Focused multi-task learning in a Gaussian process framework

Leen, Gayle; Peltonen, Jaakko; Kaski, Samuel

doi:10.1007/s10994-012-5302-y

Cited by 21 publications

(19 citation statements)

References 10 publications

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“…As the dataset with stronger significance might force its own features on to the reconstruction of less stronger dataset. Such a phenomenon is called negative transfer (please refer to [62][63][64] for extensive discussion on this issue). We demonstrate this effect in Section 4.3.…”

Section: Disadvantages/cautionsmentioning

confidence: 99%

An improved model-independent assessment of the late-time cosmic expansion

Haridasu

Luković

Moresco

et al. 2018

J. Cosmol. Astropart. Phys.

140

105

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In the current work, we have implemented an extension of the standard Gaussian Process formalism, namely the Multi-Task Gaussian Process with the ability to perform a joint learning of several cosmological data simultaneously. We have utilised the "low-redshift" expansion rate data from Supernovae Type-Ia (SN), Baryon Acoustic Oscillations (BAO) and Cosmic Chronometers (CC) data in a joint analysis. We have tested several possible models of covariance functions and find very consistent estimates for cosmologically relevant parameters. In the current formalism, we also find provisions for heuristic arguments which allow us to select the best-suited kernel for the reconstruction of expansion rate data. We also utilised our method to account for systematics in CC data and find an estimate of H 0 = 68.52 +0.94+2.51(sys) −0.94 km/s Mpc −1 and a corresponding r d = 145.61 +2.82 −2.82−4.3(sys)Mpc as our primary result. Subsequently, we find constraints on the present deceleration parameter q 0 = −0.52 ± 0.06 and the transition redshift z T = 0.64 +0.12 −0.09 . All the estimated cosmological parameters are found to be in good agreement with the standard ΛCDM scenario. Including the local model-independent H 0 estimate to the analysis we find H 0 = 71.40 +0.30+1.65(sys) −0.30 km/s Mpc −1 and the corresponding r d = 141.29 +1.31 −1.31−2.63(sys) Mpc. Also, the constraints on r d H 0 remain consistent throughout our analysis and also with the model-dependent CMB estimate. Using the Om(z) diagnostic, we find that the concordance model is very consistent within the redshift range z 2 and mildly discrepant for z 2.

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Section: Disadvantages/cautionsmentioning

confidence: 99%

An improved model-independent assessment of the late-time cosmic expansion

Haridasu

Luković

Moresco

et al. 2018

J. Cosmol. Astropart. Phys.

140

105

View full text Add to dashboard Cite

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“…They are based on approaches such as sparse linear combination of independent single-task GPs [41], multi-kernel method [42], convolved latent processes [43], and spectral mixture kernels [44]. There are also asymmetric multitask GPs, which model several tasks together with the objective of enhancing the predictions of only a subset of the tasks by transferring information from other tasks to them [45]. Readers who are interested in learning more about advanced multitask GPs are encourage to read the article by Liu et al [46].…”

Section: Multitask Learningmentioning

confidence: 99%

Gaussian Processes for Vegetation Parameter Estimation from Hyperspectral Data with Limited Ground Truth

2019

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An important application of airborne- and satellite-based hyperspectral imaging is the mapping of the spatial distribution of vegetation biophysical and biochemical parameters in an environment. Statistical models, such as Gaussian processes, have been very successful for modeling vegetation parameters from captured spectra, however their performance is highly dependent on the amount of available ground truth. This is a problem because it is generally expensive to obtain ground truth information due to difficulties and costs associated with sample collection and analysis. In this paper, we present two Gaussian processes based approaches for improving the accuracy of vegetation parameter retrieval when ground truth is limited. The first is the adoption of covariance functions based on well-established metrics, such as, spectral angle and spectral correlation, which are known to be better measures of similarity for spectral data owing to their resilience to spectral variabilities. The second is the joint modeling of related vegetation parameters by multitask Gaussian processes so that the prediction accuracy of the vegetation parameter of interest can be improved with the aid of related vegetation parameters for which a larger set of ground truth is available. We experimentally demonstrate the efficacy of the proposed methods against existing approaches on three real-world hyperspectral datasets and one synthetic dataset.

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“…We will use a hatk(s) to denote the spectral density of a covariance function k(τ ) in the frequency domain. Using the following definition, the spectral density of kernel function k(τ ) can be given by its Fourier transform:k (s) = k(τ ) e −2πτ sι dτ (7) whereι is the imaginary number. Furthermore, the inverse Fourier transform of spectral densityk(s) is the original kernel function k(τ ).…”

Section: Spectral Mixture Kernelsmentioning

confidence: 99%

“…The extension of GPs to multiple sources of data is known as multi-task Gaussian processes (MTGPs) [3]. MTGPs model temporal or spatial relationships among infinitely many random variables, as scalar GPs, but also account for the statistical dependence across different sources of data (or tasks) [3,4,5,6,7,8,9]. How to choose an appropriate kernel to jointly model the cross covariance between tasks and auto-covariance within each task is the core aspect of MTGPs design [3,10,11,12,5,13,14].…”

Section: Introductionmentioning

confidence: 99%

Generalized Convolution Spectral Mixture for Multi-Task Gaussian Processes

Chen¹,

Laarhoven²,

Groot³

et al. 2018

Preprint

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Multi-Task Gaussian processes (MTGPs) have shown a significant progress both in expressiveness and interpretation of the relatedness between different tasks: from linear combinations of independent single-output Gaussian processes (GPs), through the direct modeling of the cross-covariances such as spectral mixture kernels with phase shift, to the design of multivariate covariance functions based on spectral mixture kernels which model delays among tasks in addition to phase differences, and which provide a parametric interpretation of the relatedness across tasks. In this paper we further extend expressiveness and interpretability of MTGPs models and introduce a new family of kernels capable to model nonlinear correlations between tasks as well as dependencies between component, including time and phase delay. Specifically, we use generalized convolution spectral mixture kernels for modeling dependencies at component level, and coupling coregionalization for discovering task level correlations. The proposed kernels for MTGP are validated on artificial data and compared with existing MTGPs methods on three real-world experiments. Results indicate the benefits of our more expressive representation with respect to performance and interpretability.

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Focused multi-task learning in a Gaussian process framework

Cited by 21 publications

References 10 publications

An improved model-independent assessment of the late-time cosmic expansion

An improved model-independent assessment of the late-time cosmic expansion

Gaussian Processes for Vegetation Parameter Estimation from Hyperspectral Data with Limited Ground Truth

Generalized Convolution Spectral Mixture for Multi-Task Gaussian Processes

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