New geometric mechanism solves four envelope problems.
problem Four basic problems on envelopes created by hyperplane families.
method Simple geometric mechanism of intersections of perpendicular bisectors and normal lines.
result Solves all four basic problems on envelopes at once.
NLR models often perform worse than LR for outlying input data in environmental sciences.
problem NLR models often give poor predictions for input data outside the training domain.
method Screened input data for outliers, using linear extrapolation for outliers based on NLR within the non-outlier domain.
result NLROR approach reduces poor extrapolation and tends to outperform NLR and LR for outliers. Survey of de Casteljau's algorithm's applications in geometric data analysis.
problem No specific problem stated; focuses on algorithm applications.
method Constructive approach to generalize parametric smooth curves to manifolds.
result Algorithm provides principled way to analyze geometric data.
Proposes KAR for nonlinear causal discovery using kernel methods.
problem Learning causal relationships in nonlinear settings.
method Kernel anchor regression (KAR) with improved three-stage nonparametric regression.
result KAR outperforms existing methods in nonlinear causal discovery.
The development of algorithms for unsupervised pattern recognition by nonlinear clustering is a notable problem in data science. Markov clustering (MCL) is a renowned algorithm that simulates stochastic flows on a network of sample similarities to detect the structural organization of clusters in the data, but it has n…
New mechanism found for power laws including Zipf's law.
problem Understanding the ubiquity of power law distributions.
method Introduced nonlinear self-excited Hawkes processes with fast-accelerating intensities.
result Wide class of nonlinear Hawkes processes have power law intensity PDFs.
Upper bound on CRN reaction rates derived using information geometry.
problem Challenging task of deriving an upper bound on reaction rates of nonlinear, discrete CRNs.
method Information geometric approach using natural gradient.
result Validated through numerical simulations, demonstrating faster convergence in specific CRNs.
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse Gaussian processes. The result of learning is a tractable posterior over nonlinear dy…
Centroid-Encoder reduces high-dimensional data for better visualization.
problem Visualizing high-dimensional data efficiently and accurately.
method Centroid-Encoder integrates label information to keep similar objects close in reduced space.
result Centroid-Encoder outperforms other techniques in visualizing high-dimensional data.
The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising meaningful models out of such observations in an automated fashion still remains an op…
Spatio-temporal data and processes are prevalent across a wide variety of scientific disciplines. These processes are often characterized by nonlinear time dynamics that include interactions across multiple scales of spatial and temporal variability. The data sets associated with many of these processes are increasing …
New methods for scalable causal discovery from complex data.
problem Learning causal structures from nonlinear, continuous or mixed data.
method BF-BIC score and BF-LRT test for scalable causal discovery.
result BF-BIC score and BF-LRT test enable scalable causal discovery with competitive accuracy and runtime.
Extends causal discovery to group variables, improving performance in real-world applications.
problem Inferring cause-effect relationships from grouped data.
method Two-step approach: infer causal order and select models.
result Strong performance in simulations and real-world assembly line data.
First principles modeling of physical systems has led to significant technological advances across all branches of science. For nonlinear systems, however, small modeling errors can lead to significant deviations from the true, measured behavior. Even in mechanical systems, where the equations are assumed to be well-kn…
A new flow-based Bayesian filter tackles high-dimensional nonlinear stochastic systems.
problem Bayesian filtering for high-dimensional nonlinear systems is challenging due to non-Gaussian distributions and computational limitations.
method Integrates normalizing flows to construct a latent linear state-space model with efficient density estimation and sampling.
result Demonstrates superior accuracy and efficiency in numerical experiments.
New decompositions misattribute differences between populations, even when outcomes are identical.
problem Misattribution of differences between populations using common functional decompositions.
method Extending the Kitagawa-Oaxaca-Blinder decomposition to nonlinear functional decompositions.
result Functional ANOVA and Accumulated Local Effects can misattribute differences even when outcomes are identical in two populations.
WeldNet reduces complex dynamics to simpler, manageable segments.
problem Complex, high-dimensional time-dependent datasets from physical processes are costly to simulate.
method Windowed Encoders for Learning Dynamics, splitting time domain into windows for nonlinear dimension reduction and propagator training.
result WeldNet captures nonlinear latent structures and dynamics, outperforming existing methods.
Framework for reconstructing nonlinear systems from multi-modal time series data.
problem Reconstructing nonlinear dynamical systems from multi-modal time series data.
method Dynamic interpretable recurrent neural networks coupled with generalized linear models for multi-modal data integration.
result Framework efficiently compensates for noisy or missing information in one data channel using other channels.
FREDE efficiently embeds graphs using linear space and guarantees quality.
problem Efficiently embedding graphs with quality guarantees and linear space complexity.
method FREDE combines matrix sketching with a nonlinear transform of PageRank similarities to achieve linear space and quality guarantees.
result FREDE provides column-covariance approximation guarantees that are nearly as good as SVD, even with limited node similarities.
Kernel measures similarity of nonlinear causal structures in heterogeneous populations.
problem Learning causal structure in populations with diverse underlying structures.
method Distance covariance-based kernel for measuring similarity of causal structures.
result Kernel enables clustering of homogeneous subpopulations for causal structure learning.
New framework learns nonlinear cyclic causal models from data.
problem Challenges in learning causal relationships from real-world, cyclic systems.
method NODAGS-Flow: a novel framework using residual normalizing flows for likelihood estimation.
result Significant performance improvements in structure recovery and predictive performance compared to state-of-the-art methods.
New approach uses secants to improve sensor placement and feature selection for nonlinear systems.
problem Inadequacy of linear methods for minimal sensor placement and feature selection in nonlinear systems.
method Data-driven approach using secant vectors to develop greedy algorithms for robust, near-minimal reconstruction guarantees.
result Demonstrated on two problems where linear techniques fail, secant-based approach provides robust solutions.
New DR method uses Gromov-Wasserstein distance for high-dimensional data.
problem Analyzing relationships between high-dimensional objects.
method Optimal transportation theory and Gromov-Wasserstein distance.
result Robust and efficient solution for complex high-dimensional datasets.
Modeling how individuals evolve over time is a fundamental problem in the natural and social sciences. However, existing datasets are often cross-sectional with each individual observed only once, making it impossible to apply traditional time-series methods. Motivated by the study of human aging, we present an interpr…
Paper presents a novel method to assess boundedness and stability of nonlinear systems with variable delays.
problem Challenges in assessing boundedness and stability of vector nonlinear systems with variable delays and coefficients.
method Develops a novel framework to evaluate the evolution of solution norms in such systems by constructing scalar counterparts.
result Introduces new criteria for boundedness and stability and estimates the radii of containing balls for history functions.
The scientific literature is a rich source of information for data mining with conceptual knowledge graphs; the open science movement has enriched this literature with complementary source code that implements scientific models. To exploit this new resource, we construct a knowledge graph using unsupervised learning me…
A central area of research in nonlinear science is the study of instabilities that drive the emergence of extreme events. Unfortunately, experimental techniques for measuring such phenomena often provide only partial characterization. For example, real-time studies of instabilities in nonlinear fibre optics frequently …
Unified optimization framework for matrix seriation.
problem Discovering latent structure in relational data.
method Mathematical optimization models for seriation.
result Optimization models enhance solution quality and interpretability.
New method discovers causal models from mixed time series data.
problem Discovering causal relationships from heterogeneous time series data.
method Variational inference-based framework MCD for linear and nonlinear causal models.
result Method outperforms state-of-the-art benchmarks in causal discovery tasks.
PGPCA improves PCA for nonlinear data in neuroscience.
problem Nonlinear data distribution in neuroscience.
method Developed PGPCA for nonlinear manifolds, incorporating EM algorithm.
result PGPCA outperforms PPCA in modeling data around nonlinear manifolds.
We introduce a flexible, scalable Bayesian inference framework for nonlinear dynamical systems characterised by distinct and hierarchical variability at the individual, group, and population levels. Our model class is a generalisation of nonlinear mixed-effects (NLME) dynamical systems, the statistical workhorse for ma…
Formula for Laplace-Beltrami on orthogonal group in Euclidean coords.
problem Computing Laplace-Beltrami on constrained submanifolds.
method Embedded gradient vector field method, explicit formula derivation.
result Explicit formula for Laplace-Beltrami on orthogonal group.
Blade uses diffusion priors to accurately and calibratedly infer complex systems.
problem Derivative-free Bayesian inversion for high-dimensional, nonlinear problems with costly forward models.
method Blade employs an ensemble of interacting particles and diffusion models as priors, querying forward models only through evaluations.
result Blade produces well-calibrated posterior samples that existing methods cannot, improving with more iterations and particles.
Survey on geometric foundations of data reduction methods.
problem High-dimensional data with intrinsic nonlinear structure.
method Spectral manifold learning methods.
result Derivation and convergence analysis of spectral manifold learning.
Study improves materials discovery for high-entropy alloys using sparse linear models.
problem Inefficient materials discovery due to combinatorial explosion in alloy compositions.
method Sparse mixed linear modeling with anchor-based guidance for feature selection and prediction.
result Developed a method that balances predictive performance and interpretability for materials discovery.
Derives representations invariant under crystallographic groups for functions.
problem Representing and learning functions invariant under crystallographic groups.
method Derives linear and nonlinear representations of functions invariant under crystallographic groups.
result Derives orthonormal crystallographically invariant basis functions and embedding maps.
Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is challenged when it comes to analyzing multiple datasets jointly. In certain data scienc…
Data Science is currently a popular field of science attracting expertise from very diverse backgrounds. Current learning practices need to acknowledge this and adapt to it. This paper summarises some experiences relating to such learning approaches from teaching a postgraduate Data Science module, and draws some learn…
Data science teams collaborate extensively, using various tools and stakeholders.
problem Lack of understanding in how data science workers collaborate in practice.
method Conducted an online survey with 183 data science workers.
result Data science teams are highly collaborative and use multiple tools and stakeholders.
Many machine learning problems, especially multi-modal learning problems, have two sets of distinct features (e.g., image and text features in news story classification, or neuroimaging data and neurocognitive data in cognitive science research). This paper addresses the joint dimensionality reduction of two feature ve…
Framework for sensitivity analysis in biomanufacturing processes.
problem High complexity and uncertainty in biomanufacturing processes.
method Shapley value estimation for linear and nonlinear pKG models, using quasi-Monte Carlo and antithetic sampling.
result Improved efficiency and accuracy in sensitivity analysis for biomanufacturing processes.
Proposes a new method for causal inference in high-dimensional complex data.
problem Challenges in making causal inference with high-dimensional, nonlinear data.
method Combines deep learning techniques like sparse deep learning and stochastic neural networks.
result Outperforms existing methods in numerical studies.
ML methods improve planetary science data analysis.
problem Insufficient use of ML in planetary science.
method Ten recommendations for integrating ML in planetary science.
result Expanding planetary science insights from large datasets.
Machine learning improves wildfire science and management, but requires expert knowledge.
problem Improving wildfire science and management through AI.
method Review of popular ML approaches and their application in six wildfire science domains.
result Opportunities exist for applying more advanced ML methods in wildfire science.
Capturing the microscopic interactions that determine molecular reactivity poses a challenge across the physical sciences. Even a basic understanding of the underlying reaction mechanisms can substantially accelerate materials and compound design, including the development of new catalysts or drugs. Given the difficult…
The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations about the parallelization and scalability of realistic problems are often criti…
Causal inference from observational data is the goal of many data analyses in the health and social sciences. However, academic statistics has often frowned upon data analyses with a causal objective. The introduction of the term "data science" provides a historic opportunity to redefine data analysis in such a way tha…
Mixed effects (ME) models inform a vast array of problems in the physical and social sciences, and are pervasive in meta-analysis. We consider ME models where the random effects component is linear. We then develop an efficient approach for a broad problem class that allows nonlinear measurements, priors, and constrain…