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David C. Stenning

Publications and source records attributed to David C. Stenning.

At least 19 recordsLinked to original sources

Debiasing the Observed Fast Radio Burst Population with the CHIME/FRB Selection Function

The recent release of CHIME/FRB Catalog~2 provides the largest sample to date with which to investigate the intrinsic distributions of fast radio bursts (FRBs). Leveraging an expanded campaign of 587,367 synethetic bursts injected into the live CHIME/FRB search pipeline, we perform a population analysis of the fluence, scattering timescale, pulse width, and dispersion measure distributions of Catalog~2 FRBs. We first infer the intrinsic population using a resampling-based framework that accounts for instrumental selection effects following previous CHIME/FRB population studies. A central goal of this work is to constrain the intrinsic distribution of scattering timescales, that remained weakly constrained in Catalog~1 owing to limited statistics at moderate and large scattering times ($τ\gtrsim 10\,\mathrm{ms}$ at 600~MHz) and sparse injection coverage in this regime. Second, we construct an explicit multidimensional selection function by training a logistic regression model on the injected events. This model estimates the detection probability as a function of FRB observable properties, including higher-order interaction terms. We incorporate this selection function into a simulation-based inference framework to refine the inferred intrinsic scattering-timescale distribution. We find evidence for a slight downturn in the intrinsic FRB scattering timescale distribution, though a flat or slightly rising distribution cannot be ruled out, that is further supported through a comparison with the higher-frequency scattering timescale distribution observed by Commensal Real-time ASKAP Fast Transients (CRAFT) survey.

astro-ph.HE

Discovery of 30 Repeating Fast Radio Burst Sources and Uniform Population Statistics of 80 Repeating Sources from CHIME/FRB

We present 30 newly discovered repeating fast radio burst (FRB) sources from the second catalog of bursts detected by the FRB backend on the Canadian Hydrogen Intensity Mapping Experiment (CHIME/FRB). These repeaters have extragalactic dispersion measures (DMs) spanning $99.4-1446.0\ \text{pc cm}^{-3}$ and burst rates between $10^{-5.7}$ and $10^{-0.5}$ hr$^{-1}$ scaled to a fluence threshold of 5 Jy ms. We report evidence of monotonic, linear DM variations in four repeaters on years-long timescales. The newly discovered sources bring CHIME/FRB's total number of observed repeating FRBs to 80, 79 of which were discovered by CHIME/FRB, between 2018 July 25 and 2023 September 15. In the full CHIME/FRB sample, only 2.4$\pm 0.4\%$ of sources have been observed to repeat, and we do not find evidence for significant evolution of this value over the duration of the experiment. We find no substantial evidence for bimodal populations of one-off and repeating FRBs in their burst rate distributions; the distribution of upper limits on repeat rates implied from observations of as-yet one-offs is entirely contained within the observed range of repeater burst rates and the distributions do not appear inconsistent. Similarly, using the population analysis framework of C. W. James (2023), we find that our observations of repeating and yet-one-off FRBs are equally well fit assuming a power-law distribution of repeat rates with 50$-$100% of the population repeating.

astro-ph.HE

Estimating Complex Densities using Two-Stage Normalizing Flows

In many scientific applications, the target probability distribution cannot be evaluated in closed form or sampled from directly. Instead, it can often be decomposed into multiple components, some of which are accessible only through samples generated by simulators or external datasets, while others admit tractable mathematical expressions or are specified through statistical assumptions about variable relationships. Developing inference methods that coherently integrate these heterogeneous sources of information remains an open challenge. In this paper, we propose a Two-Stage Normalizing Flows framework for approximating and sampling from such distributions. The method first learns the densities of components for which only samples are available, and then combines the outputs with the analytically specified terms to reconstruct the full target distribution in a second stage. The resulting model enables both point-wise density evaluation and efficient generation of representative samples, without requiring direct access to the full target density or joint samples from the complete model. We assess the proposed approach through simulation studies in joint density inference and Bayesian hierarchical models with inaccessible likelihoods. The proposed framework is able to accurately recover complex, highly nonlinear target structures using only partial information about the target density, providing stable and flexible approximations in settings where standard modeling assumptions do not hold (or when complete access to the target distribution is not available). Analysis of a large scale astronomy application highlights interesting differences between our method and existing approaches. Our normalizing flows procedure offers a robust and flexible approach to inference for intractable target distributions across both simulated and real-world applications.

stat.ME

Repeating versus Nonrepeating Fast Radio Bursts: A Deep Learning Approach to Morphological Characterization

We present a deep learning approach to classify fast radio bursts (FRBs) based purely on morphology as encoded on recorded dynamic spectrum from CHIME/FRB Catalog 2. We implemented transfer learning with a pretrained ConvNext architecture, exploiting its powerful feature extraction ability. ConvNext was adapted to classify dedispersed dynamic spectra (which we treat as images) of the FRBs into one of the two sub-classes, i.e., repeater and non-repeater, based on their various temporal and spectral properties and relation between the sub-pulse structures. Additionally, we also used mathematical model representation of the total intensity data to interpret the deep learning model. Upon fine-tuning the pretrained ConvNext on the FRB spectrograms, we were able to achieve high classification metrics while substantially reducing training time and computing power as compared to training a deep learning model from scratch with random weights and biases without any feature extraction ability. Importantly, our results suggest that the morphological differences between CHIME repeating and non-repeating events persist in Catalog 2 and the deep learning model leveraged these differences for classification. The fine-tuned deep learning model can be used for inference, which enables us to predict whether an FRB's morphology resembles that of repeaters or non-repeaters. Such inferences may become increasingly significant when trained on larger data sets that will exist in the near future.

astro-ph.HE

The Second CHIME/FRB Catalog of Fast Radio Bursts

We present a catalog of 4539 fast radio bursts (FRBs) observed with the Canadian Hydrogen Intensity Mapping Experiment (CHIME) telescope between 25 July 2018 and 15 September 2023. These bursts originate from 3641 unique sources, including 981 bursts from 83 known repeating sources. For each FRB, the catalog provides a $O(10')$ estimate of sky location along with corresponding measurements of cumulative exposure time and survey sensitivity over the observing period. It includes a total-intensity dynamic spectrum between 400 and 800 MHz at 0.983 ms resolution. From this spectrum, we constrain a model of the burst morphology and measure key parameters such as arrival time, intrinsic temporal width, dispersion measure, scattering time, and flux density. This second catalog includes all FRBs from the first catalog, with every event reprocessed using a uniform and improved analysis framework. We show that previously published inferences remain valid under the updated measurements. We assess consistency of the detection rate across observational parameters, present initial distributions of burst properties, and outline ongoing and future studies that will use this catalog to investigate the nature of FRBs and their utility as astrophysical and cosmological probes.

astro-ph.HE

K-Contact Distance for Noisy Nonhomogeneous Spatial Point Data with application to Repeating Fast Radio Burst sources

This paper introduces an approach to analyze nonhomogeneous Poisson processes (NHPP) observed with noise, focusing on previously unstudied second-order characteristics of the noisy process. Utilizing a hierarchical Bayesian model with noisy data, we estimate hyperparameters governing a physically motivated NHPP intensity. Simulation studies demonstrate the reliability of this methodology in accurately estimating hyperparameters. Leveraging the posterior distribution, we then infer the probability of detecting a certain number of events within a given radius, the $k$-contact distance. We demonstrate our methodology with an application to observations of fast radio bursts (FRBs) detected by the Canadian Hydrogen Intensity Mapping Experiment's FRB Project (CHIME/FRB). This approach allows us to identify repeating FRB sources by bounding or directly simulating the probability of observing $k$ physically independent sources within some radius in the detection domain, or the $\textit{probability of coincidence}$ ($P_{\text{C}}$). The new methodology improves the repeater detection $P_{\text{C}}$ in 91% of cases when applied to the largest sample of previously classified observations, with a median improvement factor (existing metric over $P_{\text{C}}$ from our methodology) of $\sim$ 4800.

stat.AP

FRB 20250316A: A Brilliant and Nearby One-Off Fast Radio Burst Localized to 13 parsec Precision

Precise localizations of a small number of repeating fast radio bursts (FRBs) using very long baseline interferometry (VLBI) have enabled multiwavelength follow-up observations revealing diverse local environments. However, the 2--3\% of FRB sources that are observed to repeat may not be representative of the full population. Here we use the VLBI capabilities of the full CHIME Outriggers array for the first time to localize a nearby (40 Mpc), bright (kJy), and apparently one-off FRB source, FRB 20250316A, to its environment on 13-pc scales. We use optical and radio observations to place deep constraints on associated transient emission and the properties of its local environment. We place a $5σ$ upper limit of $L_{\mathrm{9.9~\mathrm{GHz}}} < 2.1\times10^{25}~\mathrm{erg~s^{-1}~Hz^{-1}}$ on spatially coincident radio emission, a factor of 100 lower than any known compact persistent radio source associated with an FRB. Our KCWI observations allow us to characterize the gas density, metallicity, nature of gas ionization, dust extinction and star-formation rate through emission line fluxes. We leverage the exceptional brightness and proximity of this source to place deep constraints on the repetition of FRB 20250316A, and find it is inconsistent with all well-studied repeaters given the non-detection of bursts at lower spectral energies. We explore the implications of a measured offset of 190$\pm20$ pc from the center of the nearest star-formation region, in the context of progenitor channels. FRB 20250316A marks the beginning of an era of routine localizations for one-off FRBs on tens of mas-scales, enabling large-scale studies of their local environments.

astro-ph.HE

Rare Event Classification with Weighted Logistic Regression for Identifying Repeating Fast Radio Bursts

An important task in the study of fast radio bursts (FRBs) remains the automatic classification of repeating and non-repeating sources based on their morphological properties. We propose a statistical model that considers a modified logistic regression to classify FRB sources. The classical logistic regression model is modified to accommodate the small proportion of repeaters in the data, a feature that is likely due to the sampling procedure and duration and is not a characteristic of the population of FRB sources. The weighted logistic regression hinges on the choice of a tuning parameter that represents the true proportion $τ$ of repeating FRB sources in the entire population. The proposed method has a sound statistical foundation, direct interpretability, and operates with only 5 parameters, enabling quicker retraining with added data. Using the CHIME/FRB Collaboration sample of repeating and non-repeating FRBs and numerical experiments, we achieve a classification accuracy for repeaters of nearly 75\% or higher when $τ$ is set in the range of $50$ to $60$\%. This implies a tentative high proportion of repeaters, which is surprising, but is also in agreement with recent estimates of $τ$ that are obtained using other methods.

astro-ph.HE

Do All Fast Radio Bursts Repeat? Constraints from CHIME/FRB Far Side-Lobe FRBs

We report ten fast radio bursts (FRBs) detected in the far side-lobe region (i.e., $\geq 5^\circ$ off-meridian) of the Canadian Hydrogen Intensity Mapping Experiment (CHIME) from 2018 August 28 to 2021 August 31. We localize the bursts by fitting their spectra with a model of the CHIME/FRB synthesized beam response. We find that the far side-lobe events have on average ~500 times greater fluxes than events detected in CHIME's main lobe. We show that the side-lobe sample is therefore statistically ~20 times closer than the main-lobe sample. We find promising host galaxy candidates (P$_{\rm cc}$ < 1%) for two of the FRBs, 20190112B and 20210310B, at distances of 38 and 16 Mpc, respectively. CHIME/FRB did not observe repetition of similar brightness from the uniform sample of 10 side-lobe FRBs in a total exposure time of 35580 hours. Under the assumption of Poisson-distributed bursts, we infer that the mean repetition interval above the detection threshold of the far side-lobe events is longer than 11880 hours, which is at least 2380 times larger than the interval from known CHIME/FRB detected repeating sources, with some caveats, notably that very narrow-band events could have been missed. Our results from these far side-lobe events suggest one of two scenarios: either (1) all FRBs repeat and the repetition intervals span a wide range, with high-rate repeaters being a rare subpopulation, or (2) non-repeating FRBs are a distinct population different from known repeaters.

astro-ph.HE

Contemporaneous X-ray Observations of 30 Bright Radio Bursts from the Prolific Fast Radio Burst Source FRB 20220912A

We present an extensive contemporaneous X-ray and radio campaign performed on the repeating fast radio burst (FRB) source FRB 20220912A for eight weeks immediately following the source's detection by CHIME/FRB. This includes X-ray data from XMM-Newton, NICER, and Swift, and radio detections of FRB 20220912A from CHIME/Pulsar and Effelsberg. We detect no significant X-ray emission at the time of 30 radio bursts with upper limits on $0.5-10.0$ keV X-ray fluence of $(1.5-14.5)\times 10^{-10}$ erg cm$^{-2}$ (99.7% credible interval, unabsorbed) on a timescale of 100 ms. Translated into a fluence ratio $η_{\text{ x/r}} = F_{\text{X-ray}}/F_{\text{radio}}$, this corresponds to $η_{\text{ x/r}} < 7\times10^{6}$. For persistent emission from the location of FRB 20220912A, we derive a 99.7% $0.5-10.0$ keV isotropic flux limit of $8.8\times 10^{-15}$ erg cm$^{-2}$ s$^{-1}$ (unabsorbed) or an isotropic luminosity limit of 1.4$\times10^{41}$ erg s$^{-1}$ at a distance of 362.4 Mpc. We derive a hierarchical extension to the standard Bayesian treatment of low-count and background-contaminated X-ray data, which allows the robust combination of multiple observations. This methodology allows us to place the best (lowest) 99.7% credible interval upper limit on an FRB $η_{\text{ x/r}}$ to date, $η_{\text{ x/r}} < 2\times10^6$, assuming that all thirty detected radio bursts are associated with X-ray bursts with the same fluence ratio. If we instead adopt an X-ray spectrum similar to the X-ray burst observed contemporaneously with FRB-like emission from Galactic magnetar SGR 1935+2154 detected on 2020 April 28, we derive a 99.7% credible interval upper limit on $η_{\text{ x/r}}$ of $8\times10^5$, which is only 3 times the observed value of $η_{\text{ x/r}}$ for SGR 1935+2154.

astro-ph.HE

Effect of Systematic Uncertainties on Density and Temperature Estimates in Coronae of Capella

We estimate the coronal density of Capella using the O VII and Fe XVII line systems in the soft X-ray regime that have been observed over the course of the Chandra mission. Our analysis combines measures of error due to uncertainty in the underlying atomic data with statistical errors in the Chandra data to derive meaningful overall uncertainties on the plasma density of the coronae of Capella. We consider two Bayesian frameworks. First, the so-called pragmatic-Bayesian approach considers the atomic data and their uncertainties as fully specified and uncorrectable. The fully-Bayesian approach, on the other hand, allows the observed spectral data to update the atomic data and their uncertainties, thereby reducing the overall errors on the inferred parameters. To incorporate atomic data uncertainties, we obtain a set of atomic data replicates, the distribution of which captures their uncertainty. A principal component analysis of these replicates allows us to represent the atomic uncertainty with a lower-dimensional multivariate Gaussian distribution. A $t$-distribution approximation of the uncertainties of a subset of plasma parameters including a priori temperature information, obtained from the temperature-sensitive-only Fe XVII spectral line analysis, is carried forward into the density- and temperature-sensitive O VII spectral line analysis. Markov Chain Monte Carlo based model fitting is implemented including Multi-step Monte Carlo Gibbs Sampler and Hamiltonian Monte Carlo. Our analysis recovers an isothermally approximated coronal plasma temperature of $\approx$5 MK and a coronal plasma density of $\approx$10$^{10}$ cm$^{-3}$, with uncertainties of 0.1 and 0.2 dex respectively.

astro-ph.SR

Constraining the selection corrected luminosity function and total pulse count for radio transients

Studying transient phenomena, such as individual pulses from pulsars, has garnered considerable attention in the era of astronomical big data. Of specific interest to this study are Rotating Radio Transients (RRATs), nulling, and intermittent pulsars. This study introduces a new algorithm named LuNfit, tailored to correct the selection biases originating from the telescope and detection pipelines. Ultimately LuNfit estimates the intrinsic luminosity distribution and nulling fraction of the single pulses emitted by pulsars. LuNfit relies on Bayesian nested sampling so that the parameter space can be fully explored. Bayesian nested sampling also provides the additional benefit of simplifying model comparisons through the Bayes ratio. The robustness of LuNfit is shown through simulations and applying LuNfit onto pulsars with known nulling fractions. LuNfit is then applied to three RRATs, J0012+5431, J1538+1523, and J2355+1523, extracting their intrinsic luminosity distribution and burst rates. We find that their nulling fraction is 0.4(2), 0.749(5) and 0.995(2) respectively. We further find that a log-normal distribution likely describes the single pulse luminosity distribution of J0012+5431 and J1538+1523, while the Bayes ratio for J2355+1523 slightly favors an exponential distribution. We show the conventional method of correcting selection effects by "scaling up" the missed fraction of radio transients can be unreliable when the mean luminosity of the source is faint relative to the telescope sensitivity. Finally, we discuss the limitations of the current implementation of LuNfit while also delving into potential enhancements that would enable LuNfit to be applied to sources with complex pulse morphologies.

astro-ph.HE

Updating the first CHIME/FRB catalog of fast radio bursts with baseband data

In 2021, a catalog of 536 fast radio bursts (FRBs) detected with the Canadian Hydrogen Intensity Mapping Experiment (CHIME) radio telescope was released by the CHIME/FRB Collaboration. This large collection of bursts, observed with a single instrument and uniform selection effects, has advanced our understanding of the FRB population. Here we update the results for 140 of these FRBs for which channelized raw voltage ('baseband') data are available. With the voltages measured by the telescope's antennas, it is possible to maximize the telescope sensitivity in any direction within the primary beam, an operation called 'beamforming'. This allows us to increase the signal-to-noise ratio (S/N) of the bursts and to localize them to sub-arcminute precision. The improved localization is also used to correct the beam response of the instrument and to measure fluxes and fluences with a ~10% uncertainty. Additionally, the time resolution is increased by three orders of magnitude relative to that in the first CHIME/FRB catalog, and, applying coherent dedispersion, burst morphologies can be studied in detail. Polarization information is also available for the full sample of 140 FRBs, providing an unprecedented dataset to study the polarization properties of the population. We release the baseband data beamformed to the most probable position of each FRB. These data are analyzed in detail in a series of accompanying papers.

astro-ph.HE

Improved Weak Lensing Photometric Redshift Calibration via StratLearn and Hierarchical Modeling

Discrepancies between cosmological parameter estimates from cosmic shear surveys and from recent Planck cosmic microwave background measurements challenge the ability of the highly successful $Λ$CDM model to describe the nature of the Universe. To rule out systematic biases in cosmic shear survey analyses, accurate redshift calibration within tomographic bins is key. In this paper, we improve photo-$z$ calibration via Bayesian hierarchical modeling of full galaxy photo-$z$ conditional densities, by employing $\textit{StratLearn}$, a recently developed statistical methodology, which accounts for systematic differences in the distribution of the spectroscopic training/source set and the photometric target set. Using realistic simulations that were designed to resemble the KiDS+VIKING-450 dataset, we show that $\textit{StratLearn}$-estimated conditional densities improve the galaxy tomographic bin assignment, and that our $\textit{StratLearn}$-Bayesian framework leads to nearly unbiased estimates of the target population means. This leads to a factor of $\sim 2$ improvement upon the previously best photo-$z$ calibration method. Our approach delivers a maximum bias per tomographic bin of $Δ\langle z \rangle = 0.0095 \pm 0.0089$, with an average absolute bias of $0.0052 \pm 0.0067$ across the five tomographic bins.

astro-ph.CO

Statistical association between the candidate repeating FRB 20200320A and a galaxy group

We present results from angular cross-correlations between select samples of CHIME/FRB repeaters and galaxies in three photometric galaxy surveys, which have shown correlations with the first CHIME/FRB catalog containing repeating and nonrepeating sources: WISE$\times$SCOS, DESI-BGS, and DESI-LRG. We find a statistically significant correlation ($p$-value $<0.001$, after accounting for look-elsewhere factors) between a sample of repeaters with extragalactic dispersion measure DM $>395$ pc cm$^{-3}$ and WISE$\times$SCOS galaxies with redshift $z>0.275$. We demonstrate that the correlation arises surprisingly because of a statistical association between FRB 20200320A (extragalactic DM $\approx550$ pc cm$^{-3}$) and a galaxy group in the same dark matter halo at redshift $z\approx0.32$. We estimate that the host halo, along with an intervening halo at redshift $z\approx0.12$, accounts for at least $\sim$$30\%$ of the extragalactic DM. Our results strongly motivate incorporating galaxy group and cluster catalogs into direct host association pipelines for FRBs with $\lesssim$$1'$ localization precision, effectively utilizing the two-point information to constrain FRB properties such as their redshift and DM distributions. In addition, we find marginal evidence for a negative correlation at 99.4% CL between a sample of repeating FRBs with baseband data (median extragalactic DM $=354$ pc cm$^{-3}$) and DESI-LRG galaxies with redshift $0.3\le z<0.45$, suggesting that the repeaters might be more prone than apparent nonrepeaters to propagation effects in FRB-galaxy correlations due to intervening free electrons over angular scales $\sim$$0\mbox{$.\!\!^\circ$}5$.

astro-ph.GA

Comprehensive Bayesian analysis of FRB-like bursts from SGR 1935+2154 observed by CHIME/FRB

The bright millisecond-duration radio burst from the Galactic magnetar SGR 1935+2154 in 2020 April was a landmark event, demonstrating that at least some fast radio burst (FRB) sources could be magnetars. The two-component burst was temporally coincident with peaks observed within a contemporaneous short X-ray burst envelope, marking the first instance where FRB-like bursts were observed to coincide with X-ray counterparts. In this study, we detail five new radio burst detections from SGR 1935+2154, observed by the CHIME/FRB instrument between October 2020 and December 2022. We develop a fast and efficient Bayesian inference pipeline that incorporates state-of-the-art Markov chain Monte Carlo techniques and use it to model the intensity data of these bursts under a flexible burst model. We revisit the 2020 April burst and corroborate that both the radio sub-components lead the corresponding peaks in their high-energy counterparts. For a burst observed in 2022 October, we find that our estimated radio pulse arrival time is contemporaneous with a short X-ray burst detected by GECAM and HEBS, and Konus-Wind and is consistent with the arrival time of a radio burst detected by GBT. We present flux and fluence estimates for all five bursts, employing an improved estimator for bursts detected in the side-lobes. We also present upper limits on radio emission for X-ray emission sources which were within CHIME/FRB's field-of-view at trigger time. Finally, we present our exposure and sensitivity analysis and estimate the Poisson rate for FRB-like events from SGR 1935+2154 to be $0.005^{+0.082}_{-0.004}$ events/day above a fluence of $10~\mathrm{kJy~ms}$ during the interval from 28 August 2018 to 1 December 2022, although we note this was measured during a time of great X-ray activity from the source.

astro-ph.HE

A CHIME/FRB study of burst rate and morphological evolution of the periodically repeating FRB 20180916B

FRB 20180916B is a repeating Fast Radio Burst (FRB) with a 16.3-day periodicity in its activity. In this study, we present morphological properties of 60 FRB 20180916B bursts detected by CHIME/FRB between 2018 August and 2021 December. We recorded raw voltage data for 45 of these bursts, enabling microseconds time resolution in some cases. We studied variation of spectro-temporal properties with time and activity phase. We find that the variation in Dispersion Measure (DM) is $\lesssim$1 pc cm$^{-3}$ and that there is burst-to-burst variation in scattering time estimates ranging from $\sim$0.16 to over 2 ms, with no discernible trend with activity phase for either property. Furthermore, we find no DM and scattering variability corresponding to the recent change in rotation measure from the source, which has implications for the immediate environment of the source. We find that FRB 20180916B has thus far shown no epochs of heightened activity as have been seen in other active repeaters by CHIME/FRB, with its burst count consistent with originating from a Poissonian process. We also observe no change in the value of the activity period over the duration of our observations and set a 1$σ$ upper limit of $1.5\times10^{-4}$ day day$^{-1}$ on the absolute period derivative. Finally, we discuss constraints on progenitor models yielded by our results, noting that our upper limits on changes in scattering and dispersion measure as a function of phase do not support models invoking a massive binary companion star as the origin of the 16.3-day periodicity.

astro-ph.HE

Stratified Learning: A General-Purpose Statistical Method for Improved Learning under Covariate Shift

We propose a simple, statistically principled, and theoretically justified method to improve supervised learning when the training set is not representative, a situation known as covariate shift. We build upon a well-established methodology in causal inference, and show that the effects of covariate shift can be reduced or eliminated by conditioning on propensity scores. In practice, this is achieved by fitting learners within strata constructed by partitioning the data based on the estimated propensity scores, leading to approximately balanced covariates and much-improved target prediction. We demonstrate the effectiveness of our general-purpose method on two contemporary research questions in cosmology, outperforming state-of-the-art importance weighting methods. We obtain the best reported AUC (0.958) on the updated "Supernovae photometric classification challenge", and we improve upon existing conditional density estimation of galaxy redshift from Sloan Data Sky Survey (SDSS) data.

stat.ML