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.
Study on signal-plus-noise decomposition in nonlinear spiked random matrices.
Proposes neural dynamic mode decomposition for end-to-end modeling of nonlinear dynamics.
IKD uses eigen-decomposition for nonlinear dimensionality reduction.
Biological neurons learn tensor decompositions of higher-order correlations using nonlinear Hebbian plasticity.
ADMM algorithm solves nonlinear matrix decompositions efficiently.
In this paper, we study a type of reflected BSDE with a constraint and introduce a new kind of nonlinear expectation via BSDE with a constraint and prove the Doob-Meyer decomposition with respect to the super(sub)martingale introduced by this nonlinear expectation. We then apply the results to the pricing of American o…
New algorithms accelerate solving nonlinear matrix decomposition with ReLU.
On the basis of loop group decompositions (Birkhoff decompositions), we give a discrete version of the nonlinear d'Alembert formula, a method of separation of variables of difference equations, for discrete constant negative Gauss curvature (pseudospherical) surfaces in Euclidean three space. We also compute two exampl…
Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in practice, and no extensive comparisons have been made between available methods. Previo…
New decompositions misattribute differences between populations, even when outcomes are identical.
New matrix approximation method using RBF components for better memory efficiency.
A new method models financial returns by separating sign and magnitude, improving forecasting accuracy.
New algorithms for interpreting complex multivariate functions.
Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often need to prepare nonlinear observables manually according to the underlying dynami…
New method identifies key genes affecting phenotypes in biological systems.
A novel algorithm converges for solving a specific matrix decomposition problem.
Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex interactions among objects are multi-linear, and are thus insufficient to repres…
New algorithms extract Koopman invariant subspaces from large-scale data.
Two methods preserve tensor structure for reduced dimensionality in tensor regression.
Proposes FOAGP for efficient orthogonal effect decomposition of black-box computer experiments.
Proposes a Gaussian process for Koopman mode decomposition.
We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the solutions to Backward Stochastic Differential Equations with Lipschitz continuous …
This article is an application of the author's paper about a construction method for discrete constant negative Gaussian curvature surfaces, the nonlinear d'Alembert formula. The heart of this formula is the Birkhoff decomposition, and we give a simple algorithm for the Birkhoff decomposition. As an application, we dra…
Deep neural networks decompose SDF into linear and nonlinear components.
Nonlinear methods such as Deep Neural Networks (DNNs) are the gold standard for various challenging machine learning problems, e.g., image classification, natural language processing or human action recognition. Although these methods perform impressively well, they have a significant disadvantage, the lack of transpar…
This paper finds a new method for decomposing insurer profits and losses.
Infinite Tucker Decomposition (InfTucker) and random function prior models, as nonparametric Bayesian models on infinite exchangeable arrays, are more powerful models than widely-used multilinear factorization methods including Tucker and PARAFAC decomposition, (partly) due to their capability of modeling nonlinear rel…
Stochastic discount factor (SDF) processes in dynamic economies admit a permanent-transitory decomposition in which the permanent component characterizes pricing over long investment horizons. This paper introduces an empirical framework to analyze the permanent-transitory decomposition of SDF processes. Specifically, …
We prove that every flat nonlinear discrete-time system can be decomposed by coordinate transformations into a smaller-dimensional subsystem and an endogenous dynamic feedback. For flat continuous-time systems, no comparable result is available. The advantage of such a decomposition is that the complete system is flat …
A new method quickly identifies key variables and interactions.
Extends RRR to capture nonlinear interactions in multi-response regression.
Unified framework detects change-points and estimates parameters in nonlinear systems with regime switching.
In this article we will analyse how to compute the contribution of each input value to its aggregate output in some nonlinear models. Regression and classification applications, together with related algorithms for deep neural networks are presented. The proposed approach merges two methods currently present in the lit…
A new method optimizes knot selection for spline dimensional decomposition in stochastic dynamic analysis.
This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this decomposition is examined in detail. In particular, the dependency of various ki…
Derives a primal-dual MLSVD formulation for multilinear data.
DTCCA learns nonlinear transformations of multi-view data for high-order correlation.
A new method reduces Volterra kernel complexity and uncertainty quantification.
DiPCA algorithm improves scalability and solution quality for time-dependent data.
Machine learning can improve 2SLS first stage predictions, but nonlinear methods often introduce bias.
DecompKAN improves time series forecasting accuracy and transparency.
We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a càdlàg nonlinear martingale which is also the value process of a superhedging problem. The superhedging strate…
Proposes a faster Isomap algorithm by reducing eigenvalue decomposition complexity.
We consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimisation, over a set of possibly non-dominated probability measures, of solutions of backward stochastic differential equations (BSDEs). Since BSDEs are nonlinear generalisations of the…
In this paper we consider general rank minimization problems with rank appearing in either objective function or constraint. We first establish that a class of special rank minimization problems has closed-form solutions. Using this result, we then propose penalty decomposition methods for general rank minimization pro…
Breaks down complex nonlinear dynamics into simpler components.
KAN-PCA improves asset return analysis by capturing more variance than classical PCA during market crises.
We establish a nondominated version of the optional decomposition theorem in a setting that includes jump processes with nonvanishing diffusion as well as general continuous processes. This result is used to derive a robust superhedging duality and the existence of an optimal superhedging strategy for general contingen…