Neural spline flows enhance flow models with rational-quadratic splines.
problem Improving flexibility and density estimation in flow models.
method Proposes a new differentiable module based on monotonic rational-quadratic splines.
result Demonstrates improved performance in density estimation, variational inference, and generative modeling of images.
Sig-Splines model uses signatures and splines for time series data, achieving universality and convexity.
problem Creating a generative model for multivariate time series data.
method Combines linear transformations and signature transforms into a neural spline flow.
result Achieves universality and introduces convexity in model parameters.
Improves spline quality and accuracy in computational microscopy.
problem Detecting slender, overlapping structures in microscopy images.
method Differentiable rendering approach for spline refinement.
result Achieves high reliability and sub-pixel accuracy.
Combines spline interpolation and ARIMA for stock market forecasting.
problem Limited predictive performance of ARIMA in noisy data.
method Integrates cubic spline interpolation and ARIMA for time series forecasting.
result Demonstrates guidance for short-term stock market forecasting.
We extend the adaptive regression spline model by incorporating saturation, the natural requirement that a function extend as a constant outside a certain range. We fit saturating splines to data using a convex optimization problem over a space of measures, which we solve using an efficient algorithm based on the condi…
Paper develops fast low-rank approximation for smoothing splines.
problem Computational infeasibility of fitting cubic smoothing splines to large datasets.
method Low-rank approximation using eigensystem truncation.
result The method provides accurate, fast estimates with error bounds.
A new knot selection method for GAMs reduces model complexity.
problem Choosing optimal knots for B-spline regression in GAMs.
method Adaptive splines combined with Fellner-Schall tuning for automatic knot selection.
result Comparable performance with P-splines but using fewer knots.
Paper finds maximum curvature of Bézier-spline curves.
problem Finding maximum curvature of Bézier-spline curves.
method Modified B-spline solutions for inverse interpolation problem.
result Determined maximum curvature of Bézier-spline curves.
We use splines and the Sasaki metric to analyze and compare manifold-valued trajectories.
problem Analyzing and comparing trajectories on Riemannian manifolds.
method Riemannian hierarchical model, Bézier splines, Sasaki metric.
result Spline-based approaches outperform state-of-the-art methods in intensity classification of trajectories.
Deep Random Splines model neural activity data with better dimensionality.
problem Modeling neural population data with shape constraints.
method Deep neural network transforming Gaussian noise into spline parameters.
result Better dimensionality reduction of neural spiking activity.
With the renewed and growing interest in geometric continuity in mind, this article gives a general definition of geometrically continuous polygonal surfaces and geometrically continuous spline functions on them. Polynomial splines defined by G1 gluing data in terms of rational functions are analyzed further. A general…
Cubic-Spline Flows improve autoregressive flow performance in density estimation.
problem Improving the performance of flow-based models in density estimation.
method Stacking a new coupling transform based on monotonic cubic splines with LU-decomposed linear layers.
result Cubic-Spline Flows close the gap with autoregressive flows on density-estimation tasks.
Revisits stochastic collocation with exponential splines for option pricing.
problem Improving the accuracy of option price interpolation using stochastic collocation.
method Uses exponential quadratic splines and optimizes abscissae or parameters of B-splines.
result Shows that fixing abscissae and optimizing parameters leads to better interpolation accuracy.
This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an arbitrage-free implied volatility surface calibrated to sparse option data. We use an extension of classical B-splines …
This paper develops a new method for constructing splines on Lie groups using Poisson equation solutions.
problem Existing methods for constructing splines on Lie groups have limitations and assumptions that may not reflect actual curves.
method The paper introduces a new approach using solutions of the Poisson equation on Lie groups to construct splines.
result The new method allows for global splines with arbitrary initial conditions, improving curve reconstruction.
A new modeling framework CSN simplifies and interprets machine learning models.
problem Complexity and interpretability issues in machine learning models.
method Combines spline transformation and cross-network to create CSN.
result CSN is as performant and interpretable as XGBoost and FCNN.
This paper introduces a spline-based method for nonparametric ADVI that handles complex posterior distributions.
problem Learning complex posterior distributions with skewness, multimodality, and bounded support.
method Develops a spline-based nonparametric approximation approach for ADVI.
result Establishes the asymptotic consistency of the derived lower bound for importance weighted autoencoder.
A new nonparametric approach for system identification has been recently proposed where the impulse response is seen as the realization of a zero--mean Gaussian process whose covariance, the so--called stable spline kernel, guarantees that the impulse response is almost surely stable. Maximum entropy properties of the …
Cubic spline smoothing improves interpolation between irregularly sampled data.
problem Interpolation discontinuity in recurrent neural networks for irregularly sampled sequences.
method Cubic spline smoothing compensation module trained end-to-end with ODE-RNN.
result Improves interpolation between irregularly sampled data points.
Paper proves regularity and existence of Riemannian splines.
problem Regularity and existence of Riemannian splines on manifolds.
method Generalization of DuBois-Reymond Lemma for higher-order splines.
result Established existence of minimizers for spline energy.
Cardiac motion modeling using LDDMM and shape splines.
problem Difficulties in probing cardiac function due to shape and deformation interactions.
method LDDMM framework, parallel transport, normalization, shape splines.
result Significant differences in model parameters between pathologies, revealing insights into disease dynamics.
Bayesian nonparametric LABS model adapts to function smoothness in Besov spaces.
problem Estimating functions with unknown smoothness in Besov spaces.
method Lévy Adaptive B-spline (LABS) regression model with automatic smoothness adaptation.
result LABS posterior contracts around true function in Besov classes at nearly minimax-optimal rates.
Improves BN graph learning with splines for scalability.
problem Learning accurate BN graph structures from data.
method Score-and-search approach with MARS for CPD modeling.
result Improves BN graph accuracy and scalability.
Smooths GPS data with splines for noisy, irregularly sampled data.
problem Noisy, irregularly sampled GPS data with non-Gaussian noise.
method Smoothing splines with chosen spline order and tension parameter, allowing for non-Gaussian noise and outliers.
result Effective smoothing and interpolation of GPS data.
Bayesian method for knot inference in multivariate spline regression.
problem Inference on knot locations in multivariate spline regression due to non-differentiability and varying dimensions.
method Fully Bayesian approach with a new prior on knot number and analytic formula for normal model, extended Bayesian information criterion for non-normal cases, reversible jump Markov chain Monte Carlo.
result Demonstrated superior performance in function fitting with jumping discontinuity.
The paper proposes a new method for density estimation using spline quasi-interpolation for clustering.
problem Density estimation and clustering modeling for multivariate data.
method Spline quasi-interpolation for mono-variate approximation, copulas for multivariate modeling.
result The proposed method achieves accurate clustering of data using copulas and spline quasi-interpolation.
Sinh-acceleration speeds up B-spline option pricing.
problem Improving efficiency in option pricing calculations.
method Using sinh-acceleration on B-spline probability density projection.
result SINH acceleration technique improves error control and reduces CPU time.
A new method evolves point clouds using B-splines for smooth surfaces.
problem Evolution of smooth surfaces from discrete point clouds.
method Adaptive Lagrangian B-spline framework for geometric evolution.
result Efficient and accurate reproduction of surface evolution phenomena.
Extends gradient-based optimization to spline functions.
problem Limitations of standard differentiable programming methods.
method Derives Jacobian of spline functions and uses it in predictive models.
result Improved performance in various applications.
A new spline method for manifold learning using Hessian-based curvature penalties.
problem Learning manifolds with curvature penalties in high dimensions.
method Generalizes thin-plate splines to flat manifolds using Hessian matrices, minimizing square error with curvature constraints.
result Existence and uniqueness of the spline solution, expressed as Green's functions and Hessian approximations.
Locally-verifiable conditions ensure exactness of spline discrete de Rham complex.
problem Ensuring cohomological equivalence of spline discrete complex to continuous de Rham complex.
method Theoretical analysis and locally-verifiable sufficient conditions for exactness.
result Locally-verifiable conditions guarantee exactness of hierarchical B-spline discrete de Rham complex.
Optimizes spectral density estimation for stationary and nonstationary processes.
problem Estimating spectral density of time series with complex structure.
method Optimally adaptive Bayesian spectral density estimation using smoothing spline covariance structure.
result Optimal eigendecomposition provides superior performance compared to alternative covariance functions.
This paper uses linear rational splines for invertible modeling, offering a simpler inverse and similar costs.
problem Creating expressive invertible models with tractable Jacobian determinants.
method Replacing affine transformations with linear rational splines in coupling layers.
result Linear rational splines offer a simpler inverse and similar costs for inference and generation.
SMART combines decision trees and MARS for better regression modeling.
problem High variance in decision trees for continuous relationships, poor performance in MARS for discontinuities.
method SMART uses a decision tree to identify subsets with distinct continuous relationships, then applies MARS to fit these relationships independently.
result SMART improves regression performance over state-of-the-art methods in capturing discontinuities and continuous relationships.
We reparametrize ReLU NNs as splines to understand their learning dynamics.
problem Understanding the learning dynamics and inductive bias of neural networks.
method Reparametrize ReLU NNs as continuous piecewise linear splines to study learning dynamics.
result Standard weight initializations yield very flat functions, leading to strength and type of implicit regularization.
The paper introduces a spline-based method for calibrating neural networks.
problem Ensuring neural network outputs are reliable for safety-critical applications.
method Approximating the empirical cumulative distribution function using splines to map network outputs to calibrated probabilities.
result The spline-based recalibration consistently outperforms existing methods on calibration measures.
We present an approach for polarimetric Synthetic Aperture Radar (SAR) image region boundary detection based on the use of B-Spline active contours and a new model for polarimetric SAR data: the GHP distribution. In order to detect the boundary of a region, initial B-Spline curves are specified, either automatically or…
Multivariate splines linked to infinitely-wide neural networks with improved numerical performance.
problem Understanding the relationship between multivariate splines and neural networks.
method Showed multivariate splines can be represented as random features in infinitely-wide neural networks with a homogeneous activation function.
result The function space of multivariate splines is a Sobolev space on a Euclidean ball with explicit norm bounds on derivatives.
Quantum walks blend patterns into splines when averaged.
problem Understanding the asymptotic patterns of quantum random walks.
method Averaging over quantum coins using the Haar measure.
result Patterns blend into splines, showing a unified behavior.
Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with countless applications in science and technology. In several emerging fields, for example computer vision and quantum control, there is a growing need for spline interpolation on curved, non-Euclidean space. The generalization…
A new method for stable vector representation of persistence diagrams.
problem Finding a stable vector representation of persistence diagrams for ML tasks.
method Persistence B-spline Grid (PBSG) based on data fitting.
result The PBSG method is stable with respect to the 1-Wasserstein distance metric.
Generative networks are analyzed using spline operators to understand their properties and limitations.
problem Understanding and optimizing the properties of deep generative networks.
method Characterizing latent space partition, manifold dimension, and disentanglement using spline operators.
result Characterized the latent space partition, manifold dimension, and disentanglement of GDNs.
This paper presents an efficient algorithm for evolving point cloud data on smooth manifolds using B-Splines.
problem Evolution of point cloud data on smooth manifolds in higher dimensions.
method Lagrangian approach using adaptive B-Spline interpolation.
result Demonstrates the convergence of geometric quantities and the effectiveness of the approach.
This work relates the framework of model-based clustering for spatial functional data where the data are surfaces. We first introduce a Bayesian spatial spline regression model with mixed-effects (BSSR) for modeling spatial function data. The BSSR model is based on Nodal basis functions for spatial regression and accom…
Deep P-Spline automates DNN structure selection for complex regression problems.
problem Challenges in selecting optimal network structures for DNNs.
method Linking neuron selection to knot placement in basis expansion techniques, introducing a difference penalty for automated knot selection.
result Deep P-Spline extends model class and forms a latent variable modeling framework with theoretical guarantees.
Deep-SITAR uses autoencoders to predict growth patterns.
problem Predicting individual growth trajectories from population data.
method Deep learning framework integrating autoencoders and B-spline models.
result Deep-SITAR predicts individual growth without full model re-estimation.
Bayesian taut splines estimate modes in probability densities.
problem Estimating the number of modes in probability density functions.
method Bayesian inference with flexible kernel estimators and compositional splines.
result The new method provides more accurate results than traditional approaches.
Develops flexible non-parametric ACFs using B-spline kernels.
problem Flexible modelling of the autocovariance function (ACF) in time-series, spatial, and spatio-temporal analysis.
method Derives the inverse Fourier transform of B-spline spectral bases to create a general class of non-parametric ACFs.
result Provides a provably dense, flexible, and general class of non-parametric ACFs for various types of processes.