Search

Galaxy clusters are one of the most powerful probes to study extensions of General Relativity and the Standard Cosmological Model. Upcoming surveys like the Vera Rubin Observatory's Legacy Survey of Space and Time are expected to revolutionise the field, by enabling the analysis of cluster samples of unprecedented size and quality. To reach this era of high-precision cluster cosmology, the mitigation of sources of systematic error is crucial. A particularly important challenge is bias in cluster mass measurements induced by inaccurate photometric redshift estimates of source galaxies. This work proposes a method to optimise the source sample selection in cluster weak lensing analyses drawn from wide-field survey lensing catalogs to reduce the bias on reconstructed cluster masses. We use a combinatorial optimisation scheme and methods from variational inference to select galaxies in latent space to produce a probabilistic galaxy source sample catalog for highly accurate cluster mass estimation. We show that our method reduces the critical surface mass density $\Sigma_{\rm crit}$ modelling bias on the 60-70% level, while maintaining up to 90% of galaxies. We highlight that our methodology has applications beyond cluster mass estimation as an approach to jointly combine galaxy selection and model inference under sources of systematics., Comment: 10 pages, 3 figures, 2 tables, submitted to the MNRAS, comments welcome

We present a systematic study of cosmological parameter bias in weak lensing and large-scale structure analyses for upcoming imaging surveys induced by the interplay of intrinsic alignments (IA) and photometric redshift (photo-z) model mis-specification error. We first examine the degeneracies between the parameters of the Tidal Alignment - Tidal Torquing (TATT) model for IA and of a photo-z model including a mean shift ($\Delta \bar{z}$) and variance ($\sigma_{z}$) for each tomographic bin of lenses and sources, under a variety of underlying true IA behaviors. We identify strong degeneracies between: (1) the redshift scaling of the tidal alignment amplitude and the mean shift and variances of source bins, (2) the redshift scaling of the tidal torquing amplitude and the variance of the lowest-$z$ source bin, and (3) the IA source density weighting and the mean shift and variance of several source bins. We then use this information to guide our exploration of the level of cosmological parameter bias which can be induced given incorrect modelling of IA, photo-z, or both. We find that marginalizing over all the parameters of TATT is generally sufficient to preclude cosmological parameter bias in the scenarios we consider. However, this does not necessarily mean that IA and photo-z parameters are themselves unbiased, nor does it mean that the best-fit model is a good fit to the data. We also find scenarios where the inferred parameters produce $\chi^2_{\rm DOF}$ values indicative of a good fit but cosmological parameter bias is significant, particularly when the IA source density weighting parameter is not marginalized over., Comment: 20 pages, 13 figures. Updated to match accepted version

We present cosmology results obtained from a blind joint analysis of the abundance, projected clustering, and weak lensing of galaxy clusters measured from the Sloan Digital Sky Survey (SDSS) redMaPPer cluster catalog and the Hyper-Suprime Cam (HSC) Year3 shape catalog. We present a full-forward model for the cluster observables, which includes empirical modeling for the anisotropic boosts on the lensing and clustering signals of optical clusters. We validate our analysis via mock cluster catalogs which include observational systematics, such as the projection effect and the effect of baryonic feedback, and find that our analysis can robustly constrain cosmological parameters in an unbiased manner without any informative priors on our model parameters. The joint analysis of our observables in the context of the flat $\Lambda$CDM model results in cosmological constraints for $S_8\equiv \sigma_8 \sqrt{\Omega_{\rm m} / 0.3}=0.816^{+0.041}_{-0.039}$. Our result is consistent with the $S_8$ inference from other cosmic microwave background- and large scale structure-based cosmology analyses, including the result from the \emph{Planck} 2018 primary CMB analysis., Comment: v1: 22 pages, 15 figures, Comments welcome

We use the Sloan Digital Sky Survey (SDSS) BOSS galaxies and their overlap with approximately 416 sq. degree of deep $grizy$-band imaging from the Subaru Hyper Suprime-Cam Survey (HSC). We measure three two-point correlations that form the basis of the cosmological inference presented in our companion papers, Miyatake et al. and Sugiyama et al. We use three approximately volume limited subsamples of spectroscopic galaxies by their $i$-band magnitude from the SDSS-BOSS: LOWZ (0.1

We present posterior sample redshift distributions for the Hyper Suprime-Cam Subaru Strategic Program Weak Lensing three-year (HSC Y3) analysis. Using the galaxies' photometry and spatial cross-correlations, we conduct a combined Bayesian Hierarchical Inference of the sample redshift distributions. The spatial cross-correlations are derived using a subsample of Luminous Red Galaxies (LRGs) with accurate redshift information available up to a photometric redshift of $z < 1.2$. We derive the photometry-based constraints using a combination of two empirical techniques calibrated on spectroscopic- and multiband photometric data that covers a spatial subset of the shear catalog. The limited spatial coverage induces a cosmic variance error budget that we include in the inference. Our cross-correlation analysis models the photometric redshift error of the LRGs to correct for systematic biases and statistical uncertainties. We demonstrate consistency between the sample redshift distributions derived using the spatial cross-correlations, the photometry, and the posterior of the combined analysis. Based on this assessment, we recommend conservative priors for sample redshift distributions of tomographic bins used in the three-year cosmological Weak Lensing analyses., Comment: 23 pages, 11 figures, 1 table, updated to match the accepted version in the MNRAS

The calibration of redshift distributions for photometric samples using spectroscopic surveys is plagued by the difficulty in modelling the selection functions of spectroscopic surveys. In this work, we analyse how these selection functions impact redshift inference and quantify the induced biases using local calibration tests in photometry space. The study is carried out using simulations that mimic the radial selection function of a spectroscopic survey and an accompanying mock catalog of a photometric galaxy survey catalog. We use a self-organizing map to partition the photometry space and perform a local $\chi^2$ test to study the probability calibration of redshift inferences that use the spectroscopic data for calibration. The goal of this work is to investigate the effect of uncorrected selection functions in the calibration data on redshift prediction accuracy and critically discuss mitigation methods. In particular we test culling-based bias correction techniques, that aim to remove redshift calibration biases by identifying regions in photometry with few spectroscopic calibration data, and propose avenues for future research. We found that removing regions in color-magnitude space that are underpopulated with spectroscopic calibration data does not remove all biases in redshift inference induced by the selection function.

In 1933, Fritz Zwicky's famous investigations of the mass of the Coma cluster led him to infer the existence of dark matter \cite{1933AcHPh...6..110Z}. His fundamental discoveries have proven to be foundational to modern cosmology; as we now know such dark matter makes up 85\% of the matter and 25\% of the mass-energy content in the universe. Galaxy clusters like Coma are massive, complex systems of dark matter in addition to hot ionized gas and thousands of galaxies, and serve as excellent probes of the dark matter distribution. However, empirical studies show that the total mass of such systems remains elusive and difficult to precisely constrain. Here, we present new estimates for the dynamical mass of the Coma cluster based on Bayesian deep learning methodologies developed in recent years. Using our novel data-driven approach, we predict Coma's $\mthc$ mass to be $10^{15.10 \pm 0.15}\ \hmsun$ within a radius of $1.78 \pm 0.03\ h^{-1}\mathrm{Mpc}$ of its center. We show that our predictions are rigorous across multiple training datasets and statistically consistent with historical estimates of Coma's mass. This measurement reinforces our understanding of the dynamical state of the Coma cluster and advances rigorous analyses and verification methods for empirical applications of machine learning in astronomy., Comment: 15 pages, 3 figures, 1 table, accepted for publication at Nature Astronomy, see https://www.nature.com/articles/s41550-022-01711-1

Recovering credible cosmological parameter constraints in a weak lensing shear analysis requires an accurate model that can be used to marginalize over nuisance parameters describing potential sources of systematic uncertainty, such as the uncertainties on the sample redshift distribution $n(z)$. Due to the challenge of running Markov Chain Monte-Carlo (MCMC) in the high dimensional parameter spaces in which the $n(z)$ uncertainties may be parameterized, it is common practice to simplify the $n(z)$ parameterization or combine MCMC chains that each have a fixed $n(z)$ resampled from the $n(z)$ uncertainties. In this work, we propose a statistically-principled Bayesian resampling approach for marginalizing over the $n(z)$ uncertainty using multiple MCMC chains. We self-consistently compare the new method to existing ones from the literature in the context of a forecasted cosmic shear analysis for the HSC three-year shape catalog, and find that these methods recover similar cosmological parameter constraints, implying that using the most computationally efficient of the approaches is appropriate. However, we find that for datasets with the constraining power of the full HSC survey dataset (and, by implication, those upcoming surveys with even tighter constraints), the choice of method for marginalizing over $n(z)$ uncertainty among the several methods from the literature may significantly impact the statistical uncertainties on cosmological parameters, and a careful model selection is needed to ensure credible parameter intervals., Comment: 16 pages, 9 figures, Accepted by MNRAS

Studies of cosmology, galaxy evolution, and astronomical transients with current and next-generation wide-field imaging surveys like the Rubin Observatory Legacy Survey of Space and Time (LSST) are all critically dependent on estimates of photometric redshifts. Capsule networks are a new type of neural network architecture that is better suited for identifying morphological features of the input images than traditional convolutional neural networks. We use a deep capsule network trained on $ugriz$ images, spectroscopic redshifts, and Galaxy Zoo spiral/elliptical classifications of $\sim$400,000 Sloan Digital Sky Survey (SDSS) galaxies to do photometric redshift estimation. We achieve a photometric redshift prediction accuracy and a fraction of catastrophic outliers that are comparable to or better than current methods for SDSS main galaxy sample-like data sets ($r\leq17.8$ and $z_{\mathrm{spec}}\leq0.4$) while requiring less data and fewer trainable parameters. Furthermore, the decision-making of our capsule network is much more easily interpretable as capsules act as a low-dimensional encoding of the image. When the capsules are projected on a 2-dimensional manifold, they form a single redshift sequence with the fraction of spirals in a region exhibiting a gradient roughly perpendicular to the redshift sequence. We perturb encodings of real galaxy images in this low-dimensional space to create synthetic galaxy images that demonstrate the image properties (e.g., size, orientation, and surface brightness) encoded by each dimension. We also measure correlations between galaxy properties (e.g., magnitudes, colours, and stellar mass) and each capsule dimension. We publicly release our code, estimated redshifts, and additional catalogues at https://biprateep.github.io/encapZulate-1 ., Comment: 22 pages, 12 figures. Published in MNRAS

Many astrophysical analyses depend on estimates of redshifts (a proxy for distance) determined from photometric (i.e., imaging) data alone. Inaccurate estimates of photometric redshift uncertainties can result in large systematic errors. However, probability distribution outputs from many photometric redshift methods do not follow the frequentist definition of a Probability Density Function (PDF) for redshift -- i.e., the fraction of times the true redshift falls between two limits $z_{1}$ and $z_{2}$ should be equal to the integral of the PDF between these limits. Previous works have used the global distribution of Probability Integral Transform (PIT) values to re-calibrate PDFs, but offsetting inaccuracies in different regions of feature space can conspire to limit the efficacy of the method. We leverage a recently developed regression technique that characterizes the local PIT distribution at any location in feature space to perform a local re-calibration of photometric redshift PDFs. Though we focus on an example from astrophysics, our method can produce PDFs which are calibrated at all locations in feature space for any use case., Comment: Fourth Workshop on Machine Learning and the Physical Sciences (NeurIPS 2021)

In the era of precision cosmology and ever-improving cosmological simulations, a better understanding of different galaxy components such as bulges and discs will give us new insight into galactic formation and evolution. Based on the fact that the stellar populations of the constituent components of galaxies differ by their dynamical properties, we develop two simple models for galaxy decomposition using the IllustrisTNG cosmological hydrodynamical simulation. The first model uses a single dynamical parameter and can distinguish 4 components: thin disc, thick disc, counter-rotating disc and bulge. The second model uses one more dynamical parameter, was defined in a probabilistic manner, and distinguishes two components: bulge and disc. The number fraction of disc-dominated galaxies at a given stellar mass obtained by our models agrees well with observations for masses exceeding $ \log_{10}(M_*/M_\odot)=10$. S\'ersic indices and half-mass radii for the bulge components agree well with those for real galaxies. The mode of the distribution of S\'ersic indices for the disc components is at the expected value of $n=1$. However, disc half-mass radii are smaller than those for real galaxies, in accordance with previous findings that the IllustrisTNG simulation produces undersized discs., Comment: 15 pages, 12 figures

Fisher forecasts are a common tool in cosmology with applications ranging from survey planning to the development of new cosmological probes. While frequently adopted, they are subject to numerical instabilities that need to be carefully investigated to ensure accurate and reproducible results. This research note discusses these challenges using the example of a weak lensing data vector and proposes procedures that can help in their solution., Comment: 9 pages, 5 figures

We study methods for reconstructing Bayesian uncertainties on dynamical mass estimates of galaxy clusters using convolutional neural networks (CNNs). We discuss the statistical background of approximate Bayesian neural networks and demonstrate how variational inference techniques can be used to perform computationally tractable posterior estimation for a variety of deep neural architectures. We explore how various model designs and statistical assumptions impact prediction accuracy and uncertainty reconstruction in the context of cluster mass estimation. We measure the quality of our model posterior recovery using a mock cluster observation catalog derived from the MultiDark simulation and UniverseMachine catalog. We show that approximate Bayesian CNNs produce highly accurate dynamical cluster mass posteriors. These model posteriors are log-normal in cluster mass and recover $68\%$ and $90\%$ confidence intervals to within $1\%$ of their measured value. We note how this rigorous modeling of dynamical mass posteriors is necessary for using cluster abundance measurements to constrain cosmological parameters., Comment: 15 pages, 5 figures. 3 tables, accepted for publication at ApJ

We perform a joint analysis of the counts and weak lensing signal of redMaPPer clusters selected from the Dark Energy Survey (DES) Year 1 dataset. Our analysis uses the same shear and source photometric redshifts estimates as were used in the DES combined probes analysis. Our analysis results in surprisingly low values for $S_8 =\sigma_8(\Omega_{\rm m}/0.3)^{0.5}= 0.65\pm 0.04$, driven by a low matter density parameter, $\Omega_{\rm m}=0.179^{+0.031}_{-0.038}$, with $\sigma_8-\Omega_{\rm m}$ posteriors in $2.4\sigma$ tension with the DES Y1 3x2pt results, and in $5.6\sigma$ with the Planck CMB analysis. These results include the impact of post-unblinding changes to the analysis, which did not improve the level of consistency with other data sets compared to the results obtained at the unblinding. The fact that multiple cosmological probes (supernovae, baryon acoustic oscillations, cosmic shear, galaxy clustering and CMB anisotropies), and other galaxy cluster analyses all favor significantly higher matter densities suggests the presence of systematic errors in the data or an incomplete modeling of the relevant physics. Cross checks with X-ray and microwave data, as well as independent constraints on the observable--mass relation from SZ selected clusters, suggest that the discrepancy resides in our modeling of the weak lensing signal rather than the cluster abundance. Repeating our analysis using a higher richness threshold ($\lambda \ge 30$) significantly reduces the tension with other probes, and points to one or more richness-dependent effects not captured by our model., Comment: 35 pages, 20 figures, submitted to Physical Review D

This work uses hierarchical logistic Gaussian processes to infer true redshift distributions of samples of galaxies, through their cross-correlations with spatially overlapping spectroscopic samples. We demonstrate that this method can accurately estimate these redshift distributions in a fully Bayesian manner jointly with galaxy-dark matter bias models. We forecast how systematic biases in the redshift-dependent galaxy-dark matter bias model affect redshift inference. Using published galaxy-dark matter bias measurements from the Illustris simulation, we compare these systematic biases with the statistical error budget from a forecasted weak gravitational lensing measurement. If the redshift-dependent galaxy-dark matter bias model is mis-specified, redshift inference can be biased. This can propagate into relative biases in the weak lensing convergence power spectrum on the 10% - 30% level. We, therefore, showcase a methodology to detect these sources of error using Bayesian model selection techniques. Furthermore, we discuss the improvements that can be gained from incorporating prior information from Bayesian template fitting into the model, both in redshift prediction accuracy and in the detection of systematic modeling biases., Comment: 17 pages, 8 figures, 4 tables, Accepted to MNRAS Nov 2019

In recent years, machine learning (ML) methods have remarkably improved how cosmologists can interpret data. The next decade will bring new opportunities for data-driven cosmological discovery, but will also present new challenges for adopting ML methodologies and understanding the results. ML could transform our field, but this transformation will require the astronomy community to both foster and promote interdisciplinary research endeavors., Comment: Submitted to the Astro2020 call for science white papers

We demonstrate the ability of convolutional neural networks (CNNs) to mitigate systematics in the virial scaling relation and produce dynamical mass estimates of galaxy clusters with remarkably low bias and scatter. We present two models, CNN$_\mathrm{1D}$ and CNN$_\mathrm{2D}$, which leverage this deep learning tool to infer cluster masses from distributions of member galaxy dynamics. Our first model, CNN$_\text{1D}$, infers cluster mass directly from the distribution of member galaxy line-of-sight velocities. Our second model, CNN$_\text{2D}$, extends the input space of CNN$_\text{1D}$ to learn on the joint distribution of galaxy line-of-sight velocities and projected radial distances. We train each model as a regression over cluster mass using a labeled catalog of realistic mock cluster observations generated from the MultiDark simulation and UniverseMachine catalog. We then evaluate the performance of each model on an independent set of mock observations selected from the same simulated catalog. The CNN models produce cluster mass predictions with lognormal residuals of scatter as low as $0.132$ dex, greater than a factor of 2 improvement over the classical $M$-$\sigma$ power-law estimator. Furthermore, the CNN model reduces prediction scatter relative to similar machine learning approaches by up to $17\%$ while executing in drastically shorter training and evaluation times (by a factor of 30) and producing considerably more robust mass predictions (improving prediction stability under variations in galaxy sampling rate by $30\%$)., Comment: 22 pages, 10 figures, 4 tables, accepted for publication at ApJ

High energy radiation from a planet host star can have strong influence on the final habitability of a system through several mechanisms. In this context we have constructed a catalogue containing the X-ray luminosities, as well as basic stellar and planetary properties of all known stars hosting giant planets (> 0.1 Mjup) that have been observed by the Chandra X-ray Observatory, XMM-Newton and/or ROSAT. Specifically in this paper we present a first application of this catalogue to search for a possible imprint of X-ray photoevaporation of planet-forming discs on the present-day orbital distribution of the observed giant planets. We found a suggestive void in the semi-major axis, a, versus X-ray luminosity, Lx, plane, roughly located between a ~ 0.05-1 au and Lx ~10^27-10^29 erg/s, which would be expected if photoevaporation played a dominant role in the migration history of these systems. However, due to the small observational sample size, the statistical significance of this feature cannot be proven at this point., Comment: 12 pages; accepted for publication on December 4, 2018 in MNRAS. The catalog presented in this paper is available for download on Harvard Dataverse (https://doi.org/10.7910/DVN/FPXFA5), updated references

We study the reionization parameter space consistent with the current measurement of the Thomson optical depth using a new parametrization of the reionization history. The mass-weighted ionization fraction is specified in terms of the redshift midpoint, duration, and asymmetry shape parameters. We perform an MCMC analysis using conservative flat priors and physical constraints. Our analysis yields a redshift midpoint of $z_{50}=7.66\substack{+0.57-0.61}\text{(68%)}\substack{+1.26-1.02}\text{(95%)}$, and upper limits on the duration $\Delta_\text{z} < 7.5$ and asymmetry $A_\text{z}<5.3$ for $\tau = 0.054 \pm 0.007$. The reconstructed mass-weighted ionization fraction $x_\text{i}(z)$ is asymmetric, but early contributions to reionization are minor., Comment: AAS Research Note

Variable stars with well-calibrated period-luminosity relationships provide accurate distance measurements to nearby galaxies and are therefore a vital tool for cosmology and astrophysics. While these measurements typically rely on samples of Cepheid and RR-Lyrae stars, abundant populations of luminous variable stars with longer periods of $10 - 1000$ days remain largely unused. We apply machine learning to derive a mapping between lightcurve features of these variable stars and their magnitude to extend the traditional period-luminosity (PL) relation commonly used for Cepheid samples. Using photometric data for long period variable stars in the Large Magellanic cloud (LMC), we demonstrate that our predictions produce residual errors comparable to those obtained on the corresponding Cepheid population. We show that our model generalizes well to other samples by performing a blind test on photometric data from the Small Magellanic Cloud (SMC). Our predictions on the SMC again show small residual errors and biases, comparable to results that employ PL relations fitted on Cepheid samples. The residual biases are complementary between the long period variable and Cepheid fits, which provides exciting prospects to better control sources of systematic error in cosmological distance measurements. We finally show that the proposed methodology can be used to optimize samples of variable stars as standard candles independent of any prior variable star classification., Comment: 14 pages, 10 figures, 1 table, updated to match the version accepted by the MNRAS

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 unchanged

Photometric redshift uncertainties are a major source of systematic error for ongoing and future photometric surveys. We study different sources of redshift error caused by choosing a suboptimal redshift histogram bin width and propose methods to resolve them. The selection of a too large bin width is shown to oversmooth small scale structure of the radial distribution of galaxies. This systematic error can significantly shift cosmological parameter constraints by up to $6 \, \sigma$ for the dark energy equation of state parameter $w$. Careful selection of bin width can reduce this systematic by a factor of up to 6 as compared with commonly used current binning approaches. We further discuss a generalised resampling method that can correct systematic and statistical errors in cosmological parameter constraints caused by uncertainties in the redshift distribution. This can be achieved without any prior assumptions about the shape of the distribution or the form of the redshift error. Our methodology allows photometric surveys to obtain unbiased cosmological parameter constraints using a minimum number of spectroscopic calibration data. For a DES-like galaxy clustering forecast we obtain unbiased results with respect to errors caused by suboptimal histogram bin width selection, using only 5k representative spectroscopic calibration objects per tomographic redshift bin., Comment: 14 pages, 1 table, 7 figures, updated to match version accepted in the MNRAS

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 unchanged

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 unchanged

We introduce an ordinal classification algorithm for photometric redshift estimation, which significantly improves the reconstruction of photometric redshift probability density functions (PDFs) for individual galaxies and galaxy samples. As a use case we apply our method to CFHTLS galaxies. The ordinal classification algorithm treats distinct redshift bins as ordered values, which improves the quality of photometric redshift PDFs, compared with non-ordinal classification architectures. We also propose a new single value point estimate of the galaxy redshift, that can be used to estimate the full redshift PDF of a galaxy sample. This method is competitive in terms of accuracy with contemporary algorithms, which stack the full redshift PDFs of all galaxies in the sample, but requires orders of magnitudes less storage space. The methods described in this paper greatly improve the log-likelihood of individual object redshift PDFs, when compared with a popular Neural Network code (ANNz). In our use case, this improvement reaches 50\% for high redshift objects ($z \geq 0.75$). We show that using these more accurate photometric redshift PDFs will lead to a reduction in the systematic biases by up to a factor of four, when compared with less accurate PDFs obtained from commonly used methods. The cosmological analyses we examine and find improvement upon are the following: gravitational lensing cluster mass estimates, modelling of angular correlation functions, and modelling of cosmic shear correlation functions., Comment: 17 pages, 19 figures, updated to match version accepted in the MNRAS

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 version

We present analyses of data augmentation for machine learning redshift estimation. Data augmentation makes a training sample more closely resemble a test sample, if the two base samples differ, in order to improve measured statistics of the test sample. We perform two sets of analyses by selecting 800k (1.7M) SDSS DR8 (DR10) galaxies with spectroscopic redshifts. We construct a base training set by imposing an artificial r band apparent magnitude cut to select only bright galaxies and then augment this base training set by using simulations and by applying the K-correct package to artificially place training set galaxies at a higher redshift. We obtain redshift estimates for the remaining faint galaxy sample, which are not used during training. We find that data augmentation reduces the error on the recovered redshifts by 40% in both sets of analyses, when compared to the difference in error between the ideal case and the non augmented case. The outlier fraction is also reduced by at least 10% and up to 80% using data augmentation. We finally quantify how the recovered redshifts degrade as one probes to deeper magnitudes past the artificial magnitude limit of the bright training sample. We find that at all apparent magnitudes explored, the use of data augmentation with tree based methods provide a estimate of the galaxy redshift with a negligible bias, although the error on the recovered values increases as we probe to deeper magnitudes. These results have applications for surveys which have a spectroscopic training set which forms a biased sample of all photometric galaxies, for example if the spectroscopic detection magnitude limit is shallower than the photometric limit., Comment: 13 pages, 4 figures, version accepted by MNRAS, added analysis, results and conclusions unchanged

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 MNRAS