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Results for “Sparse regression”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

Sparse Regression as a Sparse Eigenvalue Problem

We extend the l0-norm "subspectral" algorithms for sparse-LDA [5] and sparse-PCA [6] to general quadratic costs such as MSE in linear (kernel) regression. The resulting "Sparse Least Squares" (SLS) problem is also NP-hard, by way of its equivalence to a rank-1 sparse eigenvalue problem (e.g., binary sparse-LDA [7]). Specifically, for a general quadratic cost we use a highly-efficient technique for direct eigenvalue computation using partitioned matrix inverses which leads to dramatic x103 speed-ups over standard eigenvalue decomposition. This increased efficiency mitigates the O(n4) scaling behaviour that up to now has limited the previous algorithms' utility for high-dimensional learning problems. Moreover, the new computation prioritizes the role of the less-myopic backward elimination stage which becomes more efficient than forward selection. Similarly, branch-and-bound search for Exact Sparse Least Squares (ESLS) also benefits from partitioned matrix inverse techniques. Our Greedy Sparse Least Squares (GSLS) generalizes Natarajan's algorithm [9] also known as Order-Recursive Matching Pursuit (ORMP). Specifically, the forward half of GSLS is exactly equivalent to ORMP but more efficient. By including the backward pass, which only doubles the computation, we can achieve lower MSE than ORMP. Experimental comparisons to the state-of-the-art LARS algorithm [3] show forward-GSLS is faster, more accurate and more flexible in terms of choice of regularization

Exact Sparse Least Squares (ESLS)↗
DOE OSTI2023

Zero-truncated Poisson regression for sparse multiway count data corrupted by false zeros

Abstract We propose a novel statistical inference methodology for multiway count data that is corrupted by false zeros that are indistinguishable from true zero counts. Our approach consists of zero-truncating the Poisson distribution to neglect all zero values. This simple truncated approach dispenses with the need to distinguish between true and false zero counts and reduces the amount of data to be processed. Inference is accomplished via tensor completion that imposes low-rank tensor structure on the Poisson parameter space. Our main result shows that an $N$-way rank-$R$ parametric tensor $\boldsymbol{\mathscr{M}}\in (0,\infty )^{I\times \cdots \times I}$ generating Poisson observations can be accurately estimated by zero-truncated Poisson regression from approximately $IR^2\log _2^2(I)$ non-zero counts under the nonnegative canonical polyadic decomposition. Our result also quantifies the error made by zero-truncating the Poisson distribution when the parameter is uniformly bounded from below. Therefore, under a low-rank multiparameter model, we propose an implementable approach guaranteed to achieve accurate regression in under-determined scenarios with substantial corruption by false zeros. Several numerical experiments are presented to explore the theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanics

Data-driven constitutive modeling with neural networks has received increased interest in recent years due to its ability to easily incorporate physical and mechanistic constraints and to overcome the challenging and time-consuming task of formulating phenomenological constitutive laws that can accurately capture the observed material response. However, even though neural network-based constitutive laws have been shown to generalize proficiently, the generated representations are not easily interpretable due to their high number of trainable parameters. Sparse regression approaches exist that allow for obtaining interpretable expressions, but the user is tasked with creating a library of model forms which by construction limits their expressiveness to the functional forms provided in the libraries. Here, in this work, we propose to train regularized physics-augmented neural network-based constitutive models utilizing a smoothed version of $L^0$-regularization. This aims to maintain the trustworthiness inherited by the physical constraints, but also enables interpretability which has not been possible thus far on any type of machine learning-based constitutive model where model forms were not assumed a priori but were actually discovered. During the training process, the network simultaneously fits the training data and penalizes the number of active parameters, while also ensuring constitutive constraints such as thermodynamic consistency. We show that the method can reliably obtain interpretable and trustworthy constitutive models for compressible and incompressible hyperelasticity, yield functions, and hardening models for elastoplasticity, using synthetic and experimental data. This work aims to set a new paradigm for interpretable machine learning models in the broad area of solid mechanics where low and limited data is available along with prior knowledge of physical constraints that the learned maps need to obey. This paradigm can potentially be extended to a broader spectrum of scientific exploration.

Data-driven constitutive models↗
DOE OSTI2024

Permutation-adapted complete and independent basis for atomic cluster expansion descriptors

Atomic cluster expansion (ACE) methods provide a systematic way to describe particle local environments of arbitrary body order. For practical applications it is often required that the basis of cluster functions be symmetrized with respect to rotations and permutations. Existing methodologies yield sets of symmetrized functions that are over-complete. These methodologies thus require an additional numerical procedure, such as singular value decomposition (SVD), to eliminate redundant functions. In this work, it is shown that analytical linear relationships for subsets of cluster functions may be derived using recursion and permutation properties of generalized Wigner symbols. From these relationships, subsets (blocks) of cluster functions can be selected such that, within each block, functions are guaranteed to be linearly independent. It is conjectured that this block-wise independent set of permutation-adapted rotation and permutation invariant (PA-RPI) functions forms a complete, independent basis for ACE. Along with the first analytical proofs of block-wise linear dependence of ACE cluster functions and other theoretical arguments, numerical results are offered to demonstrate this. The utility of the method is demonstrated in the development of an ACE interatomic potential for tantalum. Using the new basis functions in combination with Bayesian compressive sensing sparse regression, some high degree descriptors are observed to persist and help achieve high-accuracy models.

Angular momentum↗
DOE OSTI2023

Modeling Intercalation Chemistry with Multiredox Reactions by Sparse Lattice Models in Disordered Rocksalt Cathodes

Modern battery materials can contain many elements with substantial site disorder, and their configurational state has been shown to be critical for their performance. The intercalation voltage profile is a critical parameter to evaluate the performance of energy storage. The application of commonly used cluster expansion techniques to model the intercalation thermodynamics of such systems ab initio is challenged by the combinatorial increase in configurational degrees of freedom as the number of species grows. Such challenges necessitate the efficient generation of lattice models without overfitting and proper sampling of the configurational space under the requirement of charge balance in ionic systems. In this work, we introduce a combined approach that addresses these challenges by (1) constructing a robust cluster expansion Hamiltonian using the sparse regression technique, including -norm regularization and structural hierarchy; and (2) implementing semigrand-canonical Monte Carlo to sample charge-balanced ionic configurations using the table-exchange method and an ensemble average approach. These techniques are applied to a disordered rocksalt oxyfluoride (LMNOF) that is part of a family of promising earth-abundant cathode materials. The simulated voltage profile is found to be in good agreement with experimental data and particularly provides a clear demonstration of the and oxygen contributions to the redox potential as a function of content.

25 ENERGY STORAGE↗
DOE OSTI2024

Role of physics in physics-informed machine learning

Physical systems are characterized by inherent symmetries, one of which is encapsulated in the units of their parameters and system states. These symmetries enable a lossless order-reduction, e.g., via dimensional analysis based on the Buckingham theorem. Despite the latter's benefits, machine learning (ML) strategies for the discovery of constitutive laws seldom subject experimental and/or numerical data to dimensional analysis. We demonstrate the potential of dimensional analysis to significantly enhance the interpretability and generalizability of ML-discovered secondary laws. Our numerical experiments with creeping fluid flow past solid ellipsoids show how dimensional analysis enable both deep neural networks and sparse regression reproduce old results, e.g., Stokes law for a sphere, and generate new ones, e.g., an expression for an ellipsoid misaligned with the flow direction. Furthermore, our results suggest the need to incorporate other physics-based symmetries and invariances into ML-based techniques for equation discovery.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

ARCH: Large-scale knowledge graph via aggregated narrative codified health records analysis

Objective: Electronic health record (EHR) systems contain a wealth of clinical data stored as both codified data and free-text narrative notes (NLP). The complexity of EHR presents challenges in feature representation, information extraction, and uncertainty quantification. Here, to address these challenges, we proposed an efficient Aggregated naRrative Codified Health (ARCH) records analysis to generate a large-scale knowledge graph (KG) for a comprehensive set of EHR codified and narrative features. Methods: Using data from 12.5 million Veterans Affairs patients, ARCH first derives embedding vectors and generates similarities along with associated p-values to measure the strength of relatedness between clinical features with statistical certainty quantification. Next, ARCH performs a sparse embedding regression to remove indirect linkage between features to build a sparse KG. Finally, ARCH was validated on various clinical tasks, including detecting known relationships between entity pairs, predicting drug side effects, disease phenotyping, as well as sub-typing Alzheimer’s disease patients. Results: ARCH produces high-quality clinical embeddings and KG for over 60,000 codified and narrative EHR concepts. The KG and embeddings are visualized in the R-shiny powered web-API.3 ARCH achieved high accuracy in detecting EHR concept relationships, with AUCs of 0.926 (codified) and 0.861 (NLP) for similar EHR concepts, and 0.810 (codified) and 0.843 (NLP) for related pairs. It detected drug side effects with a 0.723 AUC, which improved to 0.826 after fine-tuning. Using both codified and NLP features, the detection power increased significantly. Compared to other methods, ARCH has superior accuracy and enhances weakly supervised phenotyping algorithms’ performance. Notably, it successfully categorized Alzheimer’s patients into two subgroups with varying mortality rates. Conclusion: The proposed ARCH algorithm generates large-scale high-quality semantic representations and knowledge graph for both codified and NLP EHR features, useful for a wide range of predictive modeling tasks.

Electronic health records↗
DOE OSTI2024

Estimating Sparse Direct Effects in Multivariate Regression With the Spike-and-Slab LASSO

The multivariate regression interpretation of the Gaussian chain graph model simultaneously parametrizes (i) the direct effects of p predictors on q outcomes and (ii) the residual partial covariances between pairs of outcomes. We introduce a new method for fitting sparse versions of these models with spike-and-slab LASSO (SSL) priors. We develop an Expectation Conditional Maximization algorithm to obtain sparse estimates of the p × q matrix of direct effects and the q × q residual precision matrix. Our algorithm iteratively solves a sequence of penalized maximum likelihood problems with self-adaptive penalties that gradually filter out negligible regression coefficients and partial covariances. Because it adaptively penalizes individual model parameters, our method is seen to outperform fixed-penalty competitors on simulated data. We establish the posterior contraction rate for our model, buttressing our method’s excellent empirical performance with strong theoretical guarantees. Using our method, we estimated the direct effects of diet and residence type on the composition of the gut microbiome of elderly adults.

EM algorithm↗
NASA NTRS2014

Reevaluation of Stratospheric Ozone Trends From SAGE II Data Using a Simultaneous Temporal and Spatial Analysis

This paper details a new method of regression for sparsely sampled data sets for use with time-series analysis, in particular the Stratospheric Aerosol and Gas Experiment (SAGE) II ozone data set. Non-uniform spatial, temporal, and diurnal sampling present in the data set result in biased values for the long-term trend if not accounted for. This new method is performed close to the native resolution of measurements and is a simultaneous temporal and spatial analysis that accounts for potential diurnal ozone variation. Results show biases, introduced by the way data is prepared for use with traditional methods, can be as high as 10%. Derived long-term changes show declines in ozone similar to other studies but very different trends in the presumed recovery period, with differences up to 2% per decade. The regression model allows for a variable turnaround time and reveals a hemispheric asymmetry in derived trends in the middle to upper stratosphere. Similar methodology is also applied to SAGE II aerosol optical depth data to create a new volcanic proxy that covers the SAGE II mission period. Ultimately this technique may be extensible towards the inclusion of multiple data sets without the need for homogenization.

Damadeo, R. P.↗
DOE OSTI2023

Stochastic projective splitting

Here, we present a new, stochastic variant of the projective splitting (PS) family of algorithms for inclusion problems involving the sum of any finite number of maximal monotone operators. This new variant uses a stochastic oracle to evaluate one of the operators, which is assumed to be Lipschitz continuous, and (deterministic) resolvents to process the remaining operators. Our proposal is the first version of PS with such stochastic capabilities. We envision the primary application being machine learning (ML) problems, with the method’s stochastic features facilitating “mini-batch” sampling of datasets. Since it uses a monotone operator formulation, the method can handle not only Lipschitz-smooth loss minimization, but also min–max and noncooperative game formulations, with better convergence properties than the gradient descent-ascent methods commonly applied in such settings. The proposed method can handle any number of constraints and nonsmooth regularizers via projection and proximal operators. We prove almost-sure convergence of the iterates to a solution and a convergence rate result for the expected residual, and close with numerical experiments on a distributionally robust sparse logistic regression problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Identifying Differential Equations in Fourier Domain (FourierIdent)

We investigate identifying differential equations in the frequency domain. Fourier analysis is an important tool in theoretical analysis and numerical solvers of differential equations, yet there is limited work in exploring this connection in the identification of differential equations. This paper aims to identify the underlying differential equation in the frequency domain, from a given single realization of the differential equation perturbed by noise. Such setting imposes difficulties which are different from other identification methods where computation is carried out in the physical domain. We propose several ways to mitigate the challenges arising from noise in data and large differences in the magnitudes of frequency responses. The main takeaways are that identifying differential equations solely in the frequency domain is challenging, the method we propose is based on a form of domain partitions in the frequency domain, and this method shows benefits for complex data even with high level of noise. We introduce a Fourier feature denoising, and define the meaningful data region and the core regions of features to reduce the effect of noise in the frequency domain and to enhance the accuracy in coefficient identification. The proposed method is tested on various differential equations with linear, nonlinear, and high-order derivative feature terms, and shows advantages on complex data with many frequency modes, even under high level of noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Group Projected subspace pursuit for IDENTification of variable coefficient differential equations (GP-IDENT)

We propose an effective and robust algorithm for identifying partial differential equations (PDEs) with space-time varying coefficients from the noisy observation of a single solution trajectory. Identifying unknown differential equations from noisy data is a difficult task, and it is even more challenging with space and time varying coefficients in the PDE. The proposed algorithm, GP-IDENT, has three ingredients: (i) we use B-spline bases to express the unknown space and time varying coefficients, (ii) we propose Group Projected Subspace Pursuit (GPSP) to find a sequence of candidate PDEs with various levels of complexity, and (iii) we propose a new criterion for model selection using the Reduction in Residual (RR) to choose an optimal one among a pool of candidates. The new GPSP considers group projected subspaces which is more robust than existing methods in distinguishing correlated group features. We test GP-IDENT on a variety of PDEs and PDE systems, and compare it with the state-of-the-art parametric PDE identification algorithms under different settings to illustrate its outstanding performance. Furthermore, our experiments show that GP-IDENT is effective in identifying the correct terms from a large dictionary, and our model selection scheme is robust to noise.

Data-driven method↗
DOE OSTI2024

Symbolic diagnostics to interpret and analyze neural network models

Embedded machine-learned models (EMLMs) have the promise to improve the predictive accuracy of engineering simulators in environments of national interest. EMLMs often comprise complex input-output maps (e.g., neural networks), which make them unamenable to rigorous analysis and generally difficult to interpret. In the face of decades of theory, this lack of interpretability is a significant barrier to building confidence in these models. This work outlines an approach to interpret EMLMs using sparse polynomial regression for comparison with theoretical understanding. To do so, we build on the concept of Locally Interpretable Model-agnostic Explanations (LIME) using physics-informed clustering, prototype selection, and library construction. While general, we demonstrate our method on tensor-basis neural networks used in Reynolds-Averaged Navier-Stokes simulations of hypersonic fluid flows. Results are presented for a simulated toy model and for direct numerical simulations (DNS) of turbulent flows over a flat plate.

97 MATHEMATICS AND COMPUTING↗