In this paper we derive a series expansion for the price of a continuously sampled arithmetic Asian option in the Black-Scholes setting. The expansion is based on polynomials that are orthogonal with respect to the log-normal distribution. All terms in the series are fully explicit and no numerical integration nor any …
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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.
168,738 papers · 148 categories
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48 results for “orthogonal series”
OLinear forecasts time series more efficiently by transforming data orthogonally.
problem Efficiently forecasting time series with entangled dependencies.
method OLinear uses OrthoTrans to transform data orthogonally, then applies NormLin for linear layer.
result OLinear achieves state-of-the-art performance with high efficiency.
New scalable GP approximation using Fourier series decomposition.
problem Scalability and accuracy in Gaussian process approximations.
method Harmonic kernel decomposition (HKD) to decompose kernels orthogonally.
result Significantly outperforms standard variational methods in scalability and accuracy.
A new model detects anomalies in time series data efficiently.
problem Detect anomalies in high-dimensional time series data.
method r-ssGPFA, an unsupervised online anomaly detection model using state space Gaussian processes.
result The model detects anomalies efficiently and is computationally cheaper.
Study shows how lengths of geodesic arcs determine linking number of Legendrian knots.
problem Linking number of Legendrian knots on negatively curved surfaces.
method Analyzes Poincaré series on negatively curved surfaces.
result Explicit rational value of Poincaré series at 0 interprets linking number of Legendrian knots.
Bayesian Inference in High-Dimensional Time-Serieswith the Orthogonal Stochastic Linear Mixing Modelcs.LG
New model handles complex output dependence in large datasets.
problem Complex output dependence in large datasets.
method Orthogonal Stochastic Linear Mixing Model (OSLMM) with Markov chain Monte Carlo inference.
result OSLMM reduces prediction error compared to state-of-the-art methods.
Develops methods to estimate ratios of conditional expectation functions.
problem Estimating ratios of conditional expectation functions in causal inference.
method Orthogonal series estimator combined with debiased machine learning techniques.
result Valid pointwise and uniform asymptotic results for estimation and inference on CEFR.
The paper develops tensor learning methods exploiting symmetries of tensor functions.
problem Efficiently handling tensors in various scientific contexts.
method Equivariant machine learning architectures exploiting orthogonal, Lorentz, and symplectic symmetries.
result Equivariant models outperform non-equivariant baselines in time series analysis.
Orthogonal initialization does not speed up training in ultra-wide neural networks.
problem Exploring the effect of orthogonal initialization on training speed in deep neural networks.
method Study of neural tangent kernel dynamics in FCNs and CNNs with orthogonal initialization.
result The NTK of orthogonally-initialized networks remains constant during training, suggesting no speedup in the NTK regime.
New framework detects directional influence in multivariate time series.
problem Detecting directional influence in multivariate time series.
method Order-constrained spectral non-invariance.
result Unique diagnostic functional for directional influence.
Optimizes SGD for anytime neural networks, improving accuracy.
problem Training networks that produce increasingly accurate outputs over time.
method Orthogonalized SGD optimizer for nested architectures.
result Significantly improves generalization accuracy of anytime networks.
We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that our polynomial option price series expansion performs as efficiently and accura…
CWY Parametrization: a Solution for Parallelized Optimization of Orthogonal and Stiefel Matricescs.LG
Efficiently optimizes orthogonal and Stiefel matrices on parallel units.
problem Optimization over orthogonal groups on parallel units.
method CWY and T-CWY transforms for parametrization and optimization.
result CWY and T-CWY methods lead to convergence on parallel units.
We orthogonalize the NSS model to condition and diagnose its ill-conditioned parameters.
problem The ill-conditioning of the NSS model's design matrix.
method Exact orthogonal reparametrization via QR decomposition.
result Orthogonalization isolates the conditioning structure and maintains fit uncertainty.
A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has been much interest in sparse techniques, current methods do not generalize well to data with nonlinear structure. In this work, we present an orthogonal series estimator for predictors tha…
Poincare series of Klein groups, Coxeter polynomials, the Burau representation and Milnor invariantsmath.GT
For Poincare series of binary polyhedral groups and Coxeter polynomials there are obtained statements close to the Euclid algorithm and orthogonal polynomials theory: generalized Ebeling formula, decompositions into ramified continued fractions, Christoffel-Darboux identity, combinatorial formula. Known results about t…
ABO extends RLS for online learning in non-stationary time-series, improving accuracy and speed.
problem Online learning in non-stationary time-series with overparameterized models.
method QR-based exponentially weighted RLS algorithm with orthogonal-triangular updates.
result ABO maintains bounded residuals and stable condition numbers while achieving speed improvements.
The sum-product or belief propagation (BP) algorithm is a widely used message-passing technique for computing approximate marginals in graphical models. We introduce a new technique, called stochastic orthogonal series message-passing (SOSMP), for computing the BP fixed point in models with continuous random variables.…
Due to the dynamic nature, chaotic time series are difficult predict. In conventional signal processing approaches signals are treated either in time or in space domain only. Spatio-temporal analysis of signal provides more advantages over conventional uni-dimensional approaches by harnessing the information from both …
DFSOS improves sparse discriminant analysis for high-dimensional data.
problem Sparse discriminant analysis in high-dimensional settings with feature selection.
method Deflation-Free Sparse Optimal Scoring (DFSOS) using Bregman iteration and orthogonality-constrained optimization.
result DFSOS achieves comparable or better classification accuracy than deflation-based methods.
Paper introduces GDR-learners for estimating potential outcomes from observational data.
problem Lack of theoretical property of general Neyman-orthogonality in deep generative models.
method Develops flexible GDR-learners based on various deep generative models.
result GDR-learners possess quasi-oracle efficiency and rate double robustness, asymptotically optimal.
I introduce Forecastable Component Analysis (ForeCA), a novel dimension reduction technique for temporally dependent signals. Based on a new forecastability measure, ForeCA finds an optimal transformation to separate a multivariate time series into a forecastable and an orthogonal white noise space. I present a converg…
A Diagrammatic Approach to Improve Computational Efficiency in Group Equivariant Neural Networkscs.LG
New algorithm speeds up group equivariant neural networks computations.
problem Challenging computations in group equivariant neural networks.
method Diagrammatic framework based on category theory for matrix multiplication.
result Exponential improvement in time complexity for matrix multiplication.
Metric and Gauge Extensorsmath.DG
In this paper, the second in a series of eight we continue our development of the basic tools of the multivector and extensor calculus which are used in our formulation of the differential geometry of smooth manifolds of arbitrary topology . We introduce metric and gauge extensors, pseudo-orthogonal metric extensors, g…
This paper proposes a probabilistic neural network developed on the basis of time-series discriminant component analysis (TSDCA) that can be used to classify high-dimensional time-series patterns. TSDCA involves the compression of high-dimensional time series into a lower-dimensional space using a set of orthogonal tra…
GAIT-prop derives a biologically plausible learning rule from backpropagation.
problem Biological implausibility in traditional backpropagation for neural networks.
method GAIT-prop uses a top-down model to convert output error into plausible targets for weight updates.
result GAIT-prop and backpropagation give identical weight updates under certain conditions.
We give a complete classification of intertwining operators (symmetry breaking operators) between spherical principal series representations of G=O(n+1,1) and G'=O(n,1). We construct three meromorphic families of the symmetry breaking operators, and find their distribution kernels and their residues at all poles explic…
In a very high-dimensional vector space, two randomly-chosen vectors are almost orthogonal with high probability. Starting from this observation, we develop a statistical factor model, the random factor model, in which factors are chosen at random based on the random projection method. Randomness of factors has the con…
A new method ODR-BINDy improves model discovery from noisy data.
problem Discovering models from noisy datasets with error-in-variable problem.
method ODR-BINDy uses orthogonal distance regression with Bayesian model selection.
result ODR-BINDy consistently outperforms existing methods in recovering correct models.
A novel online GP model captures long-term memory in sequential data.
problem Capturing long-term memory in sequential data online.
method Integrates HiPPO framework into interdomain GP, leveraging time-varying orthogonal projections as inducing variables.
result OHSVGP outperforms existing online GP methods in predictive performance, long-term memory preservation, and computational efficiency.
Fast data inversion for high-dimensional Ornstein-Uhlenbeck processes from noisy measurementsstat.CO
Scalable approach for high-dimensional dynamical systems with noise filtering and parameter estimation.
problem Noise filtering and parameter estimation for high-dimensional dynamical systems.
method Flexible latent factor model with orthogonal factor loading matrix and closed-form parameter estimation.
result Substantial acceleration and higher accuracy compared to alternatives.
The paper creates a deformation retraction for homeomorphisms of the projective plane.
problem Deformation retraction of homeomorphisms of the projective plane.
method Equivariant strong deformation retraction from homeomorphism group to special orthogonal group.
result Induces a SO(3)-equivariant strong deformation retraction from projective plane homeomorphisms to SO(3).
We construct natural Green forms for special cycles in orthogonal and unitary Shimura varieties, in all codimensions, and, for compact Shimura varieties of type O(p,2) and U(p,1), we show that the resulting local archimedean height pairings are related to special values of derivatives of Siegel Eisentein series. A conj…
Multivariate Time Series characterization and forecasting of VoIP traffic in real mobile networkscs.NI
Researchers forecast VoIP traffic in mobile networks using multivariate time series analysis.
problem Predicting VoIP traffic behavior in real mobile networks for better resource allocation.
method Multivariate time series analysis, Vector Autoregressive models, machine learning techniques.
result Forecasting accuracy and insights into VoIP traffic dynamics.
Riemannian symmetric spaces are fundamental objects in finite dimensional differential geometry. An important problem is the construction of symmetric spaces for generalizations of simple Lie groups, especially their closest infinite dimensional analogues known as Kac-Moody groups. We solve this problem and construct a…
The Dynamic Mode Decomposition (DMD) extracted dynamic modes are the non-orthogonal eigenvectors of the matrix that best approximates the one-step temporal evolution of the multivariate samples. In the context of dynamical system analysis, the extracted dynamic modes are a generalization of global stability modes. We a…
The implementation of conventional sparse principal component analysis (SPCA) on high-dimensional data sets has become a time consuming work. In this paper, a series of subspace projections are constructed efficiently by using Household QR factorization. With the aid of these subspace projections, a fast deflation meth…
We develope a new scheme for the construction of explicit complex-valued proper biharmonic functions on Riemannian Lie groups. We exploit this and manufacture many infinite series of uncountable families of new solutions on the special unitary group . We then show that the special orthogonal group and th…
Let be a connected, simply connected real simple Lie group. Suppose that has a compact Cartan subgroup , so it has discrete series representations. Relative to there is a distinguished positive root system for which there is a unique noncompact simple root , the "Borel -- de Siebenthal s…
A new stable similarity measure for time series using persistent homology.
problem Constructing a robust measure of time series similarity.
method Persistent homology for stability, bi-conditional periodicity score for similarity.
result Stability of the bi-conditional periodicity score under perturbations and dimension reduction.
CP-factorization for high-dimensional tensor time series and double projection iterations
problem Identifying and estimating factor loadings in CP decomposition for high-dimensional tensor time series
method One-pass estimation procedure using standard eigen-analysis for matrix constructed based on serial dependence
result Asymptotic properties established under general settings, adapt to sparsity, accommodates weak factors
The study extends Jacobi-orthogonality to indefinite scalar product spaces.
problem Generalizing Jacobi-orthogonality to indefinite scalar product spaces.
method Comparing principles, investigating tensor relations, proving properties.
result Every quasi-Clifford tensor is Jacobi-orthogonal; certain tensors are Jacobi-dual or Osserman.
New characterization of Osserman tensors using Jacobi-orthogonality.
problem Characterizing Osserman tensors.
method Introducing Jacobi-orthogonality as a new potential characterization.
result Jacobi-orthogonal tensors are Osserman, and all known Osserman tensors are Jacobi-orthogonal.
Study isotropy groups for complex orthogonal and skew-symmetric matrices.
problem Understanding isotropy subgroups of orthogonal similarity transformations.
method Analysis of group structure of nonsingular block matrices.
result Group structure of isotropy subgroups related to block Toeplitz matrices.
The article proves integral formulas for foliated sub-Riemannian manifolds.
problem Integral formulas for foliated sub-Riemannian manifolds.
method Proved a series of integral formulae involving mean curvatures, Newton transformations, and curvature tensor.
result Generalized known integral formulas for codimension-one foliations.
New findings on Kähler manifolds restrict orthogonal coordinates existence.
problem Existence of orthogonal coordinates on Kähler manifolds.
method Algebraic and geometric techniques applied to Kähler manifolds.
result No nontrivial self-dual Kähler 4-manifolds or Ricci-flat Kähler 4-manifolds support orthogonal coordinates.
Constructs orthogonal coordinates in curved spaces.
problem Separating variables in curved spaces.
method Explicit construction of orthogonal coordinates and transformations.
result Explicit formulas for Killing tensors and Stäckel matrices.
OPT framework improves neural network generalization by learning an orthogonal transformation.
problem Improving neural network generalization.
method Orthogonal over-parameterized training (OPT) framework that minimizes hyperspherical energy.
result OPT framework provably minimizes hyperspherical energy and improves empirical generalization.