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.
A new GP inference method using simplices for high-dimensional data.
Develops a new neural spike train decoding framework using topological data.
Simplicial learning improves classification by generating compact sparse representations.
SKI accelerates GP inference with sparse grids to handle higher dimensions.
Paper proposes a learning-based sparse Bayesian method for accurate off-grid DOA estimation.
We present a sparse grid high-order alternating direction implicit (ADI) scheme for option pricing in stochastic volatility models. The scheme is second-order in time and fourth-order in space. Numerical experiments confirm the computational efficiency gains achieved by the sparse grid combination technique.
Efficiently prices American options with multiple assets using sparse grids.
For low-dimensional data sets with a large amount of data points, standard kernel methods are usually not feasible for regression anymore. Besides simple linear models or involved heuristic deep learning models, grid-based discretizations of larger (kernel) model classes lead to algorithms, which naturally scale linear…
Scalable algorithm for sampling Gaussian processes using sparse grids and preconditioners.
Direction of arrival (DOA) estimation is a classical problem in signal processing with many practical applications. Its research has recently been advanced owing to the development of methods based on sparse signal reconstruction. While these methods have shown advantages over conventional ones, there are still difficu…
New algorithm tackles high-dimensional simulation optimization, converging efficiently.
Grid security and open markets are two major smart grid goals. Transparency of market data facilitates a competitive and efficient energy environment, yet it may also reveal critical physical system information. Recovering the grid topology based solely on publicly available market data is explored here. Real-time ener…
Recent research in off-the-grid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few time-domain samples even though the dictionary is continuous. In particular, atomic norm minimization was proposed in \cite{tang2012csotg} to recove…
Sparse grids reduce xVA exposure evaluations by up to 6000 times.
In this work, we present a numerical method based on a sparse grid approximation to compute the loss distribution of the balance sheet of a financial or an insurance company. We first describe, in a stylised way, the assets and liabilities dynamics that are used for the numerical estimation of the balance sheet distrib…
We outline a novel clustering scheme for simplicial complexes that produces clusters of simplices in a way that is sensitive to the homology of the complex. The method is inspired by, and can be seen as a higher-dimensional version of, graph spectral clustering. The algorithm involves only sparse eigenproblems, and is …
This paper is concerned about sparse, continuous frequency estimation in line spectral estimation, and focused on developing gridless sparse methods which overcome grid mismatches and correspond to limiting scenarios of existing grid-based approaches, e.g., optimization and SPICE, with an infinitely dense grid…
New method smooths integrands for efficient option pricing.
The counting grid is a grid of microtopics, sparse word/feature distributions. The generative model associated with the grid does not use these microtopics individually. Rather, it groups them in overlapping rectangular windows and uses these grouped microtopics as either mixture or admixture components. This paper bui…
New learning scheme solves high-dimensional semi-linear PDEs using sparse grids and Picard approximations.
The potential of recovering the topology of a grid using solely publicly available market data is explored here. In contemporary whole-sale electricity markets, real-time prices are typically determined by solving the network-constrained economic dispatch problem. Under a linear DC model, locational marginal prices (LM…
New methods solve complex financial equations.
SDIFT generates full-field dynamics from sparse, irregular data.
Deep learning improves model discovery from sparse sensor data.
PhI-GPR improves power grid state estimation and forecasting.
Exact and scalable algorithm for Gaussian process regression with Matérn correlations.
Distance weighted discrimination (DWD) was originally proposed to handle the data piling issue in the support vector machine. In this paper, we consider the sparse penalized DWD for high-dimensional classification. The state-of-the-art algorithm for solving the standard DWD is based on second-order cone programming, ho…
Graph neural networks learn PDEs from sparse, irregular data.
Satellite imagery and ML improve livelihood measurements and estimate electrification's impact.
Deep learning predicts dynamics from sparse data.
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results. Coping with the infinite dimensionality and non-convexity of these problems typica…
Paper proposes a fast data-driven AC-OPF method using sparse hybrid Gaussian processes.
Study of -adic simplicial volumes and their properties.
Gaussian process modulated Poisson processes provide a flexible framework for modelling spatiotemporal point patterns. So far this had been restricted to one dimension, binning to a pre-determined grid, or small data sets of up to a few thousand data points. Here we introduce Cox process inference based on Fourier feat…
Integral foliated simplicial volume is a version of simplicial volume combining the rigidity of integral coefficients with the flexibility of measure spaces. In this article, using the language of measure equivalence of groups we prove a proportionality principle for integral foliated simplicial volume for aspherical m…
IRKSN algorithm achieves sparse recovery with wider applicability conditions.
We define the ideal simplicial volume for compact manifolds with boundary. Roughly speaking, the ideal simplicial volume of a manifold measures the minimal size of possibly ideal triangulations of "with real coefficients", thus providing a variation of the ordinary simplicial volume defined by Gromov in 1982, t…
We consider the relation between simplicial volume and two of its variants: the stable integral simplicial volume and the integral foliated simplicial volume. The definition of the latter depends on a choice of a measure preserving action of the fundamental group on a probability space. We show that integral foliated s…
Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or decided data-adaptively. Traditional computational methods rely on solving a set o…
We show that non-elliptic prime 3-manifolds satisfy integral approximation for the simplicial volume, i.e., that their simplicial volume equals the stable integral simplicial volume. The proof makes use of integral foliated simplicial volume and tools from ergodic theory.
We study the multiscale simplicial flat norm (MSFN) problem, which computes flat norm at various scales of sets defined as oriented subcomplexes of finite simplicial complexes in arbitrary dimensions. We show that the multiscale simplicial flat norm is NP-complete when homology is defined over integers. We cast the mul…
New method improves stochastic kriging for high-dimensional simulations.
The rough Bergomi (rBergomi) model, introduced recently in [5], is a promising rough volatility model in quantitative finance. It is a parsimonious model depending on only three parameters, and yet remarkably fits with empirical implied volatility surfaces. In the absence of analytical European option pricing methods f…
Alexander's conjecture extended to infinite simplicial complexes.
Integrating wind power into the grid is challenging because of its random nature. Integration is facilitated with accurate short-term forecasts of wind power. The paper presents a spatio-temporal wind speed forecasting algorithm that incorporates the time series data of a target station and data of surrounding stations…
Estimates graph process with high-frequency data, proving asymptotic properties.
Proposes a method to learn representations of higher-dimensional simplicial complexes.
Belief Propagation has been widely used for marginal inference, however it is slow on problems with large-domain variables and high-order factors. Previous work provides useful approximations to facilitate inference on such models, but lacks important anytime properties such as: 1) providing accurate and consistent mar…