A Modern Take on the Bias-Variance Tradeoff in Neural Networks

The bias-variance tradeoff tells us that as model complexity increases, bias falls and variances increases, leading to a U-shaped test error curve. However, recent empirical results with over-parameterized neural networks are marked by a striking absence of the classic U-shaped test error curve: test error keeps decreasing in wider networks. This suggests that there might not be a bias-variance tradeoff in neural networks with respect to network width, unlike was originally claimed by, e.g., Geman et al. (1992). Motivated by the shaky evidence used to support this claim in neural networks, we measure bias and variance in the modern setting. We find that both bias and variance can decrease as the number of parameters grows. To better understand this, we introduce a new decomposition of the variance to disentangle the effects of optimization and data sampling. We also provide theoretical analysis in a simplified setting that is consistent with our empirical findings

Empirical Analysis of Model Selection for Heterogeneous Causal Effect Estimation

We study the problem of model selection in causal inference, specifically for the case of conditional average treatment effect (CATE) estimation under binary treatments. Unlike model selection in machine learning, there is no perfect analogue of cross-validation as we do not observe the counterfactual potential outcome for any data point. Towards this, there have been a variety of proxy metrics proposed in the literature, that depend on auxiliary nuisance models estimated from the observed data (propensity score model, outcome regression model). However, the effectiveness of these metrics has only been studied on synthetic datasets as we can access the counterfactual data for them. We conduct an extensive empirical analysis to judge the performance of these metrics introduced in the literature, and novel ones introduced in this work, where we utilize the latest advances in generative modeling to incorporate multiple realistic datasets. Our analysis suggests novel model selection strategies based on careful hyperparameter tuning of CATE estimators and causal ensembling.Comment: Preprint. Under Revie

Optimizing outcomes for children with non-Hodgkin lymphoma in low- and middle-income countries by early correct diagnosis, reducing toxic death and preventing abandonment

In high-income countries, more than 90% of children with mature B-cell lymphomas are cured with frontline therapy. However, cure requires prompt and correct diagnosis, careful risk stratification, very intense chemotherapy and meticulous supportive care, together with logistical support for patients who live far from the cancer centre or face financial barriers to receiving care. In low- and middle-income countries (LMIC), cure rates range from 20% to 70% because of lack of diagnosis, misdiagnosis, abandonment of treatment, toxic death and excess relapse with reduced-intensity regimens. Fortunately, a wide range of successful interventions in LMIC have reduced these causes of avoidable treatment failure. Public awareness campaigns have led to societal awareness of childhood cancer; telepathology has improved diagnosis, even in remote areas; subsidized chemotherapy, transportation, housing and food have reduced abandonment; and hand hygiene, nurse training programmes and health system improvements have reduced toxic death. These interventions can be deployed everywhere and at low cost, so are highly scalable. Children and adolescents with Burkitt lymphoma can be cured in all countries by making a timely correct diagnosis, applying protocols adapted to the local context, preventing abandonment of therapy and avoiding toxic death. Reducing these causes of treatment failure is feasible and highly cost-effective everywhere.Fil: Chantada, Guillermo Luis. Hospital Universitario Austral; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lam, Catherine G.. St. Jude Children's Research Hospital; Estados UnidosFil: Howard, Scott C.. University of Tennessee; Estados Unido

The COS-Dwarfs Survey: The Carbon Reservoir Around sub-L* Galaxies

We report new observations of circumgalactic gas from the COS-Dwarfs survey, a systematic investigation of the gaseous halos around 43 low-mass z $\leq$ 0.1 galaxies using background QSOs observed with the Cosmic Origins Spectrograph. From the projected 1D and 2D distribution of C IV absorption, we find that C IV absorption is detected out to ~ 0.5 R$_{vir}$ of the host galaxies. The C IV absorption strength falls off radially as a power law and beyond 0.5 R$_{vir}$, no C IV absorption is detected above our sensitivity limit of ~ 50-100 m$\AA$. We find a tentative correlation between detected C IV absorption strength and star formation, paralleling the strong correlation seen in highly ionized oxygen for L~L* galaxies by the COS-Halos survey. The data imply a large carbon reservoir in the CGM of these galaxies, corresponding to a minimum carbon mass of $\gtrsim$ 1.2$\times 10^6$ $M_\odot$ out to ~ 110 kpc. This mass is comparable to the carbon mass in the ISM and more than the carbon mass currently in stars of these galaxies. The C IV absorption seen around these sub-L* galaxies can account for almost two-thirds of all $W_r$> 100 m$\AA$ C IV absorption detected at low z. Comparing the C IV covering fraction with hydrodynamical simulations, we find that an energy-driven wind model is consistent with the observations whereas a wind model of constant velocity fails to reproduce the CGM or the galaxy properties.Comment: 18 Pages, 11 Figures, ApJ 796 13

The COS-Halos Survey: Physical Conditions and Baryonic Mass in the Low-Redshift Circumgalactic Medium

We analyze the physical conditions of the cool, photoionized (T $\sim 10^4$ K) circumgalactic medium (CGM) using the COS-Halos suite of gas column density measurements for 44 gaseous halos within 160 kpc of $L \sim L^*$ galaxies at $z \sim 0.2$. These data are well described by simple photoionization models, with the gas highly ionized (n$_{\rm HII}$/n$_{\rm H} \gtrsim 99\%$) by the extragalactic ultraviolet background (EUVB). Scaling by estimates for the virial radius, R$_{\rm vir}$, we show that the ionization state (tracked by the dimensionless ionization parameter, U) increases with distance from the host galaxy. The ionization parameters imply a decreasing volume density profile n$_{\rm H}$ = (10$^{-4.2 \pm 0.25}$)(R/R$_{\rm vir})^{-0.8\pm0.3}$. Our derived gas volume densities are several orders of magnitude lower than predictions from standard two-phase models with a cool medium in pressure equilibrium with a hot, coronal medium expected in virialized halos at this mass scale. Applying the ionization corrections to the HI column densities, we estimate a lower limit to the cool gas mass M$_{\rm CGM}^{\rm cool} > 6.5 \times 10^{10}$ M$_{\odot}$ for the volume within R $<$ R$_{\rm vir}$. Allowing for an additional warm-hot, OVI-traced phase, the CGM accounts for at least half of the baryons purported to be missing from dark matter halos at the 10$^{12}$ M$_{\odot}$ scale.Comment: 19 pages, 12 Figures, and a 37-page Appendix with 36 additional figures. Accepted to ApJ June 21 201

Hydrogen and Metal Line Absorption Around Low-Redshift Galaxies in Cosmological Hydrodynamic Simulations

We study the physical conditions of the circum-galactic medium (CGM) around z=0.25 galaxies as traced by HI and metal line absorption, using cosmological hydrodynamic simulations that include galactic outflows. Using lines of sight targeted at impact parameters from 10 kpc to 1 Mpc around galaxies with halo masses from 10^11-10^13 M_solar, we study the physical conditions and their variation with impact parameter b and line-of-sight velocity delta v in the CGM as traced by HI, MgII, SiIV, CIV, OVI, and NeVIII absorbers. All ions show a strong excess of absorption near galaxies compared to random lines of sight. The excess continues beyond 1 Mpc, reflecting the correlation of metal absorption with large-scale structure. Absorption is particularly enhanced within about v<300 km/sec and roughly 300 kpc of galaxies (with distances somewhat larger for the highest ion), approximately delineating the CGM; this range contains the majority of global metal absorption. Low ions like MgII and SiIV predominantly arise in denser gas closer to galaxies and drop more rapidly with b, while high ions OVI and NeVIII trace more diffusely distributed gas with a comparatively flat radial profile; CIV is intermediate. All ions predominantly trace T~10^4-4.5 K photo-ionised gas at all b, but when hot CGM gas is present (mostly in larger halos), we see strong collisionally-ionised OVI and NeVIII at b <= 100 kpc. Larger halo masses generally produce more absorption, though overall the trends are not as strong as that with impact parameter. These findings arise using our favoured outflow scalings as expected for momentum-driven winds; with no winds, the CGM gas remains mostly unenriched, while our outflow model with a constant velocity and mass loading factor produce hotter, more widely dispersed metals.Comment: 26 pages, 15 figures, published in MNRAS. Updates to citations from previous versio