Self-consistent redshift estimation using correlation functions without a spectroscopic reference sample

We present a new method to estimate redshift distributions and galaxy-dark matter bias parameters using correlation functions in a fully data driven and self-consistent manner. Unlike other machine learning, template, or correlation redshift methods, this approach does not require a reference sample with known redshifts. By measuring the projected cross- and auto- correlations of different galaxy sub-samples, e.g., as chosen by simple cells in color-magnitude space, we are able to estimate the galaxy-dark matter bias model parameters, and the shape of the redshift distributions of each sub-sample. This method fully marginalises over a flexible parameterisation of the redshift distribution and galaxy-dark matter bias parameters of sub-samples of galaxies, and thus provides a general Bayesian framework to incorporate redshift uncertainty into the cosmological analysis in a data-driven, consistent, and reproducible manner. This result is improved by an order of magnitude by including cross-correlations with the CMB and with galaxy-galaxy lensing. We showcase how this method could be applied to real galaxies. By using idealised data vectors, in which all galaxy-dark matter model parameters and redshift distributions are known, this method is demonstrated to recover unbiased estimates on important quantities, such as the offset $\Delta_z$ between the mean of the true and estimated redshift distribution and the 68\% and 95\% and 99.5\% widths of the redshift distribution to an accuracy required by current and future surveys.Comment: 20pages, 11 figures, text revised for clarification, version accepted by journal, conclusions unchange

Does stellar mass assembly history vary with environment?

Using the publicly available VESPA database of SDSS Data Release 7 spectra, we calculate the stellar Mass Weighted Age (hereafter MWA) as a function of local galaxy density and dark matter halo mass. We compare our results with semi-analytic models from the public Millennium Simulation. We find that the stellar MWA has a large scatter which is inherent in the data and consistent with that seen in semi-analytic models. The stellar MWA is consistent with being independent (to first order) with local galaxy density, which is also seen in semi-analytic models. As a function of increasing dark matter halo mass (using the SDSS New York Value Added Group catalogues), we find that the average stellar MWA for member galaxies increases, which is again found in semi-analytic models. Furthermore we use public dark matter Mass Accretion History (MAH) code calibrated on simulations, to calculate the dark matter Mass Weighted Age as a function of dark matter halo mass. In agreement with earlier analyses, we find that the stellar MWA and the dark matter MWA are anti correlated for large mass halos, i.e, dark matter accretion does not seem to be the primary factor in determining when stellar mass was compiled. This effect can be described by down-sizing.Comment: 11 pages, 3 figures, submitted to MNRA

Learning from the machine: interpreting machine learning algorithms for point- and extended- source classification

We investigate star-galaxy classification for astronomical surveys in the context of four methods enabling the interpretation of black-box machine learning systems. The first is outputting and exploring the decision boundaries as given by decision tree based methods, which enables the visualization of the classification categories. Secondly, we investigate how the Mutual Information based Transductive Feature Selection (MINT) algorithm can be used to perform feature pre-selection. If one would like to provide only a small number of input features to a machine learning classification algorithm, feature pre-selection provides a method to determine which of the many possible input properties should be selected. Third is the use of the tree-interpreter package to enable popular decision tree based ensemble methods to be opened, visualized, and understood. This is done by additional analysis of the tree based model, determining not only which features are important to the model, but how important a feature is for a particular classification given its value. Lastly, we use decision boundaries from the model to revise an already existing method of classification, essentially asking the tree based method where decision boundaries are best placed and defining a new classification method. We showcase these techniques by applying them to the problem of star-galaxy separation using data from the Sloan Digital Sky Survey (hereafter SDSS). We use the output of MINT and the ensemble methods to demonstrate how more complex decision boundaries improve star-galaxy classification accuracy over the standard SDSS frames approach (reducing misclassifications by up to $\approx33\%$). We then show how tree-interpreter can be used to explore how relevant each photometric feature is when making a classification on an object by object basis.Comment: 12 pages, 8 figures, 8 table

Feature importance for machine learning redshifts applied to SDSS galaxies

We present an analysis of importance feature selection applied to photometric redshift estimation using the machine learning architecture Decision Trees with the ensemble learning routine Adaboost (hereafter RDF). We select a list of 85 easily measured (or derived) photometric quantities (or `features') and spectroscopic redshifts for almost two million galaxies from the Sloan Digital Sky Survey Data Release 10. After identifying which features have the most predictive power, we use standard artificial Neural Networks (aNN) to show that the addition of these features, in combination with the standard magnitudes and colours, improves the machine learning redshift estimate by 18% and decreases the catastrophic outlier rate by 32%. We further compare the redshift estimate using RDF with those from two different aNNs, and with photometric redshifts available from the SDSS. We find that the RDF requires orders of magnitude less computation time than the aNNs to obtain a machine learning redshift while reducing both the catastrophic outlier rate by up to 43%, and the redshift error by up to 25%. When compared to the SDSS photometric redshifts, the RDF machine learning redshifts both decreases the standard deviation of residuals scaled by 1/(1+z) by 36% from 0.066 to 0.041, and decreases the fraction of catastrophic outliers by 57% from 2.32% to 0.99%.Comment: 10 pages, 4 figures, updated to match version accepted in MNRA

Tuning target selection algorithms to improve galaxy redshift estimates

We showcase machine learning (ML) inspired target selection algorithms to determine which of all potential targets should be selected first for spectroscopic follow up. Efficient target selection can improve the ML redshift uncertainties as calculated on an independent sample, while requiring less targets to be observed. We compare the ML targeting algorithms with the Sloan Digital Sky Survey (SDSS) target order, and with a random targeting algorithm. The ML inspired algorithms are constructed iteratively by estimating which of the remaining target galaxies will be most difficult for the machine learning methods to accurately estimate redshifts using the previously observed data. This is performed by predicting the expected redshift error and redshift offset (or bias) of all of the remaining target galaxies. We find that the predicted values of bias and error are accurate to better than 10-30% of the true values, even with only limited training sample sizes. We construct a hypothetical follow-up survey and find that some of the ML targeting algorithms are able to obtain the same redshift predictive power with 2-3 times less observing time, as compared to that of the SDSS, or random, target selection algorithms. The reduction in the required follow up resources could allow for a change to the follow-up strategy, for example by obtaining deeper spectroscopy, which could improve ML redshift estimates for deeper test data.Comment: 16 pages, 9 figures, updated to match MNRAS accepted version. Minor text changes, results unchange

Combining clustering and abundances of galaxy clusters to test cosmology and primordial non-Gaussianity

We present the clustering of galaxy clusters as a useful addition to the common set of cosmological observables. The clustering of clusters probes the large-scale structure of the Universe, extending galaxy clustering analysis to the high-peak, high-bias regime. Clustering of galaxy clusters complements the traditional cluster number counts and observable-mass relation analyses, significantly improving their constraining power by breaking existing calibration degeneracies. We use the maxBCG galaxy clusters catalogue to constrain cosmological parameters and cross-calibrate the mass-observable relation, using cluster abundances in richness bins and weak-lensing mass estimates. We then add the redshift-space power spectrum of the sample, including an effective modelling of the weakly non-linear contribution and allowing for an arbitrary photometric redshift smoothing. The inclusion of the power spectrum data allows for an improved self-calibration of the scaling relation. We find that the inclusion of the power spectrum typically brings a $\sim 50$ per cent improvement in the errors on the fluctuation amplitude $\sigma_8$ and the matter density $\Omega_{\mathrm{m}}$. Finally, we apply this method to constrain models of the early universe through the amount of primordial non-Gaussianity of the local type, using both the variation in the halo mass function and the variation in the cluster bias. We find a constraint on the amount of skewness $f_{\mathrm{NL}} = 12 \pm 157$ ($1\sigma$) from the cluster data alone.Comment: 12 pages, 10 figures, 2 tables. Minor changes to match published version on MNRA

Anomaly detection for machine learning redshifts applied to SDSS galaxies

We present an analysis of anomaly detection for machine learning redshift estimation. Anomaly detection allows the removal of poor training examples, which can adversely influence redshift estimates. Anomalous training examples may be photometric galaxies with incorrect spectroscopic redshifts, or galaxies with one or more poorly measured photometric quantity. We select 2.5 million 'clean' SDSS DR12 galaxies with reliable spectroscopic redshifts, and 6730 'anomalous' galaxies with spectroscopic redshift measurements which are flagged as unreliable. We contaminate the clean base galaxy sample with galaxies with unreliable redshifts and attempt to recover the contaminating galaxies using the Elliptical Envelope technique. We then train four machine learning architectures for redshift analysis on both the contaminated sample and on the preprocessed 'anomaly-removed' sample and measure redshift statistics on a clean validation sample generated without any preprocessing. We find an improvement on all measured statistics of up to 80% when training on the anomaly removed sample as compared with training on the contaminated sample for each of the machine learning routines explored. We further describe a method to estimate the contamination fraction of a base data sample.Comment: 13 pages, 8 figures, 1 table, minor text updates to macth MNRAS accepted versio

Implications of multiple high-redshift galaxy clusters

To date, 14 high-redshift (z>1.0) galaxy clusters with mass measurements have been observed, spectroscopically confirmed and are reported in the literature. These objects should be exceedingly rare in the standard LCDM model. We conservatively approximate the selection functions of these clusters' parent surveys, and quantify the tension between the abundances of massive clusters as predicted by the standard LCDM model and the observed ones. We alleviate the tension considering non-Gaussian primordial perturbations of the local type, characterized by the parameter fnl and derive constraints on fnl arising from the mere existence of these clusters. At the 95% confidence level, fnl>467 with cosmological parameters fixed to their most likely WMAP5 values, or fnl > 123 (at 95% confidence) if we marginalize over WMAP5 parameters priors. In combination with fnl constraints from Cosmic Microwave Background and halo bias, this determination implies a scale-dependence of fnl at approx. 3 sigma. Given the assumptions made in the analysis, we expect any future improvements to the modeling of the non-Gaussian mass function, survey volumes, or selection functions to increase the significance of fnl>0 found here. In order to reconcile these massive, high-z clusters with an fnl=0, their masses would need to be systematically lowered by 1.5 sigma or the sigma8 parameter should be approx. 3 sigma higher than CMB (and large-scale structure) constraints. The existence of these objects is a puzzle: it either represents a challenge to the LCDM paradigme or it is an indication that the mass estimates of clusters is dramatically more uncertain than we think.Comment: 11 pages, 7 figures, modified to match published versio

Stacking for machine learning redshifts applied to SDSS galaxies

We present an analysis of a general machine learning technique called 'stacking' for the estimation of photometric redshifts. Stacking techniques can feed the photometric redshift estimate, as output by a base algorithm, back into the same algorithm as an additional input feature in a subsequent learning round. We shown how all tested base algorithms benefit from at least one additional stacking round (or layer). To demonstrate the benefit of stacking, we apply the method to both unsupervised machine learning techniques based on self-organising maps (SOMs), and supervised machine learning methods based on decision trees. We explore a range of stacking architectures, such as the number of layers and the number of base learners per layer. Finally we explore the effectiveness of stacking even when using a successful algorithm such as AdaBoost. We observe a significant improvement of between 1.9% and 21% on all computed metrics when stacking is applied to weak learners (such as SOMs and decision trees). When applied to strong learning algorithms (such as AdaBoost) the ratio of improvement shrinks, but still remains positive and is between 0.4% and 2.5% for the explored metrics and comes at almost no additional computational cost.Comment: 13 pages, 3 tables, 7 figures version accepted by MNRAS, minor text updates. Results and conclusions unchange