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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

The Attraction Indian Buffet Distribution

We propose the attraction Indian buffet distribution (AIBD), a distribution for binary feature matrices influenced by pairwise similarity information. Binary feature matrices are used in Bayesian models to uncover latent variables (i.e., features) that explain observed data. The Indian buffet process (IBP) is a popular exchangeable prior distribution for latent feature matrices. In the presence of additional information, however, the exchangeability assumption is not reasonable or desirable. The AIBD can incorporate pairwise similarity information, yet it preserves many properties of the IBP, including the distribution of the total number of features. Thus, much of the interpretation and intuition that one has for the IBP directly carries over to the AIBD. A temperature parameter controls the degree to which the similarity information affects feature-sharing between observations. Unlike other nonexchangeable distributions for feature allocations, the probability mass function of the AIBD has a tractable normalizing constant, making posterior inference on hyperparameters straight-forward using standard MCMC methods. A novel posterior sampling algorithm is proposed for the IBP and the AIBD. We demonstrate the feasibility of the AIBD as a prior distribution in feature allocation models and compare the performance of competing methods in simulations and an application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Non-Gaussianity in the weak lensing correlation function likelihood – implications for cosmological parameter biases

ABSTRACT We study the significance of non-Gaussianity in the likelihood of weak lensing shear two-point correlation functions, detecting significantly non-zero skewness and kurtosis in 1D marginal distributions of shear two-point correlation functions in simulated weak lensing data. We examine the implications in the context of future surveys, in particular LSST, with derivations of how the non-Gaussianity scales with survey area. We show that there is no significant bias in 1D posteriors of Ωm and σ8 due to the non-Gaussian likelihood distributions of shear correlations functions using the mock data (100 deg2). We also present a systematic approach to constructing approximate multivariate likelihoods with 1D parametric functions by assuming independence or more flexible non-parametric multivariate methods after decorrelating the data points using principal component analysis (PCA). While the use of PCA does not modify the non-Gaussianity of the multivariate likelihood, we find empirically that the 1D marginal sampling distributions of the PCA components exhibit less skewness and kurtosis than the original shear correlation functions. Modelling the likelihood with marginal parametric functions based on the assumption of independence between PCA components thus gives a lower limit for the biases. We further demonstrate that the difference in cosmological parameter constraints between the multivariate Gaussian likelihood model and more complex non-Gaussian likelihood models would be even smaller for an LSST-like survey. In addition, the PCA approach automatically serves as a data compression method, enabling the retention of the majority of the cosmological information while reducing the dimensionality of the data vector by a factor of ∼5.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

A Strong Gravitational Lens Is Worth a Thousand Dark Matter Halos: Inference on Small-scale Structure Using Sequential Methods

Strong gravitational lenses are a singular probe of the Universe’s small-scale structure—they are sensitive to the gravitational effects of low-mass (<10 10 M ⊙ ) halos even without a luminous counterpart. Recent strong-lensing analyses of dark matter structure rely on simulation-based inference (SBI). Modern SBI methods, which leverage neural networks as density estimators, have shown promise in extracting the halo-population signal. However, it is unclear whether the constraints from these models are limited by the methodology or the data. In this study, we introduce an accelerator-optimized simulation pipeline that can generate lens images with realistic subhalo populations in milliseconds. Leveraging this simulator, we identify the main limitation of our fiducial SBI analysis: training set size. We then adopt a sequential neural posterior estimation (SNPE) approach, allowing us to refine the training distribution to align with the observed data. Using only one-fifth as many mock Hubble Space Telescope images, SNPE matches the constraints on the low-mass halo population produced by our best nonsequential model. Our experiments suggest that an over 3 order-of-magnitude increase in training set size and GPU hours would be required to achieve an equivalent result without sequential methods. While the full potential of the existing lens sample remains to be explored, the notable improvement in constraining power enabled by our sequential approach highlights that current constraints are limited primarily by methodology and not the data itself. Moreover, our results emphasize the need to treat training set generation and model optimization as interconnected stages of any cosmological analysis using SBI.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1978

Estimation from incomplete multinomial data

The vector of multinomial cell probabilities was estimated from incomplete data, incomplete in that it contains partially classified observations. Each such partially classified observation was observed to fall in one of two or more selected categories but was not classified further into a single category. The data were assumed to be incomplete at random. The estimation criterion was minimization of risk for quadratic loss. The estimators were the classical maximum likelihood estimate, the Bayesian posterior mode, and the posterior mean. An approximation was developed for the posterior mean. The Dirichlet, the conjugate prior for the multinomial distribution, was assumed for the prior distribution.

Credeur, K. R.↗
DOE OSTI2024

Calibrating Bayesian generative machine learning for Bayesiamplification

Recently, combinations of generative and Bayesian deep learning have been introduced in particle physics for both fast detector simulation and inference tasks. These neural networks aim to quantify the uncertainty on the generated distribution originating from limited training statistics. The interpretation of a distribution-wide uncertainty however remains ill-defined. We show a clear scheme for quantifying the calibration of Bayesian generative machine learning models. For a Continuous Normalizing Flow applied to a low-dimensional toy example, we evaluate the calibration of Bayesian uncertainties from either a mean-field Gaussian weight posterior, or Monte Carlo sampling network weights, to gauge their behaviour on unsteady distribution edges. Well calibrated uncertainties can then be used to roughly estimate the number of uncorrelated truth samples that are equivalent to the generated sample and clearly indicate data amplification for smooth features of the distribution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Interpreting High-resolution Spectroscopy of Exoplanets using Cross-correlations and Supervised Machine Learning

We present a new method for performing atmospheric retrieval on ground-based, high-resolution data of exoplanets. Our method combines cross-correlation functions with a random forest, a supervised machine-learning technique, to overcome challenges associated with high-resolution data. A series of cross-correlation functions are concatenated to give a “CCF-sequence” for each model atmosphere, which reduces the dimensionality by a factor of ∼100. The random forest, trained on our grid of ∼65,000 models, provides a likelihood-free method of retrieval. The precomputed grid spans 31 values of both temperature and metallicity, and incorporates a realistic noise model. We apply our method to HARPS-N observations of the ultra-hot Jupiter KELT-9b and obtain a metallicity consistent with solar (logM = − 0.2 ± 0.2). Our retrieved transit chord temperature (T=6000{sub −200}{sup +0}K) is unreliable as strong ion lines lie outside of the extent of the training set, which we interpret as being indicative of missing physics in our atmospheric model. We compare our method to traditional nested sampling, as well as other machine-learning techniques, such as Bayesian neural networks. We demonstrate that the likelihood-free aspect of the random forest makes it more robust than nested sampling to different error distributions, and that the Bayesian neural network we tested is unable to reproduce complex posteriors. We also address the claim in Cobb et al. 2019 that our random forest retrieval technique can be overconfident but incorrect. We show that this is an artifact of the training set, rather than of the machine-learning method, and that the posteriors agree with those obtained using nested sampling.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Posterior Regularized Bayesian Neural Network

Traditional NNs often lack the ability for uncertainty quantification. Bayesian NNs(BNNs) could help measure the confidence level by using distributions in NNs modeling. Besides, knowledge is commonly available and could improve the performance of BNNs if it can be properly incorporated. In this work, we propose a novel Posterior-Regularized BNN(PR-BNN) model by incorporating soft and hard constraints as a posterior regularization term. We also propose an augmented Lagrangian method and stochastic optimization algorithm for efficient updating via Monte Carlo sampling. The simulations and case studies for solar PV plants have shown the performance improvement of the proposed model over traditional BNNs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Posterior Regularized Bayesian Neural Network

Traditional NNs often lack the ability for uncertainty quantification. Bayesian NNs(BNNs) could help measure the confidence level by using distributions in NNs modeling. Besides, knowledge is commonly available and could improve the performance of BNNs if it can be properly incorporated. In this work, we propose a novel Posterior-Regularized BNN(PR-BNN) model by incorporating soft and hard constraints as a posterior regularization term. We also propose an augmented Lagrangian method and stochastic optimization algorithm for efficient updating via Monte Carlo sampling. The simulations and case studies in solar energy prediction have shown the performance improvement of the proposed model over traditional BNNs.

14 SOLAR ENERGY↗
DOE OSTI2021

A composite likelihood approach for inference under photometric redshift uncertainty

ABSTRACT Obtaining accurately calibrated redshift distributions of photometric samples is one of the great challenges in photometric surveys like LSST, Euclid, HSC, KiDS, and DES. We present an inference methodology that combines the redshift information from the galaxy photometry with constraints from two-point functions, utilizing cross-correlations with spatially overlapping spectroscopic samples, and illustrate the approach on CosmoDC2 simulations. Our likelihood framework is designed to integrate directly into a typical large-scale structure and weak lensing analysis based on two-point functions. We discuss efficient and accurate inference techniques that allow us to scale the method to the large samples of galaxies to be expected in LSST. We consider statistical challenges like the parametrization of redshift systematics, discuss and evaluate techniques to regularize the sample redshift distributions, and investigate techniques that can help to detect and calibrate sources of systematic error using posterior predictive checks. We evaluate and forecast photometric redshift performance using data from the CosmoDC2 simulations, within which we mimic a DESI-like spectroscopic calibration sample for cross-correlations. Using a combination of spatial cross-correlations and photometry, we show that we can provide calibration of the mean of the sample redshift distribution to an accuracy of at least 0.002(1 + z), consistent with the LSST-Y1 science requirements for weak lensing and large-scale structure probes.

(cosmology:) large-scale structure of Universe↗
NASA NTRS2001

Quantitative molecular characterization of bovine vitreous and lens with non-invasive dynamic light scattering

The non-invasive technique of dynamic light scattering (DLS) was used to quantitatively characterize vitreous and lens structure on a molecular level by measuring the sizes of the predominant particles and mapping the three-dimensional topographic distribution of these structural macromolecules in three spatial dimensions. The results of DLS measurements in five fresh adult bovine eyes were compared to DLS measurements in model solutions of hyaluronan (HA) and collagen (Coll). In the bovine eyes DLS measurements were obtained from excised samples of gel and liquid vitreous and compared to the model solutions. Measurements in whole vitreous were obtained at multiple points posterior to the lens to generate a three-dimensional 'map' of molecular structure. The macromolecule distribution in bovine lens was similarly characterized.In each bovine vitreous (Bo Vit) specimen, DLS predominantly detected two distinct particles, which differed in diffusion properties and hence size. Comparisons with model vitreous solutions demonstrated that these most likely corresponded to the Coll and HA components of vitreous. Three-dimensional mapping of Bo Vit found heterogeneity throughout the vitreous body, with different particle size distributions for Coll and HA at different loci. In contrast, the three-dimensional distribution of lens macromolecules was more homogeneous. Thus, the non-invasive DLS technique can quantitate the average sizes of vitreous and lens macromolecules and map their three-dimensional distribution. This method to assess quantitatively the macromolecular structure of vitreous and lens should be useful for clinical as well as experimental applications in health and disease. Copyright 2001 Academic Press.

Models, Molecular↗
DOE OSTI2023

Generalized Bayesian Framework for Evaluation of Integral Benchmark Experiments

A recently published generalized Bayesian optimization framework has provided a way to retract any or all of the three common assumptions underlying the conventional Generalized Linear Least Squares (GLLS) optimization method based on the concepts introduced in Ref. [2]. These assumptions are: 1. Perfection: The model used for data evaluation and the prior probability distribution function (PDF) of generalized data are perfect. 2. Normality: The prior and posterior PDF are normal. 3. Linearity: The model is linear. In this work we outline how the framework in [1] could be directly adopted for improved evaluation of nuclear criticality integral benchmark experiments (IBEs) by: 1. Removing the first assumption alone by utilizing the concept of imperfections introduced in [1] to enable evaluation in the presence of discrepancies between the data and model or of missing covariance information by a GLLS method that will be seen as a generalization of the conventional GLLS method employed by the TSURFER code, and by 2. Removing the remaining two assumptions by implementing a Markov Chain Monte Carlo method for computation of the posterior PDF in the SAMPLER code, where TSURFER and SAMPLER are the uncertainty quantification (UQ) codes for IBEs in the SCALE code system based on the GLLS and the stochastic method, respectively. The graphic in Figure 1 categorizes the methods discussed in terms of the assumptions that they employ to determine posterior PDFs.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Generalized Bayesian Framework for Evaluation of Integral Benchmark Experiments

A recently published generalized Bayesian optimization framework has provided a way to retract any or all of the three common assumptions underlying the conventional Generalized Linear Least Squares (GLLS) optimization method based on the concepts introduced in reference two. These assumptions are: 1. Perfection: The model used for data evaluation and the prior probability distribution function (PDF) of generalized* data are perfect; 2. Normality: The prior and posterior PDF are normal; and 3. Linearity: The model is linear. In this work we outline how the framework in 1 could be directly adopted for improved evaluation of nuclear criticality integral benchmark experiments (IBEs) by: 1. Removing the first assumption alone by utilizing the concept of imperfections introduced in 1 to enable evaluation in the presence of discrepancies between the data and model or of missing covariance information by a GLLS method that will be seen as a generalization of the conventional GLLS method employed by the TSURFER code, and by 2. Removing the remaining two assumptions by implement- ing a Markov Chain Monte Carlo method for computation of the posterior PDF in the SAMPLER code, where TSURFER and SAMPLER are the uncertainty quantification (UQ) codes for IBEs in the SCALE code system based on the GLLS, and the stochastic method, respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Learning functional priors and posteriors from data and physics

In this work, we develop a new Bayesian framework based on deep neural networks to be able to extrapolate in space-time using historical data and to quantify uncertainties arising from both noisy and gappy data in physical problems. Specifically, the proposed approach has two stages: (1) prior learning and (2) posterior estimation. At the first stage, we employ the physics-informed Generative Adversarial Networks (PI-GAN) to learn a functional prior either from a prescribed function distribution, e.g., Gaussian process, or from historical data and physics. At the second stage, we employ the Hamiltonian Monte Carlo (HMC) method to estimate the posterior in the latent space of PI-GANs. In addition, we use two different approaches to encode the physics: (1) automatic differentiation, used in the physicsinformed neural networks (PINNs) for scenarios with explicitly known partial differential equations (PDEs), and (2) operator regression using the deep operator network (DeepONet) for PDE-agnostic scenarios. We then test the proposed method for (1) meta-learning for one-dimensional regression, and forward/inverse PDE problems (combined with PINNs); (2) PDE-agnostic physical problems (combined with DeepONet), e.g., fractional diffusion as well as saturated stochastic (100-dimensional) flows in heterogeneous porous media; and (3) spatial-temporal regression problems, i.e., inference of a marine riser displacement field using experimental data from the Norwegian Deepwater Programme (NDP). The results demonstrate that the proposed approach can provide accurate predictions as well as uncertainty quantification given very limited scattered and noisy data, since historical data could be available to provide informative priors. In summary, the proposed method is capable of learning flexible functional priors, e.g., both Gaussian and non-Gaussian process, and can be readily extended to big data problems by enabling mini-batch training using stochastic HMC or normalizing flows since the latent space is generally characterized as low dimensional.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Enhancing approximate modular Bayesian inference by emulating the conditional posterior

In modular Bayesian analyses, complex models are composed of distinct modules, each representing different aspects of the data or prior information. In this context, fully Bayesian approaches can sometimes lead to undesirable feedback between modules, compromising the integrity of the inference. The “cut-distribution” prevents unwanted influence between modules by “cutting” feedback. The direct sampling (DS) algorithm is standard practice for approximating the cut-distribution, but it can be computationally intensive, especially when the number of imputations required is large. An enhanced method is proposed, the Emulating the Conditional Posterior (ECP) algorithm, which leverages emulation to increase the number of imputations. Through numerical experiment it is demonstrated that the ECP algorithm outperforms the traditional DS approach in terms of accuracy and computational efficiency, particularly when resources are constrained. Here, it is also shown how the DS algorithm can be improved using ideas from design of experiments. Some practical recommendations are given for algorithm choice in modular Bayesian analyses.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Future projections and uncertainty assessment of precipitation extremes in the Korean peninsula from the CMIP5 ensemble

Abstract Projections of changes in extreme climate are sometimes predicted by multimodel ensemble methods that combine forecasts from individual simulation models using weighted averaging. One method to assign weight to each model is the Bayesian model averaging (BMA) in which posterior probability is used. For the cases of extreme climate, the generalized extreme value distribution (GEVD) is typically used. We applied the approach of GEV‐embedded BMA to a series of 35 years of the annual maximum daily precipitation data (both historical data and data gathered from simulation experiments for future periods) over the Korean peninsula as simulated by the models in the Coupled Model Intercomparison Project Phase 5 (CMIP5). Simulation data under two Representative Concentration Pathway (RCP) scenarios, namely RCP4.5 and RCP8.5, were used. Observed data and 17 CMIP5 models for 12 gird cells in Korea have been examined to predict future changes in precipitation extremes. A simple regional frequency analysis of pooling observations from three stations in each cell was employed to reduce the estimation variance and local fluctuations. A bias correction technique using the regression‐type transfer function was applied to these simulation data. Return levels spanning over 20 and 50 years, as well as the return periods relative to the reference years (1971–2005), were estimated for two future periods, namely Period 1 (2021–2050) and Period 2 (2066–2095). From these analyses, relative increase observed in the spatially averaged 20‐year (50‐year) return level was approximately 23% (16%) and 45% (36%) in the RCP4.5 and RCP8.5 experiments, respectively, by the end of the 21st century. We concluded that extreme rainfalls will likely occur two times and four times more frequently in the RCP4.5 and RCP8.5 scenarios, respectively, as compared to in the reference years by the end of the 21st century.

Lee, Youngsaeng↗
NASA NTRS1993

Two-dimensional spatiotemporal coding of linear acceleration in vestibular nuclei neurons

Response properties of vertical (VC) and horizontal (HC) canal/otolith-convergent vestibular nuclei neurons were studied in decerebrate rats during stimulation with sinusoidal linear accelerations (0.2-1.4 Hz) along different directions in the head horizontal plane. A novel characteristic of the majority of tested neurons was the nonzero response often elicited during stimulation along the "null" direction (i.e., the direction perpendicular to the maximum sensitivity vector, Smax). The tuning ratio (Smin gain/Smax gain), a measure of the two-dimensional spatial sensitivity, depended on stimulus frequency. For most vestibular nuclei neurons, the tuning ratio was small at the lowest stimulus frequencies and progressively increased with frequency. Specifically, HC neurons were characterized by a flat Smax gain and an approximately 10-fold increase of Smin gain per frequency decade. Thus, these neurons encode linear acceleration when stimulated along their maximum sensitivity direction, and the rate of change of linear acceleration (jerk) when stimulated along their minimum sensitivity direction. While the Smax vectors were distributed throughout the horizontal plane, the Smin vectors were concentrated mainly ipsilaterally with respect to head acceleration and clustered around the naso-occipital head axis. The properties of VC neurons were distinctly different from those of HC cells. The majority of VC cells showed decreasing Smax gains and small, relatively flat, Smin gains as a function of frequency. The Smax vectors were distributed ipsilaterally relative to the induced (apparent) head tilt. In type I anterior or posterior VC neurons, Smax vectors were clustered around the projection of the respective ipsilateral canal plane onto the horizontal head plane. These distinct spatial and temporal properties of HC and VC neurons during linear acceleration are compatible with the spatiotemporal organization of the horizontal and the vertical/torsional ocular responses, respectively, elicited in the rat during linear translation in the horizontal head plane. In addition, the data suggest a spatially and temporally specific and selective otolith/canal convergence. We propose that the central otolith system is organized in canal coordinates such that there is a close alignment between the plane of angular acceleration (canal) sensitivity and the plane of linear acceleration (otolith) sensitivity in otolith/canal-convergent vestibular nuclei neurons.

NASA Discipline Neuroscience↗
DOE OSTI2025

Lens Modeling of STRIDES Strongly Lensed Quasars Using Neural Posterior Estimation

Strongly lensed quasars can be used to constrain cosmological parameters through time-delay cosmography. Models of the lens masses are a necessary component of this analysis. To enable time-delay cosmography from a sample of $\mathcal{O}(10^3)$ lenses, which will soon become available from surveys like the Rubin Observatory’s Legacy Survey of Space and Time and the Euclid Wide Survey, we require fast and standardizable modeling techniques. To address this need, we apply neural posterior estimation (NPE) for modeling galaxy-scale strongly lensed quasars from the Strong Lensing Insights into the Dark Energy Survey (STRIDES) sample. NPE brings two advantages: speed and the ability to implicitly marginalize over nuisance parameters. We extend this method by employing sequential NPE to increase precision of mass model posteriors. We then fold individual lens models into a hierarchical Bayesian inference to recover the population distribution of lens mass parameters, accounting for out-of-distribution shift. After verifying our method using simulated analogs of the STRIDES lens sample, we apply our method to 14 Hubble Space Telescope single-filter observations. We find the population mean of the power-law elliptical mass distribution slope, γ lens , to be $\mathcal{M}_γ$ lens = 2.13 ± 0.06. Our result represents the first population-level constraint for these systems. This population-level inference from fully automated modeling is an important stepping stone toward cosmological inference with large samples of strongly lensed quasars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Hierarchical Inference of the Lensing Convergence from Photometric Catalogs with Bayesian Graph Neural Networks

Abstract We present a Bayesian graph neural network (BGNN) that can estimate the weak lensing convergence ( κ ) from photometric measurements of galaxies along a given line of sight (LOS). The method is of particular interest in strong gravitational time-delay cosmography (TDC), where characterizing the “external convergence” ( κ ext ) from the lens environment and LOS is necessary for precise Hubble constant ( H 0 ) inference. Starting from a large-scale simulation with a κ resolution of ∼1′, we introduce fluctuations on galaxy–galaxy lensing scales of ∼1″ and extract random sight lines to train our BGNN. We then evaluate the model on test sets with varying degrees of overlap with the training distribution. For each test set of 1000 sight lines, the BGNN infers the individual κ posteriors, which we combine in a hierarchical Bayesian model to yield constraints on the hyperparameters governing the population. For a test field well sampled by the training set, the BGNN recovers the population mean of κ precisely and without bias (within the 2 σ credible interval), resulting in a contribution to the H 0 error budget well under 1%. In the tails of the training set with sparse samples, the BGNN, which can ingest all available information about each sight line, extracts a stronger κ signal compared to a simplified version of the traditional method based on matching galaxy number counts, which is limited by sample variance. Our hierarchical inference pipeline using BGNNs promises to improve the κ ext characterization for precision TDC. The code is available as a public Python package, Node to Joy ⏬ .

79 ASTRONOMY AND ASTROPHYSICS↗