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.
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.
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.
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 …
PIE-PINN estimates elastic properties from noisy, low-res displacement data.
problem Estimating heterogeneous elastic properties from low-resolution, noisy data.
method Probabilistic Physics-Informed Neural Network (PIE-PINN) framework combining B-spline and hierarchical scale model.
result Robust estimation of Young's modulus and Poisson's ratio from noisy, low-resolution displacement data.
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.
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.
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…
Many attempts have been made in recent decades to integrate machine learning (ML) and topological data analysis. A prominent problem in applying persistent homology to ML tasks is finding a vector representation of a persistence diagram (PD), which is a summary diagram for representing topological features. From the pe…
Kolmogorov-Arnold Networks achieve optimal convergence rates in nonparametric regression.
problem Nonparametric function approximation in multivariate settings.
method Structured additive and multiplicative KANs using B-splines.
result Achieve minimax-optimal convergence rate O(n−2r/(2r+1)) for Sobolev space functions. Smooth neural TPPs using B-splines for better efficiency and accuracy.
problem Efficiently modeling sequences of events in continuous time with neural networks.
method Directly parametrize the CIF as a non-negative combination of B-spline basis functions, predicting coefficients with a neural network.
result Improved computational efficiency and predictive accuracy compared to existing methods.
Efficient numerical method for time-fractional Black-Scholes model.
problem Solving time-fractional Black-Scholes equations for European options.
method Crank-Nicolson discretization for time, exponential B-spline for space.
result The proposed method is unconditionally stable and superior to existing approaches.
Dropout improves regularization in flexible models for rare features.
problem Understanding theoretical properties of dropout in generalized linear models.
method Theoretical analysis and application to adaptive smoothing with B-splines.
result Dropout prefers rare features in mean and dispersion parameters.
New method speeds up sparse Gaussian processes for large datasets.
problem Efficiently modeling large datasets with many inducing variables.
method Projecting a GP onto B-spline basis functions for sparse linear algebra.
result Efficiently models fast-varying spatial phenomena with tens of thousands of inducing variables.
Motivated by applications in architecture and design, we present a novel method for increasing the developability of a B-spline surface. We use the property that the Gauss image of a developable surface is 1-dimensional and can be locally well approximated by circles. This is cast into an algorithm for thinning the Gau…
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.
A new model approximates complex functions in parameter space.
problem Complex and nonlinear functional regression problems.
method Mapping-to-Parameter function model with B-spline free knot placement.
result Robust knot placement algorithms improve model performance.
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.
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.
Group convolutional neural networks (G-CNNs) can be used to improve classical CNNs by equipping them with the geometric structure of groups. Central in the success of G-CNNs is the lifting of feature maps to higher dimensional disentangled representations, in which data characteristics are effectively learned, geometri…
Parametric spatial transformation models have been successfully applied to image registration tasks. In such models, the transformation of interest is parameterized by a fixed set of basis functions as for example B-splines. Each basis function is located on a fixed regular grid position among the image domain, because…
We present SplineNets, a practical and novel approach for using conditioning in convolutional neural networks (CNNs). SplineNets are continuous generalizations of neural decision graphs, and they can dramatically reduce runtime complexity and computation costs of CNNs, while maintaining or even increasing accuracy. Fun…
Efficiently estimates covariance for sparse functional data.
problem Sparse data in functional analysis.
method Random-knots and B-spline estimators for covariance function.
result Asymptotic pointwise covariance estimates for sparsified data.
The vision of automated driving is to increase both road safety and efficiency, while offering passengers a convenient travel experience. This requires that autonomous systems correctly estimate the current traffic scene and its likely evolution. In highway scenarios early recognition of cut-in maneuvers is essential f…
Proposes a new model for high-dimensional data analysis with unknown link function.
problem Estimating link function, component functions, and variable interactions in high-dimensional data.
method Generalized Sparse Additive Model with Unknown Link Function (GSAMUL) using B-spline basis and MLP network for link estimation, with ℓ2,1-norm regularizer for variable selection. result Can realize both variable selection and hidden interaction.
Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By certified, we mean that the approximation can approximate the given curve to any given pr…
DecompKAN improves time series forecasting accuracy and transparency.
problem Accurate and transparent time series forecasting in scientific domains.
method Combines decomposition, patching, normalization, and B-spline KAN edge functions.
result Achieves best or tied-best MSE on 20 of 36 comparisons across 9 datasets.
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.
KANHedge improves hedging of high-dimensional options using learnable B-spline activation functions.
problem Challenges in high-dimensional option pricing and hedging due to the curse of dimensionality.
method Introduces KANHedge, a novel BSDE-based hedger leveraging Kolmogorov-Arnold Networks with learnable B-spline activation functions.
result KANHedge provides improved hedging performance, achieving significant reductions in hedging cost metrics.
RST improves environmental time series classification accuracy using randomized B-spline trees.
problem Improving accuracy in classifying complex environmental time series.
method Randomized Spline Trees (RST) integrates randomized functional representations into ensemble learning.
result RST variants outperform standard Random Forests and Gradient Boosting on most environmental time series datasets.
T-KAN improves HFT LOB forecasting with learnable splines.
problem Alpha decay in HFT LOB forecasting models.
method T-KAN uses learnable B-spline activation functions to model market signals.
result 19.1% relative improvement in F1-score at k = 100 horizon.
Independent component analysis (ICA) has been widely used for blind source separation in many fields such as brain imaging analysis, signal processing and telecommunication. Many statistical techniques based on M-estimates have been proposed for estimating the mixing matrix. Recently, several nonparametric methods have…
Isogeometric analysis is a recently developed computational approach that integrates finite element analysis directly into design described by non-uniform rational B-splines (NURBS). In this paper we show that price surfaces that occur in option pricing can be easily described by NURBS surfaces. For a class of stochast…
We develop a new nonparametric approach for estimating the risk-neutral density of asset prices and reformulate its estimation into a double-constrained optimization problem. We evaluate our approach using the S\&P 500 market option prices from 1996 to 2015. A comprehensive cross-validation study shows that our approac…
We propose a nonparametric method for detecting nonlinear causal relationship within a set of multidimensional discrete time series, by using sparse additive models (SpAMs). We show that, when the input to the SpAM is a β-mixing time series, the model can be fitted by first approximating each unknown function with a …
Deep neural network is a state-of-art method in modern science and technology. Much statistical literature have been devoted to understanding its performance in nonparametric estimation, whereas the results are suboptimal due to a redundant logarithmic sacrifice. In this paper, we show that such log-factors are not nec…
Enhances FM models for numerical features using function basis encoding.
problem Challenges in incorporating numerical features into FM variants.
method Encoding numerical features into a vector of function values for learning segmentized functions.
result Improves model accuracy by learning segmentized functions of numerical features.
Paper introduces hierarchical softmax for global hierarchical classification tasks.
problem Improving classification accuracy in tasks with class hierarchies.
method Global hierarchical neural networks using hierarchical softmax.
result Hierarchical softmax outperforms regular softmax in multiple datasets.
This study compares hierarchical and non-hierarchical models for open-domain multi-turn dialog generation.
problem Which kind of models (hierarchical or non-hierarchical) is better for open-domain multi-turn dialog generation?
method Systematically compared nearly all representative hierarchical and non-hierarchical models over the same experimental settings.
result Nearly all hierarchical models are worse than non-hierarchical models in open-domain multi-turn dialog generation, except for HRAN.
We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps, and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally we descr…
Stochastic volatility (SV) models mimic many of the stylized facts attributed to time series of asset returns, while maintaining conceptual simplicity. The commonly made assumption of conditionally normally distributed or Student-t-distributed returns, given the volatility, has however been questioned. In this manuscri…
Paper proposes a Renyi entropy-based method for tuning hierarchical topic models.
problem Tuning hierarchical topic models, especially determining the number of topics at each level, is challenging.
method The paper introduces a Renyi entropy-based metric for quality assessment and a practical tuning concept.
result The proposed method can estimate the number of topics for two hierarchical levels in hARTM model.
Neural NMF discovers hierarchical topics in multilayer data.
problem Detecting latent hierarchical structure in multilayer data.
method Recursive application of nonnegative matrix factorization (NMF) in layers with backpropagation optimization.
result Neural NMF outperforms other hierarchical NMF methods in synthetic and real-world datasets.
The paper develops a decision support system for hierarchical text classification of conference proceedings.
problem Classifying documents with a fixed hierarchical structure of topics.
method Developed a weighted hierarchical similarity function to calculate topic relevance, using entropy of words to estimate weights.
result The weighted hierarchical similarity function improves ranking accuracy compared to other methods.
Bayesian Hierarchical Invariant Prediction refines ICP for better scalability and prior integration.
problem Improving computational scalability and invariance testing for causal inference.
method Bayesian Hierarchical structure to test invariance under heterogeneous data.
result Demonstrated improved scalability and potential as an alternative to ICP.
Uber optimizes marketplace levers using machine learning to improve resource allocation efficiency.
problem Optimizing budget allocation for drivers and riders to maximize business value.
method End-to-end machine learning and optimization procedure using feature store, model training, and ADMM.
result Substantially improved Uber's resource allocation efficiency through high-dimensional optimization.
Hierarchical causal models help understand cause and effect in nested data.
problem Learning cause and effect from nested hierarchical data.
method Extend structural causal models and causal graphical models with inner plates, develop graphical identification technique and estimation methods.
result Hierarchical data can enable causal identification even when non-hierarchical data cannot.