Gaussian processes are typically used for smoothing and interpolation on small datasets. We introduce a new Bayesian nonparametric framework -- GPatt -- enabling automatic pattern extrapolation with Gaussian processes on large multidimensional datasets. GPatt unifies and extends highly expressive kernels and fast exact…
On-device research index
arXiv research
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.
168,657 papers · 148 categories
Trend · papers per month
48 results for “multidimensional Gaussianization”
UAPCA projects uncertain data to low dimensions using GMMs.
problem Uncertain multidimensional data not well described by normal distributions.
method Model data with Gaussian mixture models, derive UAPCA projection from general formulation.
result Low-dimensional projections better represent multidimensional distributions.
Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure inherent in particular covariance functions, including GPs with implied Markov st…
We present a scalable Gaussian process model for identifying and characterizing smooth multidimensional changepoints, and automatically learning changes in expressive covariance structure. We use Random Kitchen Sink features to flexibly define a change surface in combination with expressive spectral mixture kernels to …
Proposes a method to compute information theory measures via Gaussianization.
problem Challenges of computing information from multidimensional data.
method Indirect computation using a multivariate Gaussianization transform.
result Proposed methods outperform existing estimators, especially in high dimensions.
A new model captures multifractal volatility in stock returns.
problem Capturing multifractal volatility in stock returns.
method Introduced mLog S-fBM model, defined mS-fBM, and developed calibration procedure.
result Validated model on synthetic and real data, showing multifractal behavior.
Gaussian processes model geospatial trajectories with uncertainty.
problem Interpolating and predicting complex spatiotemporal data.
method Gaussian process models trajectories as multidimensional Gaussian distributions.
result Gaussian processes provide a flexible and probabilistic way to interpolate geospatial data.
Quantum computing speeds up option pricing for multiple assets.
problem High-dimensional integration bottleneck in option pricing.
method Calibrated marginal distributions, Gaussian copula, QAMC with QAE.
result QAMC reduces integration queries by 10-100 times for similar precision.
A new model captures multifractal volatility in stock returns.
problem Capturing multifractal volatility in stock returns.
method Introduced mLog S-fBM model, defined mS-fBM, and developed calibration procedure.
result Model captures multifractal behavior in stock returns, validating on real data.
Bayesian Complementary Kernelized Learning models complex spatiotemporal data.
problem Modeling complex, nonstationary, and nonseparable spatiotemporal data.
method Integrates kernelized low-rank tensor factorization and short-range spatiotemporal Gaussian Processes.
result BCKL offers superior performance in providing accurate posterior mean and high-quality uncertainty estimates.
Most signal processing problems involve the challenging task of multidimensional probability density function (PDF) estimation. In this work, we propose a solution to this problem by using a family of Rotation-based Iterative Gaussianization (RBIG) transforms. The general framework consists of the sequential applicatio…
Study of a risk-averse informed trader in a multi-asset market with non-Gaussian prices.
problem Existence of equilibrium in a multi-asset market with non-Gaussian prices and a risk-averse informed trader.
method Constructed equilibrium using Fokker-Planck equation and coupled partial differential equations with an optimal transport constraint.
result Equilibrium exists in a market with multiple assets and non-Gaussian prices.
A method for accurate pricing of multidimensional derivatives under uncertain volatility.
problem High-dimensional stochastic control problem in uncertain volatility model.
method Backward actor-critic stochastic policy gradient scheme combining DP, PPO, and neural networks.
result Accurate and efficient pricing of multidimensional derivatives compared to benchmarks.
New neural network captures spatial correlations in wind speed predictions.
problem Uncertainty quantification in neural network predictions for high-dimensional, correlated data.
method Training neural networks with multidimensional Gaussian loss, preserving spatial correlation and computational tractability.
result Demonstrated super-resolution of surface wind speed with explicit correlation modeling.
Study improves sample complexity for distinguishing continuous distributions and causal relationships.
problem Distinguishing continuous distributions and causal relationships in the presence of unobserved confounding.
method Proposed an estimator of KL divergence based on von Mises expansion for closeness testing.
result Established sample complexity guarantees for causal discovery in non-linear models with continuous variables and unobserved confounding.
Non-Gaussian component analysis (NGCA) is a problem in multidimensional data analysis which, since its formulation in 2006, has attracted considerable attention in statistics and machine learning. In this problem, we have a random variable in -dimensional Euclidean space. There is an unknown subspace of the …
A new method reduces memory requirements for sorting high-dimensional data.
problem Efficiently sorting and organizing high-dimensional data with low memory usage.
method Iteratively shuffles N indices and applies SoftSort optimization steps.
result Significantly improves sorting quality for multidimensional data.
RS-HDMR-GPR simplifies complex functions with machine-learned lower-dimensional terms.
problem Representing and understanding complex multidimensional functions with sparse data.
method Random Sampling High Dimensional Model Representation Gaussian Process Regression (RS-HDMR-GPR).
result Facilitates recovery of functional dependence and adds insight into input variable importance.
This paper deals with multidimensional dynamic risk measures induced by conditional -expectations. A notion of multidimensional -expectation is proposed to provide a multidimensional version of nonlinear expectations. By a technical result on explicit expressions for the comparison theorem, uniqueness theorem and…
The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and v…
This paper improves conditional multidimensional scaling for incomplete data.
problem Handling missing data in known features for multidimensional scaling.
method Proposes a method to learn low-dimensional configurations with missing known feature values.
result Can learn low-dimensional configurations and impute missing values.
The paper explores multidimensional critic output in GANs, improving convergence and diversity.
problem Underexplored in GANs literature, multidimensional critic output.
method Generalized Wasserstein GAN framework, SRVT block, maximal p-centrality discrepancy.
result High-dimensional critic output improves GAN performance in convergence and diversity.
Improved algorithm for multidimensional scaling reduces stress.
problem Stress in multidimensional scaling.
method Proposed modifications of the smacof algorithm.
result Convergent majorization algorithm for Kruskal's stress formula two.
Robust estimators for Gaussian sparse tasks with optimal error under contamination.
problem Robust mean estimation, PCA, and linear regression in the presence of Huber contamination.
method Novel multidimensional filtering method for sparse regime.
result Optimal error guarantees within constant factors for Gaussian robust -sparse mean estimation.
The paper provides non-asymptotic Edgeworth expansions for neural network outputs.
problem Approximating deviations of finite-width neural networks from their Gaussian limit.
method Multidimensional Edgeworth expansions of arbitrary order for neural network outputs.
result Established a bound on the total variation distance between neural network output and its Edgeworth approximation.
A method to visualize multidimensional local subspaces using implicit differentiation.
problem Understanding the effect of multidimensional projection on local subspaces.
method Implicit function differentiation to analyze local subspaces shaped by multidimensional ellipses.
result Visualization of local subspaces provides insights into the global structure of data.
New algorithm profiles nuisance parameters for multidimensional deconvolution.
problem Statistical removal of instrumental effects in experimental measurements.
method Iterative algorithm called Profile OmniFold that profiles nuisance parameters.
result Illustrated with a Gaussian example, highlighting promising capabilities.
We establish large deviation principles for convolutional neural networks.
problem Understanding the behavior of convolutional neural networks in the infinite-channel limit.
method We establish large deviation principles for convolutional neural networks under Gaussian prior and posterior distributions.
result We provide a large deviation principle for the sequence of conditional covariance matrices and the posterior distribution.
The cumulant analysis plays an important role in non Gaussian distributed data analysis. The shares' prices returns are good example of such data. The purpose of this research is to develop the cumulant based algorithm and use it to determine eigenvectors that represent investment portfolios with low variability. Such …
Global minima found for multidimensional scaling with penalties.
problem Finding global minima in multidimensional scaling.
method Combining stress loss function with a quadratic penalty term to find minimizers.
result Trajectory of minimizers leads to global minima.
We present the multidimensional membership mixture (M3) models where every dimension of the membership represents an independent mixture model and each data point is generated from the selected mixture components jointly. This is helpful when the data has a certain shared structure. For example, three unique means and …
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a unified framework that includes low, moderate and high dimensions, we study multidim…
Study uses multidimensional SE-NBD process to analyze default portfolios and identify shock amplification.
problem Analyzing interactions and shock propagation in default portfolios with multiple sectors.
method Applied multidimensional self-exciting negative binomial distribution (SE-NBD) process to 13 sectors.
result Identified upstream and downstream sectors, showing shock amplification in default portfolios.
We consider a long-term optimal investment problem where an investor tries to minimize the probability of falling below a target growth rate. From a mathematical viewpoint, this is a large deviation control problem. This problem will be shown to relate to a risk-sensitive stochastic control problem for a sufficiently l…
Efficiently recovers piecewise linear functions from noisy samples.
problem Recovering a piecewise linear function from noisy samples with unknown segmentation.
method Iterative merging approach for multidimensional segmented regression.
result First sample and computationally efficient algorithm in any fixed dimension.
We investigate aspects of semimartingale decompositions, approximation and the martingale representation for multidimensional correlated Markov processes. A new interpretation of the dependence among processes is given using the martingale approach. We show that it is possible to represent, in both continuous and discr…
A Multiclass ROC Curvestat.ME
Novel method for multiclass ROC curves using multidimensional Gini index.
problem Multiclass performance evaluation, especially for imbalanced datasets.
method Extends ROC curve methodology to multiclass settings using multidimensional Gini index.
result Validated through case studies in health care and finance.
Shortfall Risk Approximations for American Options in the multidimensional Black--Scholes Modelq-fin.CP
We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black--Scholes (BS) market converge to the corresponding quantities for similar American options in the multidimensional BS market with path dependent payoffs. In comparison to previous papers we conside…
A novel online framework for analyzing multidimensional functional data.
problem Analysis of multidimensional functional data streams poses significant challenges.
method Online functional principal component analysis using tensor product splines on a Stiefel manifold with Riemannian stochastic gradient descent.
result Efficient and scalable modeling of multidimensional functional data.
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.
Paper presents adaptive minimax risk classifiers for multidimensional concept drift.
problem Multidimensional concept drift in supervised classification.
method Adaptive minimax risk classifiers (AMRCs) tracking multivariate and high-order distribution changes.
result AMRCs provide computable tight performance guarantees and improve classification.
sWk-means clusters multidimensional financial time series into distinct market regimes.
problem Classifying distinct market regimes in multidimensional financial time series.
method Approximated multidimensional Wasserstein distance as sliced Wasserstein distance for clustering.
result sWk-means successfully identifies distinct market regimes in real financial data.
Classical multidimensional scaling is an important dimension reduction technique. Yet few theoretical results characterizing its statistical performance exist. This paper provides a theoretical framework for analyzing the quality of embedded samples produced by classical multidimensional scaling. This lays the foundati…
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.
Identifying changes in model parameters is fundamental in machine learning and statistics. However, standard changepoint models are limited in expressiveness, often addressing unidimensional problems and assuming instantaneous changes. We introduce change surfaces as a multidimensional and highly expressive generalizat…
Path-dependent PDEs model VIX and Realised Variance options.
problem Modeling volatility derivatives with path-dependence.
method Continuous stochastic volatility model with Gaussian Volterra process, proving well-posedness of PDEs.
result Formulae for greeks and implied volatility provided, finite-dimensional pricing PDEs obtained in Markovian models.
Simulation of Multidimensional Diffusions with Sticky Boundaries via Markov Chain Approximationmath.PR
New method simulates sticky boundaries in multidimensional diffusions.
problem Simulating sticky boundaries in multidimensional diffusions.
method Approximate sticky diffusion by a Markov chain, using either finite difference or matching local moments.
result Validates both construction methods for first-order simulation schemes.
Extends Carathéodory's theorem to multidimensional domains with constant curvature.
problem Characterizing biholomorphic domains with constant holomorphic curvature.
method Using Bergman representative coordinates and Calabi's diastasis.
result Provides sufficient conditions for the boundary of a biholomorphic ball to be a topological sphere.