882 research outputs found
A unifying probabilistic perspective for spectral dimensionality reduction: Insights and new models
We introduce a new perspective on spectral dimensionality reduction which
views these methods as Gaussian Markov random fields (GRFs). Our unifying
perspective is based on the maximum entropy principle which is in turn inspired
by maximum variance unfolding. The resulting model, which we call maximum
entropy unfolding (MEU) is a nonlinear generalization of principal component
analysis. We relate the model to Laplacian eigenmaps and isomap. We show that
parameter fitting in the locally linear embedding (LLE) is approximate maximum
likelihood MEU. We introduce a variant of LLE that performs maximum likelihood
exactly: Acyclic LLE (ALLE). We show that MEU and ALLE are competitive with the
leading spectral approaches on a robot navigation visualization and a human
motion capture data set. Finally the maximum likelihood perspective allows us
to introduce a new approach to dimensionality reduction based on L1
regularization of the Gaussian random field via the graphical lasso
Bottom-up data Trusts: Disturbing the âone size fits allâ approach to data governance
Key Points
The current lack of legal mechanisms that may
plausibly empower us, data subjects to âtake the
reinsâ of our personal data leaves us vulnerable.
Recent regulatory endeavours to curb contractual
freedom acknowledge this vulnerability but cannot,
by themselves, remedy itânor can data
ownership. The latter is both unlikely and inadequate
as an answer to the problems at stake.
We argue that the power that stems from aggregated
data should be returned to individuals
through the legal mechanism of Trusts.
Bound by a fiduciary obligation of undivided loyalty,
the data trustees would exercise the data
rights conferred by the GDPR (or other topdown
regulation) on behalf of the Trustâs beneficiaries.
The data trustees would hence be placed
in a position where they can negotiate data use in
conformity with the Trustâs terms, thus introducing
an independent intermediary between data
subjects and data collectors.
Unlike the current âone size fits allâ approach to
data governance, there should be a plurality of
Trusts, allowing data subjects to choose a Trust
that reflects their aspirations, and to switch
Trusts when needed. Data Trusts may arise out
of publicly or privately funded initiatives.
By potentially facilitating access to âpre-authorizedâ,
aggregated data (consent would be negotiated
on a collective basis), our data Trust
proposal may remove key obstacles to the realization
of the potential underlying large datasets
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Computationally Efficient Convolved Multiple Output Gaussian Processes
Recently there has been an increasing interest in methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes perspective, the problem reduces to specifying an appropriate covariance function that, whilst being positive semi-definite, captures the dependencies between all the data points and across all the outputs. One approach to account for non-trivial correlations between outputs employs convolution processes. Under a latent function interpretation of the convolution transform we establish dependencies between output variables. The main drawbacks of this approach are the associated computational and storage demands. In this paper we address these issues. We present different sparse approximations for dependent output Gaussian processes constructed through the convolution formalism. We exploit the conditional independencies present naturally in the model. This leads to a form of the covariance similar in spirit to the so called PITC and FITC approximations for a single output. We show experimental results with synthetic and real data, in particular, we show results in pollution prediction, school exams score prediction and gene expression data
Gaussian Process Latent Force Models for Learning and Stochastic Control of Physical Systems
© 1963-2012 IEEE. This paper is concerned with learning and stochastic control in physical systems that contain unknown input signals. These unknown signals are modeled as Gaussian processes (GP) with certain parameterized covariance structures. The resulting latent force models can be seen as hybrid models that contain a first-principle physical model part and a nonparametric GP model part. We briefly review the statistical inference and learning methods for this kind of models, introduce stochastic control methodology for these models, and provide new theoretical observability and controllability results for them.The work of S. Sarkka was financially supported by the Academy of Finland. The work of M. A. Alvarez was supported in part by the EPSRC under Research Project EP/N014162/1
Variational inference for latent variables and uncertain inputs in Gaussian processes
The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where the latent projection variables are maximised over rather than integrated out. In this paper we present a Bayesian method for training GP-LVMs by introducing a non-standard variational inference framework that allows to approximately integrate out the latent variables and subsequently train a GP-LVM by maximising an analytic lower bound on the exact marginal likelihood. We apply this method for learning a GP-LVM from i.i.d. observations and for learning non-linear dynamical systems where the observations are temporally correlated. We show that a benefit of the variational Bayesian procedure is its robustness to overfitting and its ability to automatically select the dimensionality of the non-linear latent space. The resulting framework is generic, flexible and easy to extend for other purposes, such as Gaussian process regression with uncertain or partially missing inputs. We demonstrate our method on synthetic data and standard machine learning benchmarks, as well as challenging real world datasets, including high resolution video data.This research was partially funded by the European research project EU FP7-ICT (Project
Ref 612139 \WYSIWYD"), the Greek State Scholarships Foundation (IKY) and the University
of She eld Moody endowment fund. We also thank Colin Litster and \Fit Fur Life"
for allowing us to use their video les as datasets
Overlapping Mixtures of Gaussian Processes for the data association problem
In this work we introduce a mixture of GPs to address the data association
problem, i.e. to label a group of observations according to the sources that
generated them. Unlike several previously proposed GP mixtures, the novel
mixture has the distinct characteristic of using no gating function to
determine the association of samples and mixture components. Instead, all the
GPs in the mixture are global and samples are clustered following
"trajectories" across input space. We use a non-standard variational Bayesian
algorithm to efficiently recover sample labels and learn the hyperparameters.
We show how multi-object tracking problems can be disambiguated and also
explore the characteristics of the model in traditional regression settings
Recurrent Gaussian processes
We define Recurrent Gaussian Processes (RGP) models, a general family of
Bayesian nonparametric models with recurrent GP priors which are able to learn
dynamical patterns from sequential data. Similar to Recurrent Neural Networks
(RNNs), RGPs can have different formulations for their internal states,
distinct inference methods and be extended with deep structures. In such
context, we propose a novel deep RGP model whose autoregressive states are
latent, thereby performing representation and dynamical learning
simultaneously. To fully exploit the Bayesian nature of the RGP model we
develop the Recurrent Variational Bayes (REVARB) framework, which enables
efficient inference and strong regularization through coherent propagation of
uncertainty across the RGP layers and states. We also introduce a RGP extension
where variational parameters are greatly reduced by being reparametrized
through RNN-based sequential recognition models. We apply our model to the
tasks of nonlinear system identification and human motion modeling. The
promising obtained results indicate that our RGP model maintains its highly
flexibility while being able to avoid overfitting and being applicable even
when larger datasets are not available
Validation of nonlinear PCA
Linear principal component analysis (PCA) can be extended to a nonlinear PCA
by using artificial neural networks. But the benefit of curved components
requires a careful control of the model complexity. Moreover, standard
techniques for model selection, including cross-validation and more generally
the use of an independent test set, fail when applied to nonlinear PCA because
of its inherent unsupervised characteristics. This paper presents a new
approach for validating the complexity of nonlinear PCA models by using the
error in missing data estimation as a criterion for model selection. It is
motivated by the idea that only the model of optimal complexity is able to
predict missing values with the highest accuracy. While standard test set
validation usually favours over-fitted nonlinear PCA models, the proposed model
validation approach correctly selects the optimal model complexity.Comment: 12 pages, 5 figure
Experimental GHZ Entanglement beyond Qubits
The Greenberger-Horne-Zeilinger (GHZ) argument provides an all-or-nothing
contradiction between quantum mechanics and local-realistic theories. In its
original formulation, GHZ investigated three and four particles entangled in
two dimensions only. Very recently, higher dimensional contradictions
especially in three dimensions and three particles have been discovered but it
has remained unclear how to produce such states. In this article we
experimentally show how to generate a three-dimensional GHZ state from
two-photon orbital-angular-momentum entanglement. The first suggestion for a
setup which generates three-dimensional GHZ entanglement from these entangled
pairs came from using the computer algorithm Melvin. The procedure employs
novel concepts significantly beyond the qubit case. Our experiment opens up the
possibility of a truly high-dimensional test of the GHZ-contradiction which,
interestingly, employs non-Hermitian operators.Comment: 6+6 pages, 8 figure
Mindfulness based interventions in multiple sclerosis: a systematic review
<b>Background</b> Multiple sclerosis (MS) is a stressful condition; depression, anxiety, pain and fatigue are all common problems. Mindfulness based interventions (MBIs) mitigate stress and prevent relapse in depression and are increasingly being used in healthcare. However, there are currently no systematic reviews of MBIs in people with MS. This review aims to evaluate the effectiveness of MBIs in people with MS.<p></p>
<b>Methods</b> Systematic searches were carried out in seven major databases, using both subject headings and key words. Papers were screened, data extracted, quality appraised, and analysed by two reviewers independently, using predefined criteria. Study quality was assessed using the Cochrane Collaboration risk of bias tool. Perceived stress was the primary outcome. Secondary outcomes include mental health, physical health, quality of life, and health service utilisation. Statistical meta-analysis was not possible. Disagreements were adjudicated by a third party reviewer.<p></p>
<b>Results</b> Three studies (nâ=â183 participants) were included in the final analysis. The studies were undertaken in Wales (nâ=â16, randomised controlled trial - (RCT)), Switzerland (nâ=â150, RCT), and the United States (nâ=â17, controlled trial). 146 (80%) participants were female; mean age (SD) was 48.6 (9.4) years. Relapsing remitting MS was the main diagnostic category (nâ=â123, 67%); 43 (26%) had secondary progressive disease; and the remainder were unspecified. MBIs lasted 6â8Â weeks; attrition rates were variable (5-43%); all employed pre- post- measures; two had longer follow up; one at 3, and one at 6 months. Socio-economic status of participants was not made explicit; health service utilisation and costs were not reported. No study reported on perceived stress. All studies reported quality of life (QOL), mental health (anxiety and depression), physical (fatigue, standing balance, pain), and psychosocial measures. Statistically significant beneficial effects relating to QOL, mental health, and selected physical health measures were sustained at 3- and 6- month follow up.<p></p>
<b>Conclusion</b> From the limited data available, MBIs may benefit some MS patients in terms of QOL, mental health, and some physical health measures. Further studies are needed to clarify how MBIs might best serve the MS population.<p></p>
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