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Fast and efficient identification of anomalous galaxy spectra with neural density estimation
ABSTRACT Current large-scale astrophysical experiments produce unprecedented amounts of rich and diverse data. This creates a growing need for fast and flexible automated data inspection methods. Deep learning algorithms can capture and pick up subtle variations in rich data sets and are fast to apply once trained. Here, we study the applicability of an unsupervised and probabilistic deep learning framework, the probabilistic auto-encoder, to the detection of peculiar objects in galaxy spectra from the SDSS survey. Different to supervised algorithms, this algorithm is not trained to detect a specific feature or type of anomaly, instead it learns the complex and diverse distribution of galaxy spectra from training data and identifies outliers with respect to the learned distribution. We find that the algorithm assigns consistently lower probabilities (higher anomaly score) to spectra that exhibit unusual features. For example, the majority of outliers among quiescent galaxies are E+A galaxies, whose spectra combine features from old and young stellar population. Other identified outliers include LINERs, supernovae, and overlapping objects. Conditional modelling further allows us to incorporate additional information. Namely, we evaluate the probability of an object being anomalous given a certain spectral class, but other information such as metrics of data quality or estimated redshift could be incorporated as well. We make our code publicly available.
Classifying anomalies through outer density estimation
Not Available
Neural Density Estimation and Uncertainty Quantification for ChemCam Spectra [Slides]
The ChemCam instrument of Curiosity uses laser-induced breakdown spectroscopy (LIBS). It fires a laser at target and vaporizes rock surfaces, creating a plasma. Three spectrographs divide the plasma light into wavelengths for chemical analysis: ultraviolet, violet, and visible near-infrared. Regression methods (SVR, PCR, CNN) have been employed for calibration (prediction of the elemental composition of samples); however, labeled ChemCam samples are limited. Here, we focus on unsupervised learning and employ generative models from ChemCam analysis. Further, we use labels (supervised) in combination to the generative model to compute uncertainties related to predictions. We report generative modeling can be successfully applied to model real-world data. Normalizing flow models can be efficiently constructed on latent spaces for fast downstream inference. Unsupervised and supervised learning can be combined to form an uncertainty quantification framework.
Leveraging Physics-based Surrogates for Efficient Density Estimation of Sparse Observable Data on Low-dimensional Manifolds.
Abstract not provided.
Density Estimation via Measure Transport
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Comparison of removal and spatial mark‐resight models for estimating wild pig density
Density estimation is critical to effectively manage invasive species and elucidate areas of highest concern. For wild pigs (Sus scrofa), the ability to estimate density is complicated because of their variable home range sizes and social structure. Common methods for estimating density (e.g., mark-recapture) may be unsuitable in management applications because additional data needs to be collected before and after management. Removal models offer a suitable alternative to estimate density changes following management and can be applied broadly across areas where management of wild pigs is ongoing. We collected wild pig removal and camera trap data from 25 private properties ranging in size from approximately 0.5 km 2 to 95 km 2 across 3 ecoregions in South Carolina, USA, from 2020–2023. We compared factors affecting consistency and precision of property-level density estimates between removal and spatial mark-resight (SMR) models. In general, excluding 1 large outlier, density estimates from removal models were between 0.60 and 15.85 wild pigs/km 2 (median = 5.34) with a median coefficient of variation (CV) of 0.76 and 95% confidence intervals for the CV between 0.70 and 0.94. Similarly, excluding 1 large outlier, density estimates from SMR were between 0.22 and 30.97 wild pigs/km 2 (median = 5.48) with a median CV of 0.39 and 95% confidence intervals for the CV between 0.38 and 1.20. We found the precision of removal models was affected primarily by the number of wild pigs dispatched in the removal period (3 months) and the ecoregion in which they were removed. None of the covariates, including the number of recaptures (a corresponding measure of sample size), influenced precision of the SMR models, although recaptures did influence the density estimates. At the individual property level, density estimates from our 2 estimators were dissimilar from each other in approximately 80% of instances, although none of the covariates we examined influenced dissimilarity. Our results provide unique insight into how sample size affects density estimates using 2 common methods and into novel SMR models that incorporate both marked and unmarked detections. In addition, the density estimates in this study can be used as a reference for wild pig densities in common land cover types throughout the southeastern United States.
Raccoon densities across four land cover types in the southeastern United States
Raccoons (Procyon lotor) are the primary reservoir for rabies virus in eastern North America. Management of rabies in raccoons is achieved primarily with the use of oral rabies vaccination (ORV) and effective ORV bait densities are determined in part by the densities of raccoons. Decisions regarding ORV bait densities, however, are limited by an incomplete understanding of raccoon densities across the spectrum of landscapes they occupy. We carried out a mark-recapture study of raccoons on the Savannah River Site in South Carolina, USA, from 2017–2019, to develop sex- and landscape-specific raccoon density estimates across 4 rural land cover types in the southeastern United States: bottomland hardwood, riparian forest, isolated wetland, and upland pine (Pinus spp.). We captured 404 unique raccoons 773 times over the 3-year trapping period. Estimated densities were 5.44 ± 0.37 (SE) animals/km 2 in bottomland hardwood forest, 2.62 ± 0.32 animals/km 2 in riparian forest, 2.19 ± 0.29 animals/km 2 in isolated wetlands, and 2.14 ± 0.23 animals/km 2 in upland pine. Densities were significantly higher in bottomland hardwood than all other land cover types, whereas densities among the remaining cover types were similar. These patterns are likely the result of landscape fragmentation and configuration, with riparian forests typically embedded in a matrix of less suitable cover types, leading to low densities despite presumably high resource availability. There were higher densities of males than females in every cover type except upland pine, where the sex ratio was balanced. Densities on our site were low compared to other rural areas, which likely results from the lack of human influence in terms of agriculture or development. The financial cost of baiting for ORV distribution may be reduced by considering the comparatively low densities of raccoons in these rural landscapes in the southeastern United States.
Detecting Anomalies in Time Series Using Kernel Density Approaches
This paper introduces a novel anomaly detection approach tailored for time series data with exclusive reliance on normal events during training. Our key innovation lies in the application of kernel-density estimation (KDE) to scrutinize reconstruction errors, providing an empirically derived probability distribution for normal events post-reconstruction. This non-parametric density estimation technique offers a nuanced understanding of anomaly detection, differentiating it from prevalent threshold-based mechanisms in existing methodologies. In post-training, events are encoded, decoded, and evaluated against the estimated density, providing a comprehensive notion of normality. In addition, we propose a data augmentation strategy involving variational autoencoder-generated events and a smoothing step for enhanced model robustness. The significance of our autoencoder-based approach is evident in its capacity to learn normal representation without prior anomaly knowledge. Through the KDE step on reconstruction errors, our method addresses the versatility of anomalies, departing from assumptions tied to larger reconstruction errors for anomalous events. Our proposed likelihood measure then distinguishes normal from anomalous events, providing a concise yet comprehensive anomaly detection solution. The extensive experimental results support the feasibility of our proposed method, yielding significantly improved classification performance by nearly 10% on the UCR benchmark data.
High-dimensional and permutation invariant anomaly detection
Methods for anomaly detection of new physics processes are often limited to low-dimensional spaces due to the difficulty of learning high-dimensional probability densities. Particularly at the constituent level, incorporating desirable properties such as permutation invariance and variable-length inputs becomes difficult within popular density estimation methods. In this work, we introduce a permutation-invariant density estimator for particle physics data based on diffusion models, specifically designed to handle variable-length inputs. We demonstrate the efficacy of our methodology by utilizing the learned density as a permutation-invariant anomaly detection score, effectively identifying jets with low likelihood under the background-only hypothesis. To validate our density estimation method, we investigate the ratio of learned densities and compare to those obtained by a supervised classification algorithm.
Application of the Redlich-Kister expansion for estimating the density of molten fluoride psuedo-ternary salt systems of nuclear industry interest
The development of next-generation molten salt reactors relies on accurate knowledge of the thermophysical properties of the candidate coolant and fueled molten salts. These thermophysical properties include density, viscosity, thermal conductivity, and heat capacity. Because of difficulties in measuring thermophysical properties of molten salts, there are many gaps in the current state of thermophysical property knowledge of these salts, particularly those that contain actinides or beryllium. Therefore, leveraging modeling techniques to estimate unknown molten salt thermophysical properties and guide future experimental measurements has high value for the nuclear industry. Here, the densities of molten fluoride pseudo-ternary salt systems, which are of interest to the nuclear industry, were estimated using Redlich-Kister expansion and Muggianu interpolation techniques. The pseudo-ternary systems considered for estimation in this study were NaF-LiF-ZrF 4 , LiF-BeF 2 -ZrF 4 , LiF-BeF 2 -ThF 4 , NaF-LiF-BeF 2 , NaF-KF-BeF 2 , NaF-ZrF 4 -UF 4 , and NaF-BeF 2 -UF 4 . This Redlich-Kister estimation approach accounts for nonideal mixing behavior based on pseudo-binary subsystem interaction parameters determined from experimentally measured pseudo-binary system density data sets. The Redlich-Kister estimation was compared with the method of additive molar volumes, which assumes ideal mixing. Additionally, the Redlich-Kister approach was used to determine previously unknown binary and ternary interaction parameters based on experimentally measured density data sets for select pseudo-ternary salt systems. The results of this study show improvement in density estimation using the Redlich-Kister approach for all systems considered compared with estimation by additive molar volumes. Furthermore, this analysis allowed for the estimation of nonideal density behavior in experimentally unstudied ZrF 4 -UF 4 and BeF 2 -UF 4 , as well as the quantification of ternary interaction in NaF-LiF-ZrF 4 , NaF-BeF 2 -UF 4 , and NaF-ZrF 4 -UF 4 .
Mixture density network estimation of continuous variable maximum likelihood using discrete training samples
Abstract Mixture density networks (MDNs) can be used to generate posterior density functions of model parameters $$\varvec{\theta }$$ θ given a set of observables $${\mathbf {x}}$$ x . In some applications, training data are available only for discrete values of a continuous parameter $$\varvec{\theta }$$ θ . In such situations, a number of performance-limiting issues arise which can result in biased estimates. We demonstrate the usage of MDNs for parameter estimation, discuss the origins of the biases, and propose a corrective method for each issue.
Empirical estimation of densities in NaCl-KCl-UCl 3 and NaCl-KCl-YCl 3 molten salts using Redlich-Kister expansion
Densities of molten KCl-NaCl-UCl 3 and KCl-NaCl-YCl 3 ternary systems have been estimated using a multidimensional Redlich-Kister model. Temperature and composition dependent Redlich-Kister functions have been used to generate binary interaction parameters in the outlined ternary salt systems. These binary interactions have been used in the extrapolation to ternary system densities. The results of the density extrapolations by Muggianu interpolation scheme provide agreement within 2–3% for the NaCl-KCl-YCl 3 liquids and 11% in NaCl-KCl-UCl 3 liquids compared to the available experimental data. Modeling NaCl-KCl-UCl 3 molten phase density with a ternary interaction parameter improved the agreement within 4%. Thermophysical modeling used in this study has shown promising results for use in other material properties, such as viscosity, thermal conductivity, and heat capacity of the molten salts. Lastly, the outlined modeling method applied in these specific molten salt ternaries can be used for quaternary or higher multicomponent molten salt systems.
Dimensional Reduction for Sampled Priors and Application to Photometric Redshift Distributions
A typical Bayesian inference on the values of some parameters of interest q from some data D involves running a Markov Chain (MC) to sample from the posterior $p$($q$,$n$|$D$) $\propto$ $\mathcal{L}$($D$|$q$,$n$)$p$(q)$p$($n$), where n are some nuisance parameters with a separable prior. In some cases, the nuisance parameters are high-dimensional, and their prior p(n) is itself defined only by a set of samples that have been drawn from some other MC. The MC for the posterior will typically require evaluation of p(n) at arbitrary values of n, i.e., one needs to provide a density estimator over the full n space from the provided samples. But the high dimensionality of n hinders both the density estimation and the efficiency of the MC for the posterior. We describe a solution to this problem: a linear compression of the n space into a much lower-dimensional space u, which projects away directions in n space that cannot appreciably alter $\mathcal{L}$. The algorithm for doing so is a slight modification to principal components analysis, and is less restrictive on p(n) than other proposed solutions to this issue. We demonstrate this “mode projection” technique using the analysis of 2-point correlation functions of weak lensing fields and galaxy density in the Dark Energy Survey, where n is a binned representation of the redshift distribution n(z) of the galaxies.
Noise and error analysis and optimization in particle-based kinetic plasma simulations
In this paper we analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We begin by describing kernel density estimation for continuous values of the spatial variable x, expressing the kernel in a form in which its shape and width are represented separately. The covariance matrix of the noise in the density is computed, first for uniform true density. The bandwidth of the covariance matrix C(x,y) is related to the width of the kernel. A feature that stands out is the presence of constant negative terms in the elements of the covariance matrix both on and off-diagonal. These negative correlations are related to the fact that the total number of particles is fixed at each time step; they also lead to the property ∫C(x,y)dy = 0. We investigate the effect of these negative correlations on the electric field computed by Gauss's law, finding that the noise in the electric field is related to a process called the Ornstein-Uhlenbeck bridge, leading to a covariance matrix of the electric field with variance significantly reduced relative to that of a Brownian process. For non-constant density, p(x), still with continuous x, we analyze the total error in the density estimation and discuss it in terms of bias-variance optimization (BVO). For some characteristic length l, determined by the density and its second derivative, and kernel width h, having too few particles within h leads to too much variance; for h that is large relative to l, there is too much smoothing of the density. The optimum between these two limits is found by BVO. For kernels of the same width, it is shown that this optimum (minimum) is weakly sensitive to the kernel shape. Next, we repeat the analysis for x discretized on a grid. In this case the charge deposition rule is determined by a particle shape. An important property to be respected in the discrete system is the exact preservation of total charge on the grid; this property is necessary to ensure that the electric field is equal at both ends, consistent with periodic boundary conditions. We find that if the particle shapes satisfy a partition of unity property, the particle charge deposited on the grid is conserved exactly. Further, if the particle shape is expressed as the convolution of a kernel with another kernel that satisfies the partition of unity, then the particle shape obeys the partition of unity. This property holds for kernels of arbitrary width, including widths that are not integer multiples of the grid spacing. Furthermore, we show results relaxing the approximations used to do BVO optimization analytically, by doing numerical computations of the total error as a function of the kernel width, on a grid in x. The comparison between numerical and analytical results shows good agreement over a range of particle shapes. We discuss the practical implications of our results, including the criteria for design and implementation of computationally efficient particle shapes that take advantage of the developed theory.
Graph-Augmented Normalizing Flows for Anomaly Detection of Multiple Time Series
Anomaly detection is a widely studied task for a broad variety of data types; among them, multiple time series appear frequently in applications, including for example, power grids and traffic networks. Detecting anomalies for multiple time series, however, is a challenging subject, owing to the intricate interdependencies among the constituent series. We hypothesize that anomalies occur in low density regions of a distribution and explore the use of normalizing flows for unsupervised anomaly detection, because of their superior quality in density estimation. Moreover, we propose a novel flow model by imposing a Bayesian network among constituent series. A Bayesian network is a directed acyclic graph (DAG) that models causal relationships; it factorizes the joint probability of the series into the product of easy-to-evaluate conditional probabilities. We call such a graph-augmented normalizing flow approach GANF and propose joint estimation of the DAG with flow parameters. We conduct extensive experiments on real-world datasets and demonstrate the effectiveness of GANF for density estimation, anomaly detection, and identification of time series distribution drift.
Spatial patterns in occupancy and density of larval lampreys in freshwater habitats restored to a Stage 0 condition
Abstract We examined occupancy and density of larval lampreys ( Entosphenus tridentatus and Lampetra spp.) in two rivers in Oregon (USA) restored to a Stage 0 condition 1–5 years prior, using a multiscale occupancy model and a zero‐inflated Poisson mixture model. We sampled lampreys using backpack electrofishing in randomly distributed, paired, 1‐m 2 quadrats and recorded environmental data. Probabilities of occupancy and density were higher when water velocity was low, the substrate was noncompacted, and sediment was dominated by fines (<4 mm). At mean water depth (0.34 m) and velocity (0.09 m/s), estimated densities in occupied quadrats were 4.8 lampreys/m 2 (95%: 3.4–6.9) when the substrate was compacted, and fines were not dominant, and 21.1 lampreys/m 2 (95%: 17.7–25.3) when the substrate was noncompacted and fines were dominant. Probabilities of detecting occupancy in a 1‐m 2 quadrat sampled by backpack electrofishing were 0.76 (95%: 0.64–0.87) when captured after visual observation and 0.80 (95%: 0.71–0.88) with blind sweeps (i.e., constantly moving the net regardless of observation). The probability of capturing a single lamprey in a quadrat sampled by blind sweeps was 0.32 (95%: 0.27–0.37). Sampling in paired 1‐m 2 quadrats facilitated concurrent examination of patterns in occupancy and density while accounting for capture probability, which could aid temporal monitoring of restored habitats. To the best of our knowledge, this is the first study to document occupancy and estimate densities of larval lampreys in habitats that underwent valley floor restoration to Stage 0. We observed both lamprey genera within 5 years of restoration. Aquatic restoration that increases low‐velocity, noncompacted, fine sediment habitats could benefit lampreys.
Next-Cycle Optimal Fuel Control for Cycle-to-Cycle Variability Reduction in EGR-Diluted Combustion
In this simulation study, cycle-to-cycle fuel control was used to reduce CCV by injecting additional fuel in operating conditions with sporadic misfires and partial burns. An optimal control policy was proposed that utilizes 1) a physics-based model that tracks in-cylinder gas composition and 2) a one-step-ahead prediction of the combustion efficiency based on a kernel density estimator. The optimal solution, however, presents a tradeoff between the reduction in combustion CCV and the increase in fuel injection quantity required to stabilize the charge. Such a tradeoff can be ad- just by a single parameter embedded in the cost function.