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.
New method integrates sparse parametric and nonparametric techniques for complex system modeling.
Semi-parametric framework for nonlinear system identification
Framework improves data-driven ROMs for complex systems using Bayesian operator inference.
Variationality of conformal geodesics fails in higher dimensions.
We propose a discretization of classical confocal coordinates. It is based on a novel characterization thereof as factorizable orthogonal coordinate systems. Our geometric discretization leads to factorizable discrete nets with a novel discrete analog of the orthogonality property. A discrete confocal coordinate system…
Bayesian approach for solving systems of linear PDEs with boundary conditions.
Method recovers causal diffusion mechanisms from steady-state data without parametric assumptions.
We propose further conformal parametrizations for initial data in some modified Einstein gravity theories. Some of them give rise to conformally covariant systems.
Cyclidic nets are introduced as discrete analogs of curvature line parametrized surfaces and orthogonal coordinate systems. A 2-dimensional cyclidic net is a piecewise smooth -surface built from surface patches of Dupin cyclides, each patch being bounded by curvature lines of the supporting cyclide. An explicit de…
We analyze numerically the training dynamics of deep neural networks (DNN) by using methods developed in statistical physics of glassy systems. The two main issues we address are (1) the complexity of the loss landscape and of the dynamics within it, and (2) to what extent DNNs share similarities with glassy systems. O…
We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, semi-parametric noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle inequality which demonstrates that this procedure provably mitigates the variance in…
We begin an exploration of parametric Backlund transformations for hyperbolic Monge-Ampere systems. We compute invariants for such transformations and explore the behavior of four examples regarding their invariants, symmetries, and conservation laws. We prove some preliminary results and indicate directions for furthe…
Model inference for dynamical systems aims to estimate the future behaviour of a system from observations. Purely model-free statistical methods, such as Artificial Neural Networks, tend to perform poorly for such tasks. They are therefore not well suited to many questions from applications, for example in Bayesian fil…
Optimally explores dynamical systems with varying properties using context inference.
Study of Ricci flow on discrete surfaces of revolution with constant Gaussian curvature.
A framework solves parametric families of MFGs efficiently.
We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning,…
Deep adaptive sampling improves surrogate modeling for complex systems.
We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix through a system of Wiener-Hopf integral equations. A Wiener-Hopf argument allows one to prove that this system (in which the kernel matrix is the unknown) possesses a unique causal solution and consequentl…
This article is concerned with learning and stochastic control in physical systems which contain unknown input signals. These unknown signals are modeled as Gaussian processes (GP) with certain parametrized covariance structures. The resulting latent force models (LFMs) can be seen as hybrid models that contain a first…
New limits of minimal surface systems have surprising large interior parts.
Parametric Cartan theory of exterior differential systems, and explicit cohomology of projective manifolds reveal united rationality features of differential algebraic geometry.
New method learns particle system potentials from unlabeled data.
This research uses DPPs to improve semi-parametric regression models.
This work develops a non-parametric test for relational independence in non-i.i.d. data.
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework for the computation of optimal reaction coordinates of such systems that is based …
A formula for the Riemannian metric tensor of differentiable manifolds of linear dynamical systems of same McMillan degree is presented in terms of their transfer function matrices. The necessary calculations for its application to ARMA and state space overlapping parametrizations are drafted. The importance of this ap…
Proposes using DII to identify non-linear causal relationships in EU Allowances returns.
Generalizes abelianization for framed local systems over surfaces.
A GAN method for stochastic boundary conditions in fast dynamics.
We consider a class of misspecified dynamical models where the governing term is only approximately known. Under the assumption that observations of the system's evolution are accessible for various initial conditions, our goal is to infer a non-parametric correction to the misspecified driving term such as to faithful…
We construct a geometric, real analytic parametrization of the Hitchin component Hit_n(S) of the PSL_n(R)-character variety R_{PSL_n(R)}(S) of a closed surface S. The approach is explicit and constructive. In essence, our parametrization is an extension of Thurston's shear coordinates for the Teichmueller space of a cl…
Study uses non-parametric method to analyze EU ETS price determinants.
Physical modeling of robotic system behavior is the foundation for controlling many robotic mechanisms to a satisfactory degree. Mechanisms are also typically designed in a way that good model accuracy can be achieved with relatively simple models and model identification strategies. If the modeling accuracy using phys…
This paper compares classical parametric methods with recently developed Bayesian methods for system identification. A Full Bayes solution is considered together with one of the standard approximations based on the Empirical Bayes paradigm. Results regarding point estimators for the impulse response as well as for conf…
This paper presents a novel approach for incremental semiparametric inverse dynamics learning. In particular, we consider the mixture of two approaches: Parametric modeling based on rigid body dynamics equations and nonparametric modeling based on incremental kernel methods, with no prior information on the mechanical …
Bayesian parametric matrix models provide uncertainty quantification for spectral learning.
This paper introduces a new method for neural networks that doesn't need a global coordinate system.
We construct a symplectic realization and a bi-hamiltonian formulation of a 3-dimensional system whose solution are the Jacobi elliptic functions. We generalize this system and the related Poisson brackets to higher dimensions. These more general systems are parametrized by lines in projective space. For these rank 2 P…
This work describes and discusses an algorithm submitted to the Sound Event Localization and Detection Task of DCASE2019 Challenge. The proposed methodology relies on parametric spatial audio analysis for source localization and detection, combined with a deep learning-based monophonic event classifier. The evaluation …
Estimates classifier errors without ground truth using algebraic geometry.
We use variational Gaussian approximations to analyze parametric models with unknown data-generating distributions.
We show that every coarse moduli space, parametrizing complex special linear rank two local systems with fixed boundary traces on a surface with nonempty boundary, is log Calabi-Yau in that it has a normal projective compactification with trivial log canonical divisor. We connect this to a novel symmetry of generating …
Polynomial chaos surrogates handle intrinsic noise in stochastic models.
Study geodesics on nested non-holonomic systems.
Drawing an inspiration from behavioral studies of human decision making, we propose here a general parametric framework for a reinforcement learning problem, which extends the standard Q-learning approach to incorporate a two-stream framework of reward processing with biases biologically associated with several neurolo…
Highly Autonomous Driving (HAD) systems rely on deep neural networks for the visual perception of the driving environment. Such networks are trained on large manually annotated databases. In this work, a semi-parametric approach to one-shot learning is proposed, with the aim of bypassing the manual annotation step requ…
ARX models predict thermal behavior of WBG semiconductors accurately.