How to measure metallicity from five-band photometry with supervised machine learning algorithms

We demonstrate that it is possible to measure metallicity from the SDSS five-band photometry to better than 0.1 dex using supervised machine learning algorithms. Using spectroscopic estimates of metallicity as ground truth, we build, optimize and train several estimators to predict metallicity. We use the observed photometry, as well as derived quantities such as stellar mass and photometric redshift, as features, and we build two sample data sets at median redshifts of 0.103 and 0.218 and median r-band magnitude of 17.5 and 18.3 respectively. We find that ensemble methods, such as Random Forests of Trees and Extremely Randomized Trees, and Support Vector Machines all perform comparably well and can measure metallicity with a Root Mean Square Error (RMSE) of 0.081 and 0.090 for the two data sets when all objects are included. The fraction of outliers (objects for which |Z_true - Z_pred| > 0.2 dex) is 2.2 and 3.9%, respectively and the RMSE decreases to 0.068 and 0.069 if those objects are excluded. Because of the ability of these algorithms to capture complex relationships between data and target, our technique performs better than previously proposed methods that sought to fit metallicity using an analytic fitting formula, and has 3x more constraining power than SED fitting-based methods. Additionally, this method is extremely forgiving of contamination in the training set, and can be used with very satisfactory results for training sample sizes of just a few hundred objects. We distribute all the routines to reproduce our results and apply them to other data sets.Comment: Minor revisions, matching version published in MNRA

The CMB as a dark energy probe

We give a brief review of the known effects of a dynamical vacuum cosmological component, the dark energy, on the anisotropies of the cosmic microwave background (CMB). We distinguish between a "classic" class of observables, used so far to constrain the average of the dark energy abundance in the redshift interval in which it is relevant for acceleration, and a "modern" class, aiming at the measurement of its differential redshift behavior. We show that the gravitationally lensed CMB belongs to the second class, as it can give a measure of the dark energy abundance at the time of equality with matter, occurring at about redshift 0.5. Indeed, the dark energy abundance at that epoch influences directly the lensing strength, which is injected at about the same time, if the source is the CMB. We illustrate this effect focusing on the curl (BB) component of CMB polarization, which is dominated by lensing on arcminute angular scales. An increasing dark energy abundance at the time of equality with matter, parameterized by a rising first order redshift derivative of its equation of state today, makes the BB power dropping with respect to a pure LambdaCDM cosmology, keeping the other cosmological parameters and primordial amplitude fixed. We briefly comment on the forthcoming probes which might measure the lensing power on CMB.Comment: 12 pages, 9 figures, proceedings of the invited talk at the CMB and Physics of the Early Universe Conference, Ischia, Italy, April 20-22, 200

SED fitting with MCMC: methodology and application to large galaxy surveys

We present GalMC (Acquaviva et al 2011), our publicly available Markov Chain Monte Carlo algorithm for SED fitting, show the results obtained for a stacked sample of Lyman Alpha Emitting galaxies at z ~ 3, and discuss the dependence of the inferred SED parameters on the assumptions made in modeling the stellar populations. We also introduce SpeedyMC, a version of GalMC based on interpolation of pre-computed template libraries. While the flexibility and number of SED fitting parameters is reduced with respect to GalMC, the average running time decreases by a factor of 20,000, enabling SED fitting of each galaxy in about one second on a 2.2GHz MacBook Pro laptop, and making SpeedyMC the ideal instrument to analyze data from large photometric galaxy surveys.Comment: Proceedings of the IAU Symposium 284, "The Spectral Energy Distribution of galaxies"; typos fixed; refs adde

Simultaneous Estimation of Photometric Redshifts and SED Parameters: Improved Techniques and a Realistic Error Budget

We seek to improve the accuracy of joint galaxy photometric redshift estimation and spectral energy distribution (SED) fitting. By simulating different sources of uncorrected systematic errors, we demonstrate that if the uncertainties on the photometric redshifts are estimated correctly, so are those on the other SED fitting parameters, such as stellar mass, stellar age, and dust reddening. Furthermore, we find that if the redshift uncertainties are over(under)-estimated, the uncertainties in SED parameters tend to be over(under)-estimated by similar amounts. These results hold even in the presence of severe systematics and provide, for the first time, a mechanism to validate the uncertainties on these parameters via comparison with spectroscopic redshifts. We propose a new technique (annealing) to re-calibrate the joint uncertainties in the photo-z and SED fitting parameters without compromising the performance of the SED fitting + photo-z estimation. This procedure provides a consistent estimation of the multidimensional probability distribution function in SED fitting + z parameter space, including all correlations. While the performance of joint SED fitting and photo-z estimation might be hindered by template incompleteness, we demonstrate that the latter is "flagged" by a large fraction of outliers in redshift, and that significant improvements can be achieved by using flexible stellar populations synthesis models and more realistic star formation histories. In all cases, we find that the median stellar age is better recovered than the time elapsed from the onset of star formation [abridged].Comment: 11 pages, 5 figures, 3 tables. Accepted for publication in the Astrophysical Journa

Teaching Machine Learning for the Physical Sciences: A summary of lessons learned and challenges

This paper summarizes some challenges encountered and best practices established in several years of teaching Machine Learning for the Physical Sciences at the undergraduate and graduate level. I discuss motivations for teaching ML to physicists, desirable properties of pedagogical materials, such as accessibility, relevance, and likeness to real-world research problems, and give examples of components of teaching units

Weak lensing and gravity theories

We present the theory of weak gravitational lensing in cosmologies with generalized gravity, described in the Lagrangian by a generic function depending on the Ricci scalar and a non-minimally coupled scalar field. We work out the generalized Poisson equations relating the dynamics of the fluctuating components to the two gauge invariant scalar gravitational potentials, fixing the new contributions from the modified background expansion and fluctuations. We show how the lensing observables are affected by the cosmic expansion as well as by the presence of the anisotropic stress, which is non-null at the linear level both in scalar-tensor gravity and in theories where the gravitational Lagrangian term features a non-minimal dependence on the Ricci scalar. We derive the generalized expressions for the convergence power spectrum, and illustrate phenomenologically the new effects in Extended Quintessence scenarios, where the scalar field coupled to gravity plays the role of the dark energy.Comment: 6 pages, to appear in "Impact of Gravitational Lensing on Cosmology", IAU Symposium 225, Mellier & Meylan ed

Dark energy records in lensed cosmic microwave background

We consider the weak lensing effect induced by linear cosmological perturbations on the cosmic microwave background (CMB) polarization anisotropies. We find that the amplitude of the lensing peak in the BB mode power spectrum is a faithful tracer of the dark energy dynamics at the onset of cosmic acceleration. This is due to two reasons. First, the lensing power is non-zero only at intermediate redshifts between the observer and the source, keeping record of the linear perturbation growth rate at the corresponding epoch. Second, the BB lensing signal is expected to dominate over the other sources. The lensing distortion on the TT and EE spectra do exhibit a similar dependence on the dark energy dynamics, although those are dominated by primary anisotropies. We investigate and quantify the effect by means of exact tracking quintessence models, as well as parameterizing the dark energy equation of state in terms of the present value ($w_{0}$) and its asymptotic value in the past ($w_{\infty}$); in the interval allowed by the present constraints on dark energy, the variation of $w_{\infty}$ induces a significant change in the BB mode lensing amplitude. A Fisher matrix analysis, under conservative assumptions concerning the increase of the sample variance due to the lensing non-Gaussian statistics, shows that a precision of order 10% on both $w_{0}$ and $w_{\infty}$ is achievable by the future experiments probing a large sky area with angular resolution and sensitivity appropriate to detect the lensing effect on the CMB angular power spectrum. These results show that the CMB can probe the differential redshift behavior of the dark energy equation of state, beyond its average.Comment: New version including substantial text change, three more figures and two more table