2,010 research outputs found
Gaussian Process priors with uncertain inputs? Application to multiple-step ahead time series forecasting
We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model. k-step ahead forecasting of a discrete-time non-linear dynamic system can be performed by doing repeated one-step ahead predictions. For a state-space model of the form y t = f(Yt-1 ,..., Yt-L ), the prediction of y at time t + k is based on the point estimates of the previous outputs. In this paper, we show how, using an analytical Gaussian approximation, we can formally incorporate the uncertainty about intermediate regressor values, thus updating the uncertainty on the current prediction
Healing the Relevance Vector Machine through Augmentation
The Relevance Vector Machine (RVM) is a sparse approximate Bayesian kernel method. It provides full predictive distributions for test cases. However, the predictive uncertainties have the unintuitive property, that emphthey get smaller the further you move away from the training cases. We give a thorough analysis. Inspired by the analogy to non-degenerate Gaussian Processes, we suggest augmentation to solve the problem. The purpose of the resulting model, RVM*, is primarily to corroborate the theoretical and experimental analysis. Although RVM* could be used in practical applications, it is no longer a truly sparse model. Experiments show that sparsity comes at the expense of worse predictive distributions
NMR Investigation of the Low Temperature Dynamics of solid 4He doped with 3He impurities
The lattice dynamics of solid 4He has been explored using pulsed NMR methods
to study the motion of 3He impurities in the temperature range where
experiments have revealed anomalies attributed to superflow or unexpected
viscoelastic properties of the solid 4He lattice. We report the results of
measurements of the nuclear spin-lattice and spin-spin relaxation times that
measure the fluctuation spectrum at high and low frequencies, respectively, of
the 3He motion that results from quantum tunneling in the 4He matrix. The
measurements were made for 3He concentrations 16<x_3<2000 ppm. For 3He
concentrations x_3 = 16 ppm and 24 ppm, large changes are observed for both the
spin-lattice relaxation time T_1 and the spin-spin relaxation time T_2 at
temperatures close to those for which the anomalies are observed in
measurements of torsional oscillator responses and the shear modulus. These
changes in the NMR relaxation rates were not observed for higher 3He
concentrations.Comment: 23 pages, 10 figure
Lessons on Economics and Political Economy from the Soviet Tragedy
This paper explores the economics and politics of the tragic Soviet experiment with socialism. Beginning with the period of “War Communism” between 1917 and 1921, the Soviet government’s attempt to implement socialism failed to achieve its stated objectives, namely to create social harmony, eliminate class struggle, and to unleash advanced material production. It attempted to achieve these ends by abolishing private property and market prices in the means of production, eliminating the incentives and information necessary to guide production in an efficient manner. The unintended political and economic results were disastrous, leading to tyranny, famine, and oppression. Failing to achieve its stated objectives, after 1921 the Soviet Communist regime continued to survive only by changing the meaning of socialism. De jure socialism in the Soviet Union continued to mean the abolition of private property and market competition of the means of production. However, de facto, this meant the monetization of political control over resources, via black market exchange, in a shortage economy, and competition for leadership in the Communist Party to control such resources. As a result, the Soviet political system failed to achieve the ideals of socialism on its own terms, not only because central planning eliminated the institutional conditions necessary to allocate resources productively, but also because central planning created the institutional conditions by which the worst men, those most able and willing to exercise force in a totalitarian environment, got to the top of the political hierarchy
On the completeness of impulsive gravitational wave space-times
We consider a class of impulsive gravitational wave space-times, which
generalize impulsive pp-waves. They are of the form ,
where is a Riemannian manifold of arbitrary dimension and carries
the line element with the line
element of and the Dirac measure. We prove a completeness result
for such space-times with complete Riemannian part .Comment: 13 pages, minor changes suggested by the referee
Propagation of Uncertainty in Bayesian Kernel Models - Application to Multiple-Step Ahead Forecasting
The object of Bayesian modelling is the predictive distribution, which in a forecasting scenario enables improved estimates of forecasted values and their uncertainties. In this paper we focus on reliably estimating the predictive mean and variance of forecasted values using Bayesian kernel based models such as the Gaussian Process and the Relevance Vector Machine. We derive novel analytic expressions for the predictive mean and variance for Gaussian kernel shapes under the assumption of a Gaussian input distribution in the static case, and of a recursive Gaussian predictive density in iterative forecasting. The capability of the method is demonstrated for forecasting of time-series and compared to approximate methods
Nonparametric Bayesian Mixed-effect Model: a Sparse Gaussian Process Approach
Multi-task learning models using Gaussian processes (GP) have been developed
and successfully applied in various applications. The main difficulty with this
approach is the computational cost of inference using the union of examples
from all tasks. Therefore sparse solutions, that avoid using the entire data
directly and instead use a set of informative "representatives" are desirable.
The paper investigates this problem for the grouped mixed-effect GP model where
each individual response is given by a fixed-effect, taken from one of a set of
unknown groups, plus a random individual effect function that captures
variations among individuals. Such models have been widely used in previous
work but no sparse solutions have been developed. The paper presents the first
sparse solution for such problems, showing how the sparse approximation can be
obtained by maximizing a variational lower bound on the marginal likelihood,
generalizing ideas from single-task Gaussian processes to handle the
mixed-effect model as well as grouping. Experiments using artificial and real
data validate the approach showing that it can recover the performance of
inference with the full sample, that it outperforms baseline methods, and that
it outperforms state of the art sparse solutions for other multi-task GP
formulations.Comment: Preliminary version appeared in ECML201
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