arXiv subjects

Adam Foster

Publications and source records attributed to Adam Foster.

At least 55 records · Page 3Linked to original sources

arXiv2021

Implicit Deep Adaptive Design: Policy-Based Experimental Design without Likelihoods

We introduce implicit Deep Adaptive Design (iDAD), a new method for performing adaptive experiments in real-time with implicit models. iDAD amortizes the cost of Bayesian optimal experimental design (BOED) by learning a design policy network upfront, which can then be deployed quickly at the time of the experiment. The iDAD network can be trained on any model which simulates differentiable samples, unlike previous design policy work that requires a closed form likelihood and conditionally independent experiments. At deployment, iDAD allows design decisions to be made in milliseconds, in contrast to traditional BOED approaches that require heavy computation during the experiment itself. We illustrate the applicability of iDAD on a number of experiments, and show that it provides a fast and effective mechanism for performing adaptive design with implicit models.

stat.ML↗

arXiv2021

On Contrastive Representations of Stochastic Processes

Learning representations of stochastic processes is an emerging problem in machine learning with applications from meta-learning to physical object models to time series. Typical methods rely on exact reconstruction of observations, but this approach breaks down as observations become high-dimensional or noise distributions become complex. To address this, we propose a unifying framework for learning contrastive representations of stochastic processes (CReSP) that does away with exact reconstruction. We dissect potential use cases for stochastic process representations, and propose methods that accommodate each. Empirically, we show that our methods are effective for learning representations of periodic functions, 3D objects and dynamical processes. Our methods tolerate noisy high-dimensional observations better than traditional approaches, and the learned representations transfer to a range of downstream tasks.

stat.ML↗

arXiv2021

Unbiased MLMC stochastic gradient-based optimization of Bayesian experimental designs

In this paper we propose an efficient stochastic optimization algorithm to search for Bayesian experimental designs such that the expected information gain is maximized. The gradient of the expected information gain with respect to experimental design parameters is given by a nested expectation, for which the standard Monte Carlo method using a fixed number of inner samples yields a biased estimator. In this paper, applying the idea of randomized multilevel Monte Carlo (MLMC) methods, we introduce an unbiased Monte Carlo estimator for the gradient of the expected information gain with finite expected squared $\ell_2$-norm and finite expected computational cost per sample. Our unbiased estimator can be combined well with stochastic gradient descent algorithms, which results in our proposal of an optimization algorithm to search for an optimal Bayesian experimental design. Numerical experiments confirm that our proposed algorithm works well not only for a simple test problem but also for a more realistic pharmacokinetic problem.

stat.CO↗

arXiv2021

Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design

We introduce Deep Adaptive Design (DAD), a method for amortizing the cost of adaptive Bayesian experimental design that allows experiments to be run in real-time. Traditional sequential Bayesian optimal experimental design approaches require substantial computation at each stage of the experiment. This makes them unsuitable for most real-world applications, where decisions must typically be made quickly. DAD addresses this restriction by learning an amortized design network upfront and then using this to rapidly run (multiple) adaptive experiments at deployment time. This network represents a design policy which takes as input the data from previous steps, and outputs the next design using a single forward pass; these design decisions can be made in milliseconds during the live experiment. To train the network, we introduce contrastive information bounds that are suitable objectives for the sequential setting, and propose a customized network architecture that exploits key symmetries. We demonstrate that DAD successfully amortizes the process of experimental design, outperforming alternative strategies on a number of problems.

stat.ML↗

arXiv2021

Improving Transformation Invariance in Contrastive Representation Learning

We propose methods to strengthen the invariance properties of representations obtained by contrastive learning. While existing approaches implicitly induce a degree of invariance as representations are learned, we look to more directly enforce invariance in the encoding process. To this end, we first introduce a training objective for contrastive learning that uses a novel regularizer to control how the representation changes under transformation. We show that representations trained with this objective perform better on downstream tasks and are more robust to the introduction of nuisance transformations at test time. Second, we propose a change to how test time representations are generated by introducing a feature averaging approach that combines encodings from multiple transformations of the original input, finding that this leads to across the board performance gains. Finally, we introduce the novel Spirograph dataset to explore our ideas in the context of a differentiable generative process with multiple downstream tasks, showing that our techniques for learning invariance are highly beneficial.

cs.LG↗

arXiv2020

A Unified Stochastic Gradient Approach to Designing Bayesian-Optimal Experiments

We introduce a fully stochastic gradient based approach to Bayesian optimal experimental design (BOED). Our approach utilizes variational lower bounds on the expected information gain (EIG) of an experiment that can be simultaneously optimized with respect to both the variational and design parameters. This allows the design process to be carried out through a single unified stochastic gradient ascent procedure, in contrast to existing approaches that typically construct a pointwise EIG estimator, before passing this estimator to a separate optimizer. We provide a number of different variational objectives including the novel adaptive contrastive estimation (ACE) bound. Finally, we show that our gradient-based approaches are able to provide effective design optimization in substantially higher dimensional settings than existing approaches.

stat.ML↗

arXiv2020

Variational Bayesian Optimal Experimental Design

Bayesian optimal experimental design (BOED) is a principled framework for making efficient use of limited experimental resources. Unfortunately, its applicability is hampered by the difficulty of obtaining accurate estimates of the expected information gain (EIG) of an experiment. To address this, we introduce several classes of fast EIG estimators by building on ideas from amortized variational inference. We show theoretically and empirically that these estimators can provide significant gains in speed and accuracy over previous approaches. We further demonstrate the practicality of our approach on a number of end-to-end experiments.

stat.ML↗

arXiv2019

Unlocking the Capabilities of Future High-Resolution X-ray Spectroscopy Missions Through Laboratory Astrophysics

Thanks to high-resolution and non-dispersive spectrometers onboard future X-ray missions such as XRISM and Athena, we are finally poised to answer important questions about the formation and evolution of galaxies and large-scale structure. However, we currently lack an adequate understanding of many atomic processes behind the spectral features we will soon observe. Large error bars on parameters as critical as transition energies and atomic cross sections can lead to unacceptable uncertainties in the calculations of e.g., elemental abundance, velocity, and temperature. Unless we address these issues, we risk limiting the full scientific potential of these missions. Laboratory astrophysics, which comprises theoretical and experimental studies of the underlying physics behind observable astrophysical processes, is therefore central to the success of these missions.

astro-ph.HE↗

arXiv2019

Eigenvalue Method for NEI Unit in FLASH Code

We describe an improved nonequilibrium ionization (NEI) method that we have developed as an optional module for the FLASH magnetohydrodynamic simulation code. The method employs an eigenvalue approach rather than the earlier iterative ordinary differential equation approach to solve the stiff differential equations involved in NEI calculations. The new code also allows the atomic data to be easily updated from the AtomDB database. We compare both the updated atomic data and the methods separately. The new atomic data are shown to make a significant difference in some circumstances, although the general trends remain the same. Additionally, the new method also allows simultaneous calculation of the nonequilibrium radiative cooling, which is not included in the original method. The eigenvalue method improves the calculation efficiency overall with no loss of accuracy. We explore some common ways to present the NEI state with a sample simulation and find that using the average ionic charge difference from the equilibrium tends to be the clearest method.

astro-ph.IM↗

arXiv2019

Non-equilibrium ionization in mixed-morphology supernova remnants

The mixed morphology class of supernova remnants (MMSNRs) comprises a substantial fraction of observed remnants and yet there is as yet no consensus on their origin. A clue to their nature is the presence of regions that show X-ray evidence of recombining plasmas. Recent calculations of remnant evolution in a cloudy interstellar medium (ISM) that included thermal conduction but not non-equilibrium ionization (NEI) showed promise in explaining observed surface brightness distributions but could not determine if recombining plasmas were present. In this paper, we present numerical hydrodynamical models of MMSNRs in 2D and 3D including explicit calculation of NEI effects. Both the spatial ionization distribution and temperature-density diagrams show that recombination occurs inside the simulated MMSNR, and that both adiabatic expansion and thermal conduction cause recombination, albeit in different regions. Features created by the adiabatic expansion stand out in the spatial and temperature-density diagrams, but thermal conduction also plays a role. Thus thermal conduction and adiabatic expansion both contribute significantly to the cooling of high-temperature gas. Realistic observational data are simulated with both spatial and spectral input from various regions. We also discuss the possibility of analyzing the sources of recombination and dominant hydrodynamical processes in observations using temperature-density diagrams and spatial maps.

astro-ph.HE↗

arXiv2018

Laboratory Measurements of X-Ray Emission from Highly Charged Argon Ions

Uncertainties in atomic models will introduce noticeable additional systematics in calculating the flux of weak dielectronic recombination (DR) satellite lines, affecting the detection and flux measurements of other weak spectral lines. One important example is the Ar XVII He-beta DR, which is expected to be present in emission from the hot intracluster medium (ICM) of galaxy clusters and could impact measurements of the flux of the 3.5 keV line that has been suggested as a secondary emission from a dark matter interaction. We perform a set of experiments using the Lawrence Livermore National Laboratory's electron beam ion trap (EBIT-I) and the X-Ray Spectrometer quantum calorimeter (XRS/EBIT), to test the Ar XVII He-beta DR origin of the 3.5 keV line. We measured the X-ray emission following resonant DR onto helium-like and lithium-like Argon using EBIT-I's Maxwellian simulator mode at a simulated electron temperature of Te=1.74 keV. The measured flux of the Ar XVII He-beta DR lined is too weak to account for the flux in the 3.5 keV line assuming reasonable plasma parameters. We, therefore, rule out Ar XVII He-beta DR as a significant contributor to the 3.5 keV line. A comprehensive comparison between the atomic theory and the EBIT experiment results is also provided.

astro-ph.HE↗

arXiv2018

Sampling and Inference for Beta Neutral-to-the-Left Models of Sparse Networks

Empirical evidence suggests that heavy-tailed degree distributions occurring in many real networks are well-approximated by power laws with exponents $η$ that may take values either less than and greater than two. Models based on various forms of exchangeability are able to capture power laws with $η< 2$, and admit tractable inference algorithms; we draw on previous results to show that $η> 2$ cannot be generated by the forms of exchangeability used in existing random graph models. Preferential attachment models generate power law exponents greater than two, but have been of limited use as statistical models due to the inherent difficulty of performing inference in non-exchangeable models. Motivated by this gap, we design and implement inference algorithms for a recently proposed class of models that generates $η$ of all possible values. We show that although they are not exchangeable, these models have probabilistic structure amenable to inference. Our methods make a large class of previously intractable models useful for statistical inference.

stat.ML↗

arXiv2018

Searching for the 3.5 keV Line in the Deep Fields with Chandra: the 10 Ms observations

In this paper we report a systematic search for an emission line around 3.5 keV in the spectrum of the Cosmic X-ray Background using a total of $\sim$10 Ms Chandra observations towards the COSMOS Legacy and CDFS survey fields. We find a marginal evidence of a feature at an energy of $\sim$3.51 keV with a significance of 2.5-3 $σ$, depending on the choice of the statistical treatment. The line intensity is best fit at $8.8\ \pm\ {2.9}\times10^{-7}$ ph cm$^{-2}$s$^{-1}$ when using a simple $Δχ^2$ or $10.2\ ^{+0.2}_{-0.4} \times10^{-7}$ ph cm$^{-2}$s$^{-1}$ when MCMC is used. Based on our knowledge of $Chandra$, and the reported detection of the line by other instruments, an instrumental origin for the line remains unlikely. We cannot though rule out a statistical fluctuation and in that case our results provide a 3$σ$ upper limit at 1.85$\times$10$^{-6}$ ph cm$^{-2}$s$^{-1}$. We discuss the interpretation of this observed line in terms of the iron line background; S {\sc XVI} charge exchange as well as potentially from sterile neutrino decay. We note that our detection is consistent with previous measurements of this line toward the Galactic center, and can be modeled as the result of sterile neutrino decay from the Milky Way for the dark matter distribution modeled as an NFW profile. For this case, we estimate a mass m$_ν\sim$7.01 keV and a mixing angle sin$^2$(2$θ$)= 0.83--2.75 $\times 10^{-10}$. These derived values are in agreement with independent estimates from galaxy clusters; the Galactic center and M31.

astro-ph.CO↗

arXiv2017

Numerical Simulations of Supernova Remnant Evolution in a Cloudy Interstellar Medium

The mixed morphology class of supernova remnants has centrally peaked X-ray emission along with a shell-like morphology in radio emission. White & Long proposed that these remnants are evolving in a cloudy medium wherein the clouds are evaporated via thermal conduction once being overrun by the expanding shock. Their analytical model made detailed predictions regarding temperature, density and emission profiles as well as shock evolution. We present numerical hydrodynamical models in 2D and 3D including thermal conduction, testing the White & Long model and presenting results for the evolution and emission from remnants evolving in a cloudy medium. We find that, while certain general results of the White & Long model hold, such as the way the remnants expand and the flattening of the X-ray surface brightness distribution, in detail there are substantial differences. In particular we find that the X-ray luminosity is dominated by emission from shocked cloud gas early on, leading to a bright peak which then declines and flattens as evaporation becomes more important. In addition, the effects of thermal conduction on the intercloud gas, which is not included in the White & Long model, are important and lead to further flattening of the X-ray brightness profile as well as lower X-ray emission temperatures.

astro-ph.HE↗

arXiv2016

Searching for the 3.5 keV Line in the Stacked Suzaku Observations of Galaxy Clusters

We perform a detailed study of the stacked Suzaku observations of 47 galaxy clusters, spanning a redshift range of 0.01-0.45, to search for the unidentified 3.5 keV line. This sample provides an independent test for the previously detected line. We detect only a 2sigma-significant spectral feature at 3.5 keV in the spectrum of the full sample. When the sample is divided into two subsamples (cool-core and non-cool core clusters), cool-core subsample shows no statistically significant positive residuals at the line energy. A very weak (2sigma-confidence) spectral feature at 3.5 keV is permitted by the data from the non-cool core clusters sample. The upper limit on a neutrino decay mixing angle from the full Suzaku sample is consistent with the previous detections in the stacked XMM-Newton sample of galaxy clusters (which had a higher statistical sensitivity to faint lines), M31, and Galactic Center at a 90% confidence level. However, the constraint from the present sample, which does not include the Perseus cluster, is in tension with previously reported line flux observed in the core of the Perseus cluster with XMM-Newton and Suzaku.

astro-ph.HE↗

arXiv2016

The Quiescent Intracluster Medium in the Core of the Perseus Cluster

Clusters of galaxies are the most massive gravitationally-bound objects in the Universe and are still forming. They are thus important probes of cosmological parameters and a host of astrophysical processes. Knowledge of the dynamics of the pervasive hot gas, which dominates in mass over stars in a cluster, is a crucial missing ingredient. It can enable new insights into mechanical energy injection by the central supermassive black hole and the use of hydrostatic equilibrium for the determination of cluster masses. X-rays from the core of the Perseus cluster are emitted by the 50 million K diffuse hot plasma filling its gravitational potential well. The Active Galactic Nucleus of the central galaxy NGC1275 is pumping jetted energy into the surrounding intracluster medium, creating buoyant bubbles filled with relativistic plasma. These likely induce motions in the intracluster medium and heat the inner gas preventing runaway radiative cooling; a process known as Active Galactic Nucleus Feedback. Here we report on Hitomi X-ray observations of the Perseus cluster core, which reveal a remarkably quiescent atmosphere where the gas has a line-of-sight velocity dispersion of 164+/-10 km/s in a region 30-60 kpc from the central nucleus. A gradient in the line-of-sight velocity of 150+/-70 km/s is found across the 60 kpc image of the cluster core. Turbulent pressure support in the gas is 4% or less of the thermodynamic pressure, with large scale shear at most doubling that estimate. We infer that total cluster masses determined from hydrostatic equilibrium in the central regions need little correction for turbulent pressure.

astro-ph.GA↗

arXiv2016

Radial Profile of the 3.55 keV line out to $R_{200}$ in the Perseus Cluster

The recent discovery of the unidentified emission line at 3.55 keV in galaxies and clusters has attracted great interest from the community. As the origin of the line remains uncertain, we study the surface brightness distribution of the line in the Perseus cluster since that information can be used to identify its origin. We examine the flux distribution of the 3.55 keV line in the deep Suzaku observations of the Perseus cluster in detail. The 3.55 keV line is observed in three concentric annuli in the central observations, although the observations of the outskirts of the cluster did not reveal such a signal. We establish that these detections and the upper limits from the non-detections are consistent with a dark matter decay origin. However, absence of positive detection in the outskirts is also consistent with some unknown astrophysical origin of the line in the dense gas of the Perseus core, as well as with a dark matter origin with a steeper dependence on mass than the dark matter decay. We also comment on several recently published analyses of the 3.55 keV line.

astro-ph.CO↗

arXiv2016

SNR 1E 0102.2-7219 as an X-ray Calibration Standard in the 0.5-1.0 keV Bandpass and Its Application to the CCD Instruments aboard Chandra, Suzaku, Swift and XMM-Newton

We desire a simple comparison of the absolute effective areas of the current generation of CCD instruments onboard the following observatories: Chandra ACIS-S3, XMM-Newton (EPIC-MOS and EPIC-pn), Suzaku XIS, and Swift XRT and a straightforward comparison of the time-dependent response of these instruments across their respective mission lifetimes. We have been using 1E 0102.2-7219, the brightest supernova remnant in the Small Magellanic Cloud, to evaluate and modify the response models of these instruments. 1E 0102.2-7219 has strong lines of O, Ne, and Mg below 1.5 keV and little or no Fe emission to complicate the spectrum. As part of the activities of the International Astronomical Consortium for High Energy Calibration (IACHEC), we have developed a standard spectral model for 1E 0102.2-7219. The model is empirical in that it includes Gaussians for the identified lines, an absorption component in the Galaxy, another absorption component in the SMC, and two thermal continuum components. In our fits, the model is highly constrained in that only the normalizations of the four brightest lines/line complexes (the O vii He$α$ triplet, O viii Ly$α$ line, the Ne ix He$α$ triplet, and the Ne x Ly$α$ line) and an overall normalization are allowed to vary. We have examined these measured line fluxes as a function of time for each instrument after applying the most recent calibrations that account for the time-dependent response of each instrument. We perform our effective area comparison with representative, early mission data when the radiation damage and contamination layers were at a minimum. We find that the measured fluxes of these lines generally agree to within +/-10% for all instruments, with 38 of our 48 fitted normalizations within +/-10% of the IACHEC model value.

astro-ph.IM↗