A sparse Gaussian process framework for photometric redshift estimation

Abstract

Accurate photometric redshifts are a lynchpin for many future experiments to pin down the cosmological model and for studies of galaxy evolution. In this study, a novel sparse regression framework for photometric redshift estimation is presented. Synthetic dataset simulating the Euclid survey and real data from SDSS DR12 are used to train and test the proposed models. We show that approaches which include careful data preparation and model design offer a significant improvement in comparison with several competing machine learning algorithms. Standard implementations of most regression algorithms use the minimization of the sum of squared errors as the objective function. For redshift inference, this induces a bias in the posterior mean of the output distribution, which can be problematic. In this paper we directly minimize the target metric ∆z = (z s − z p )/(1 + z s ) and address the bias problem via a distribution-based weighting scheme, incorporated as part of the optimization objective. The results are compared with other machine learning algorithms in the field such as Artificial Neural Networks (ANN), Gaussian Processes (GPs) and sparse GPs. The proposed framework reaches a mean absolute ∆z = 0.0026(1 + z s ), over the redshift range of 0 z s 2 on the simulated data, and ∆z = 0.0178(1 + z s ) over the entire redshift range on the SDSS DR12 survey, outperforming the standard ANNZ used in the literature. We also investigate how the relative size of the training sample affects the photometric redshift accuracy. We find that a training sample of >30 per cent of total sample size, provides little additional constraint on the photometric redshifts, and note that our GP formalism strongly outperforms ANNZ in the sparse data regime for the simulated data set.

Using Sparse Gaussian Processes for Predicting Robust Inertial Confinement Fusion Implosion Yields

“…A higher m corresponds to higher model complexity and longer training times. Figure 2 shows algorithm performance as a function of m; best performance is achieved for m ≈ 10 − 100, in line with findings in [6], [7].…”

“…GPz is a sparse Gaussian process based code, a fast and a scalable approximation of a full Gaussian Process [22], with the added feature of being able to produce input-dependent variance estimations (heteroscedastic noise). For the full details of the algorithm see [6], [7], [23], but we summarise the main details here. The model assumes that the probability of the observing a target variable y given the vector input x is p(y|x) = N (µ(x), σ(x) 2 ).…”

“…Unless otherwise stated, we use the settings in Table I (see [6], [7] for precise definitions and interpretations). GPz requires very little fine-tuning.…”

“…2) Cost-Sensitive Learning: Figure 3 shows a comparison of GPz w = 1 ('normal' in [6]) and using cost-sensitive learning (w = √ Y ). Figure 5 and 6 show the bias (mean of Y test − Y prediction ) and root-mean-squared-error (RMSE) on the predictions, illustrating that performance in higher yield parts of parameter space (logY ∼ 15 − 17) is indeed improved at the cost of performance in lower yield regions.…”

Estimating dayside effective temperatures of hot Jupiters and associated uncertainties through Gaussian process regression

“…GPs have gained traction in the astrophysical community in recent years, being employed to fit stellar oscillations (Brewer & Stello 2009), model the occurrence rate density of exoplanets (Foreman-Mackey et al 2014), and estimate photometric redshifts (Almosallam et al 2016), among other applications. In the field of exoplanetary atmospheres, GPs have been used to account for instrument systematics in primary transit and secondary eclipse light curves (Gibson et al 2012;Evans et al 2015), although further applications remain to be explored.…”