excellent scalability when the number of
outputs is large and minimizes the negative transfer of knowledge between
uncorrelated outputs. Statistical guarantees for the proposed method are
studied and its advantageous features are demonstrated through numerical
studies
Realized volatility: a review
This paper reviews the exciting and rapidly expanding literature on realized volatility. After presenting a general univariate framework for estimating realized volatilities, a simple discrete time model is presented in order to motivate the main results. A continuous time specification provides the theoretical foundation for the main results in this literature. Cases with and without microstructure noise are considered, and it is shown how microstructure noise can cause severe problems in terms of consistent estimation of the daily realized volatility. Independent and dependent noise processes are examined. The most important methods for providing consistent estimators are presented, and a critical exposition of different techniques is given. The finite sample properties are discussed in comparison with their asymptotic properties. A multivariate model is presented to discuss estimation of the realized covariances. Various issues relating to modelling and forecasting realized volatilities are considered. The main empirical findings using univariate and multivariate methods are summarized.
Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
Computing Functions of Random Variables via Reproducing Kernel Hilbert Space Representations
We describe a method to perform functional operations on probability
distributions of random variables. The method uses reproducing kernel Hilbert
space representations of probability distributions, and it is applicable to all
operations which can be applied to points drawn from the respective
distributions. We refer to our approach as {\em kernel probabilistic
programming}. We illustrate it on synthetic data, and show how it can be used
for nonparametric structural equation models, with an application to causal
inference
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