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.
Proposes MVGPR for spatiotemporal data modal analysis.
This paper develops efficient surrogate models for optimization of complex dynamical systems.
SVD-based methods reduce computational cost for stochastic systems.
Decomposing tensors into orthogonal factors is a well-known task in statistics, machine learning, and signal processing. We study orthogonal outer product decompositions where the factors in the summands in the decomposition are required to be orthogonal across summands, by relating this orthogonal decomposition to the…
Proposes FOAGP for efficient orthogonal effect decomposition of black-box computer experiments.
The paper explores geometric decompositions for Ricci tensors and their applications.
We construct a decomposition of the identity operator on a Riemannian manifold as a sum of smooth orthogonal projections subordinate to an open cover of . This extends a decomposition of the real line by smooth orthogonal projection due to Coifman, Meyer and Auscher, Weiss, Wickerhauser, and a similar decomposit…
Existing feature selection methods fail to properly account for interactions between features when evaluating feature subsets. In this paper, we attempt to remedy this issue by using orthogonal variance decomposition to evaluate features. The orthogonality of the decomposition allows us to directly calculate the total …
A new method combines POD and PCE for predicting multidimensional physical fields.
PROD method improves high-dimensional regression by handling strong correlations.
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference di…
The paper extends orthogonal decomposition results to hermitian Higgs bundles.
Convolutional networks predict turbulence from wall quantities.
Paper uses autoencoders for efficient reduced-order modeling of eigenvalue problems.
This work introduces a bias-variance decomposition for proper scores, improving uncertainty estimation in predictive models.
TreeHFD algorithm explains tree ensemble models through hierarchical orthogonality.
The paper shows how gradient flow on over-parametrized tensor decomposition behaves like deflation.
Optimizing over the set of orthogonal matrices is a central component in problems like sparse-PCA or tensor decomposition. Unfortunately, such optimization is hard since simple operations on orthogonal matrices easily break orthogonality, and correcting orthogonality usually costs a large amount of computation. Here we…
We present an algorithm for the decomposition of periodic financial return data into orthogonal factors of expected return and "systemic", "productive", and "nonproductive" risk. Generally, when the number of funds does not exceed the number of periods, the expected return of a portfolio is an affine function of its pr…
New algorithms improve tensor CP decomposition under mild conditions.
The BPS decomposition theorem splits cohomology of symmetric stacks into invariant parts.
New scalable GP approximation using Fourier series decomposition.
A novel framework quantifies uncertainty using proper scores for various tasks.
Study optimizes estimation of orthogonal and rotation matrices from noisy data.
In this paper, we present a new nonintrusive reduced basis method when a cheap low-fidelity model and expensive high-fidelity model are available. The method relies on proper orthogonal decomposition (POD) to generate the high-fidelity reduced basis and a shallow multilayer perceptron to learn the high-fidelity reduced…
TGCCA analyzes higher-order tensors using orthogonal rank-R CP decomposition.
In this paper, we study the nonnegative tensor data and propose an orthogonal nonnegative Tucker decomposition (ONTD). We discuss some properties of ONTD and develop a convex relaxation algorithm of the augmented Lagrangian function to solve the optimization problem. The convergence of the algorithm is given. We employ…
Paper uses sparse learning to estimate quasi-potential and drift components in stochastic systems.
Discrete conjugate systems are quadrilateral nets with all planar faces. Discrete orthogonal systems are defined by the additional property of all faces being concircular. Their geometric properties allow one to consider them as proper discretization of conjugate, resp. orthogonal coordinate systems of classical differ…
OPT framework improves neural network generalization by learning an orthogonal transformation.
We present an algebraic investigation of generalized and equiaffine curvature tensors in a given pseudo-Euclidean vector space and study different orthogonal, irreducible decompositions in analogy to the known decomposition of algebraic curvature tensors. We apply the decomposition results to characterize geometric pro…
We orthogonalize the NSS model to condition and diagnose its ill-conditioned parameters.
We provide a unified view of additive explanations for dependent inputs.
New model reconstructs flow from sparse data with uncertainty quantification.
A new method decomposes subjective risk into epistemic and aleatoric uncertainties.
Enhances Gaussian processes with spherical features for better scalability and flexibility.
It is well known that the curvature tensor of a pseudo-Riemannian manifold can be decomposed with respect to the pseudo-orthogonal group into the sum of the Weyl conformal curvature tensor, the traceless part of the Ricci tensor and of the scalar curvature. A similar decomposition with respect to the pseudo-unitary gro…
Revisits CP tensor decomposition for noisy, non-orthogonal data.
We analyze stochastic gradient descent for optimizing non-convex functions. In many cases for non-convex functions the goal is to find a reasonable local minimum, and the main concern is that gradient updates are trapped in saddle points. In this paper we identify strict saddle property for non-convex problem that allo…
Inverted file and asymmetric distance computation (IVFADC) have been successfully applied to approximate nearest neighbor search and subsequently maximum inner product search. In such a framework, vector quantization is used for coarse partitioning while product quantization is used for quantizing residuals. In the ori…
BayPOD-AL learns reduced-order models from high-fidelity data efficiently.
Tensor CANDECOMP/PARAFAC (CP) decomposition is an important tool that solves a wide class of machine learning problems. Existing popular approaches recover components one by one, not necessarily in the order of larger components first. Recently developed simultaneous power method obtains only a high probability recover…
The Temperley-Lieb algebra is a fundamental component of SU(2) topological quantum field theories. We construct chain complexes corresponding to minimal idempotents in the Temperley-Lieb algebra. Our results apply to the framework which determines Khovanov homology. Consequences of our work include semi-orthogonal deco…
Study of homeomorphisms on infinite type surfaces with a classification theorem.
Complex equivalence classes found in graph homotopy.
Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network structures via layers of sparse latent factors ranked by importance. Yet sparsit…
The paper proposes and discusses semiorthogonal decompositions for moduli spaces of vector bundles.
This is a report on our long term project to find an algorithm to decide if a finitely presented group has a non-trivial action on a tree.