A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Bayesian nonparametric method partitions shapes using curves.
Batch normalization improves deep networks by aligning their decision boundaries with data.
The paper proposes a new method for density estimation using spline quasi-interpolation for clustering.
We build a rigorous bridge between deep networks (DNs) and approximation theory via spline functions and operators. Our key result is that a large class of DNs can be written as a composition of max-affine spline operators (MASOs), which provide a powerful portal through which to view and analyze their inner workings. …
We connect a large class of Generative Deep Networks (GDNs) with spline operators in order to derive their properties, limitations, and new opportunities. By characterizing the latent space partition, dimension and angularity of the generated manifold, we relate the manifold dimension and approximation error to the sam…
A new method optimizes knot selection for spline dimensional decomposition in stochastic dynamic analysis.
Let G be a torus acting linearly on a complex vector space M, and let X be the list of weights of G in M. We determine the equivariant K-theory of the open subset of M consisting of points with finite stabilizers. We identify it to the space DM(X) of functions on the lattice of weights of G, satisfying the cocircuit di…
We will discuss the equivariant cohomology of a manifold endowed with the action of a Lie group. Localization formulae for equivariant integrals are explained by a vanishing theorem for equivariant cohomology with generalized coefficients. We then give applications to integration of characteristic classes on symplectic…
Paper finds maximum curvature of Bézier-spline curves.
Revisits stochastic collocation with exponential splines for option pricing.
Paper proves regularity and existence of Riemannian splines.
Improves spline quality and accuracy in computational microscopy.
This paper develops a new method for constructing splines on Lie groups using Poisson equation solutions.
Sig-Splines model uses signatures and splines for time series data, achieving universality and convexity.
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…
We study the geometry of deep (neural) networks (DNs) with piecewise affine and convex nonlinearities. The layers of such DNs have been shown to be {\em max-affine spline operators} (MASOs) that partition their input space and apply a region-dependent affine mapping to their input to produce their output. We demonstrat…
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…
Sinh-acceleration speeds up B-spline option pricing.
Combines spline interpolation and ARIMA for stock market forecasting.
A new method evolves point clouds using B-splines for smooth surfaces.
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 …
A new spline method for manifold learning using Hessian-based curvature penalties.
Locally-verifiable conditions ensure exactness of spline discrete de Rham complex.
We use splines and the Sasaki metric to analyze and compare manifold-valued trajectories.
Cubic spline smoothing improves interpolation between irregularly sampled data.
We reparametrize ReLU NNs as splines to understand their learning dynamics.
Smoothing splines provide a powerful and flexible means for nonparametric estimation and inference. With a cubic time complexity, fitting smoothing spline models to large data is computationally prohibitive. In this paper, we use the theoretical optimal eigenspace to derive a low rank approximation of the smoothing spl…
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 introduces a spline-based method for nonparametric ADVI that handles complex posterior distributions.
The paper introduces a spline-based method for calibrating neural networks.
Multivariate splines linked to infinitely-wide neural networks with improved numerical performance.
Quantum walks blend patterns into splines when averaged.
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 modeling framework CSN simplifies and interprets machine learning models.
We present arguments for the formulation of unified approach to different standard continuous inference methods from partial information. It is claimed that an explicit partition of information into a priori (prior knowledge) and a posteriori information (data) is an important way of standardizing inference approaches …
A comprehensive methodology is provided for smoothing noisy, irregularly sampled data with non-Gaussian noise using smoothing splines. We demonstrate how the spline order and tension parameter can be chosen a priori from physical reasoning. We also show how to allow for non-Gaussian noise and outliers which are typical…
This paper presents an efficient algorithm for evolving point cloud data on smooth manifolds using B-Splines.
Cardiac motion modeling using LDDMM and shape splines.
Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we propose Deep Random Splines, a flexible class of random functions obtained by tr…
Improves BN graph learning with splines for scalability.
Bayesian nonparametric LABS model adapts to function smoothness in Besov spaces.
Researchers modify distance to handle long, thin splines.
Deep neural networks (DNNs) generate much richer function spaces than shallow networks. Since the function spaces induced by shallow networks have several approximation theoretic drawbacks, this explains, however, not necessarily the success of deep networks. In this article we take another route by comparing the expre…
The paper addresses optimal control on Riemannian manifolds, introducing biased splines for robotic systems.
We study trend filtering, a recently proposed tool of Kim et al. [SIAM Rev. 51 (2009) 339-360] for nonparametric regression. The trend filtering estimate is defined as the minimizer of a penalized least squares criterion, in which the penalty term sums the absolute th order discrete derivatives over the input points…
A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the parameterization of an easily invertible elementwise transformation, whose choic…
Bayesian method for knot inference in multivariate spline regression.
We propose a novel method to determine the dissimilarity between subjects for functional data clustering. Spline smoothing or interpolation is common to deal with data of such type. Instead of estimating the best-representing curve for each subject as fixed during clustering, we measure the dissimilarity between subjec…