Learning Fair Representations with High-Confidence Guarantees

Representation learning is increasingly employed to generate representations that are predictive across multiple downstream tasks. The development of representation learning algorithms that provide strong fairness guarantees is thus important because it can prevent unfairness towards disadvantaged groups for all downstream prediction tasks. To prevent unfairness towards disadvantaged groups in all downstream tasks, it is crucial to provide representation learning algorithms that provide fairness guarantees. In this paper, we formally define the problem of learning representations that are fair with high confidence. We then introduce the Fair Representation learning with high-confidence Guarantees (FRG) framework, which provides high-confidence guarantees for limiting unfairness across all downstream models and tasks, with user-defined upper bounds. After proving that FRG ensures fairness for all downstream models and tasks with high probability, we present empirical evaluations that demonstrate FRG's effectiveness at upper bounding unfairness for multiple downstream models and tasks

Prospects for extending the Mass-Metallicity Relation to low mass at high redshift: a case study at z~1

We report J-band MOSFIRE spectroscopy of a low-mass (log$(M_*/M_\odot)=8.62^{+0.10}_{-0.06}$) star-forming galaxy at $z=0.997$ showing the detection of [NII] and [SII] alongside a strong H$\alpha$ line. We derive a gas-phase metallicity of log$(\text{O}/\text{H})=7.99^{+0.13}_{-0.23}$, placing this object in a region of $M_* - Z$ space that is sparsely populated at this redshift. Furthermore, many existing metallicity measurements in this $M_* - z$ regime are derived from only [NII]/H$\alpha$ (N2), a diagnostic widely used in high-redshift metallicity studies despite the known strong degeneracy with the ionization parameter and resulting large systematic uncertainty. We demonstrate that even in a regime where [NII] and [SII] are at the detection limit and the measurement uncertainty associated with the [NII]/[SII] ratio is high (S/N~3), the more sophisticated Dopita et al. diagnostic provides an improved constraint compared to N2 by reducing the systematic uncertainty due to the ionization parameter. This approach does not, however, dispel uncertainty associated with stochastic or systematic variations in the nitrogen-to-oxygen abundance ratio. While this approach improves upon N2, future progress in extending metallicity studies into this low-mass regime will require larger samples to allow for stochastic variations, as well as careful consideration of the global trends among dwarf galaxies in all physical parameters, not just metallicity.Comment: 11 pages, 3 figure

The Grism Lens-Amplified Survey from Space (GLASS). IX. The dual origin of low-mass cluster galaxies as revealed by new structural analyses

Using deep Hubble Frontier Fields imaging and slitless spectroscopy from the Grism Lens-Amplified Survey from Space, we analyze 2200 cluster and 1748 field galaxies at $0.2\leq z\leq0.7$ to determine the impact of environment on galaxy size and structure at $\log M_*/M_\odot>7.8$, an unprecedented limit at these redshifts. Based on simple assumptions-$r_e=f(M_*)$-we find no significant differences in half-light radii ($r_e$) between equal-mass cluster or field systems. More complex analyses-$r_e=f(M_*,U-V,n,z,\Sigma$)-reveal local density $(\Sigma$) to induce only a $7\% \pm 3\%$ ($95\%$ confidence) reduction in $r_e$ beyond what can be accounted for by $U-V$ color, Sersic index ($n$), and redshift ($z$) effects.Almost any size difference between galaxies in high- and low-density regions is thus attributable to their different distributions in properties other than environment. Indeed, we find a clear color-$r_e$ correlation in low-mass passive cluster galaxies ($\log M_*/M_\odot<9.8$) such that bluer systems have larger radii, with the bluest having sizes consistent with equal-mass star-forming galaxies. We take this as evidence that large-$r_e$ low-mass passive cluster galaxies are recently acquired systems that have been environmentally quenched without significant structural transformation (e.g., by ram pressure stripping or starvation).Conversely, $\sim20\%$ of small-$r_e$ low-mass passive cluster galaxies appear to have been in place since $z\sim3$. Given the consistency of the small-$r_e$ galaxies' stellar surface densities (and even colors) with those of systems more than ten times as massive, our findings suggest that clusters mark places where galaxy evolution is accelerated for an ancient base population spanning most masses, with late-time additions quenched by environment-specific mechanisms are mainly restricted to the lowest masses.Comment: The accepted version. The catalog is available through the GLASS web page (http://glass.astro.ucla.edu), or https://www.astr.tohoku.ac.jp/~mtakahiro/Publication/Morishita17

Inferences on the Timeline of Reionization at z~8 From the KMOS Lens-Amplified Spectroscopic Survey

Detections and non-detections of Lyman alpha (Ly$\alpha$) emission from $z>6$ galaxies ($<1$ Gyr after the Big Bang) can be used to measure the timeline of cosmic reionization. Of key interest to measuring reionization's mid-stages, but also increasing observational challenge, are observations at z > 7, where Ly$\alpha$ redshifts to near infra-red wavelengths. Here we present a search for z > 7.2 Ly$\alpha$ emission in 53 intrinsically faint Lyman Break Galaxy candidates, gravitationally lensed by massive galaxy clusters, in the KMOS Lens-Amplified Spectroscopic Survey (KLASS). With integration times of ~7-10 hours, we detect no Ly$\alpha$ emission with S/N>5 in our sample. We determine our observations to be 80% complete for 5$\sigma$ spatially and spectrally unresolved emission lines with integrated line flux $>5.7\times10^{-18}$ erg s$^{-1}$ cm$^{-2}$. We define a photometrically selected sub-sample of 29 targets at $z=7.9\pm0.6$, with a median 5$\sigma$ Ly$\alpha$ EW limit of 58A. We perform a Bayesian inference of the average intergalactic medium (IGM) neutral hydrogen fraction using their spectra. Our inference accounts for the wavelength sensitivity and incomplete redshift coverage of our observations, and the photometric redshift probability distribution of each target. These observations, combined with samples from the literature, enable us to place a lower limit on the average IGM neutral hydrogen fraction of $> 0.76 \; (68\%), \; > 0.46 \; (95\%)$ at z ~ 8, providing further evidence of rapid reionization at z~6-8. We show that this is consistent with reionization history models extending the galaxy luminosity function to $M_\textrm{UV} \lesssim -12$, with low ionizing photon escape fractions, $f_\textrm{esc} \lesssim 15\%$.Comment: Accepted for publication in MNRA

HST Grism Observations of a Gravitationally Lensed Redshift 10 Galaxy

We present deep spectroscopic observations of a Lyman-break galaxy candidate (hereafter MACS1149-JD) at $z\sim9.5$ with the $\textit{Hubble}$ Space Telescope ($\textit{HST}$) WFC3/IR grisms. The grism observations were taken at 4 distinct position angles, totaling 34 orbits with the G141 grism, although only 19 of the orbits are relatively uncontaminated along the trace of MACS1149-JD. We fit a 3-parameter ($z$, F160W mag, and Ly$\alpha$ equivalent width) Lyman-break galaxy template to the three least contaminated grism position angles using an MCMC approach. The grism data alone are best fit with a redshift of $z_{\mathrm{grism}}=9.53^{+0.39}_{-0.60}$ ($68\%$ confidence), in good agreement with our photometric estimate of $z_{\mathrm{phot}}=9.51^{+0.06}_{-0.12}$ ($68\%$ confidence). Our analysis rules out Lyman-alpha emission from MACS1149-JD above a $3\sigma$ equivalent width of 21 \AA{}, consistent with a highly neutral IGM. We explore a scenario where the red $\textit{Spitzer}$/IRAC $[3.6] - [4.5]$ color of the galaxy previously pointed out in the literature is due to strong rest-frame optical emission lines from a very young stellar population rather than a 4000 \AA{} break. We find that while this can provide an explanation for the observed IRAC color, it requires a lower redshift ($z\lesssim9.1$), which is less preferred by the $\textit{HST}$ imaging data. The grism data are consistent with both scenarios, indicating that the red IRAC color can still be explained by a 4000 \AA{} break, characteristic of a relatively evolved stellar population. In this interpretation, the photometry indicate that a $340^{+29}_{-35}$ Myr stellar population is already present in this galaxy only $\sim500~\mathrm{Myr}$ after the Big Bang.Comment: Accepted to ApJ. This is the accepted versio

Spectroscopic confirmation of an ultra-faint galaxy at the epoch of reionization

Within one billion years of the Big Bang, intergalactic hydrogen was ionized by sources emitting ultraviolet and higher energy photons. This was the final phenomenon to globally affect all the baryons (visible matter) in the Universe. It is referred to as cosmic reionization and is an integral component of cosmology. It is broadly expected that intrinsically faint galaxies were the primary ionizing sources due to their abundance in this epoch. However, at the highest redshifts ($z>7.5$; lookback time 13.1 Gyr), all galaxies with spectroscopic confirmations to date are intrinsically bright and, therefore, not necessarily representative of the general population. Here, we report the unequivocal spectroscopic detection of a low luminosity galaxy at $z>7.5$. We detected the Lyman-$\alpha$ emission line at $\sim 10504$ {\AA} in two separate observations with MOSFIRE on the Keck I Telescope and independently with the Hubble Space Telescope's slit-less grism spectrograph, implying a source redshift of $z = 7.640 \pm 0.001$. The galaxy is gravitationally magnified by the massive galaxy cluster MACS J1423.8+2404 ($z = 0.545$), with an estimated intrinsic luminosity of $M_{AB} = -19.6 \pm 0.2$ mag and a stellar mass of $M_{\star} = 3.0^{+1.5}_{-0.8} \times 10^8$ solar masses. Both are an order of magnitude lower than the four other Lyman-$\alpha$ emitters currently known at $z > 7.5$, making it probably the most distant representative source of reionization found to date

Detection of Lyman-Alpha Emission From a Triple Imaged z=6.85 Galaxy Behind MACS J2129.4-0741

We report the detection of Ly$\alpha$ emission at $\sim9538$\AA{} in the Keck/DEIMOS and \HST WFC3 G102 grism data from a triply-imaged galaxy at $z=6.846\pm0.001$ behind galaxy cluster MACS J2129.4$-$0741. Combining the emission line wavelength with broadband photometry, line ratio upper limits, and lens modeling, we rule out the scenario that this emission line is \oii at $z=1.57$. After accounting for magnification, we calculate the weighted average of the intrinsic Ly$\alpha$ luminosity to be $\sim1.3\times10^{42}~\mathrm{erg}~\mathrm{s}^{-1}$ and Ly$\alpha$ equivalent width to be $74\pm15$\AA{}. Its intrinsic UV absolute magnitude at 1600\AA{} is $-18.6\pm0.2$ mag and stellar mass $(1.5\pm0.3)\times10^{7}~M_{\odot}$, making it one of the faintest (intrinsic $L_{UV}\sim0.14~L_{UV}^*$) galaxies with Ly$\alpha$ detection at $z\sim7$ to date. Its stellar mass is in the typical range for the galaxies thought to dominate the reionization photon budget at $z\gtrsim7$; the inferred Ly$\alpha$ escape fraction is high ($\gtrsim 10$\%), which could be common for sub-$L^*$ $z\gtrsim7$ galaxies with Ly$\alpha$ emission. This galaxy offers a glimpse of the galaxy population that is thought to drive reionization, and it shows that gravitational lensing is an important avenue to probe the sub-$L^*$ galaxy population.Comment: Accepted by ApJ Letter

The Grism lens-amplified survey from space (GLASS). VIII. The influence of the cluster properties on Halpha emitter galaxies at 0.3<z<0.7

Exploiting the data of the Grism Lens-Amplified Survey from Space (GLASS), we characterize the spatial distribution of star formation in 76 high star forming galaxies in 10 clusters at 0.3< z <0.7. All these galaxies are likely restricted to first infall. In a companion paper we contrast the properties of field and cluster galaxies, whereas here we correlate the properties of H{\alpha} emitters to a number of tracers of the cluster environment to investigate its role in driving galaxy transformations. H{\alpha} emitters are found in the clusters out to 0.5 virial radii, the maximum radius covered by GLASS. The peak of the H{\alpha} emission is offset with respect to the peak of the UV-continuum. We decompose this offsets into a radial and tangential component. The radial compo- nent points away from the cluster center in 60% of the cases, with 95% confidence. The decompositions agree with cosmological simulations, i.e. the H{\alpha} emission offset correlates with galaxy velocity and ram-pressure stripping signatures. Trends between H{\alpha} emitter properties and surface mass density distributions and X-ray emissions emerge only for unrelaxed clusters. The lack of strong correlations with the global environment does not allow us to identify a unique environmental effect originating from the cluster center. In contrast, correla- tions between H{\alpha} morphology and local number density emerge. We conclude that local effects, uncorrelated to the cluster-centric radius, play a more important role in shaping galaxy properties.Comment: ApJ in press (16 pages, 8 figures