A method for multidimensional probabilistic electricity market forecasting is proposed.
problem Uncertainty in simultaneous multivariate predictions of electricity markets.
method Repeated resampling to estimate uncertainty of simultaneous multivariate predictions.
result The method provides highly accurate predictions and gains are largest when considering functions of variables.
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.
A new method ranks uncertainty vectors from multiple measures for robust prediction.
problem Single scalar measures of model reliability are insufficient for comprehensive uncertainty quantification.
method Optimal transport ranks vectors of uncertainty measures, supporting flexible fusion of aleatoric and epistemic uncertainties.
result The method provides a robust ranking of uncertainty that supports various downstream tasks.
Large-scale and multidimensional spatiotemporal data sets are becoming ubiquitous in many real-world applications such as monitoring urban traffic and air quality. Making predictions on these time series has become a critical challenge due to not only the large-scale and high-dimensional nature but also the considerabl…
A new tensor regression model preserves multidimensional data structure.
problem Complex multidimensional data loses intrinsic connections and parameter explosion.
method Developed a parsimonious tensor regression model using Tucker structure and shrinkage penalization.
result The model outperforms benchmark models in forecasting.
Extends Bayesian theory to handle complex interdependencies in multidimensional event spaces.
problem Complex interdependencies between events and hypotheses sets in real-world systems.
method Developed a mathematical formalism for modeling complex relationships through rigorous derivation and validated using analytical proofs, simulations, and case studies.
result MDSE theory improves prediction accuracy by 15-20% compared to standard Bayesian methods in high interdimensionality datasets.
New risk control method for non-monotonic losses in complex parameters.
problem Controlling risk for non-monotonic losses with multidimensional parameters.
method Stability-based guarantees for generic algorithms applied to non-monotonic losses.
result Guarantees depend on algorithm stability, with looser guarantees for unstable algorithms.
This paper deals with multidimensional dynamic risk measures induced by conditional g-expectations. A notion of multidimensional g-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…
Unified model combines neural networks and dictionary learning for clinical predictions from brain data.
problem Predicting clinical severity from brain imaging data.
method Combines neural networks with dictionary learning to model patient-specific and shared features.
result Unified model outperforms state-of-the-art methods in predicting clinical severity.
Timer-XL predicts multidimensional time series using a unified Transformer approach.
problem Unified time series forecasting across various tasks and contexts.
method Decoder-only Transformers with a universal TimeAttention mechanism and deft position embedding.
result State-of-the-art performance across multiple forecasting benchmarks.
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.
A new method combines POD and PCE for predicting multidimensional physical fields.
problem Predicting multidimensional non-linear fields from limited data.
method Combines Proper Orthogonal Decomposition (POD) and Polynomial Chaos Expansion (PCE).
result Demonstrates improved prediction accuracy and interpretability.
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.
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.
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.
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…
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…
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.
A new framework enhances IDW models for complex industrial datasets.
problem Low performance of IDW models in complex industrial datasets.
method Deep reinforcement learning network to enhance IDW models and learn hyperparameters.
result The proposed framework achieves differential spatial prediction and is more accurate than current IDW models.
The paper presents a machine learning approach to multidimensional item response theory.
problem Modeling and predicting student performance from assessment data.
method Inspired by collaborative filtering, the paper defines a general class of models using penalized joint maximum likelihood (JML) for estimation and cross-validation for model selection.
result The high-dimensional model fit to large and sparse data does not lend itself well to traditional factor interpretation.
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…
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…
Framework integrates brain connectivity data for clinical predictions.
problem Predicting clinical outcomes from brain connectivity data.
method Structurally-regularized Dynamic Dictionary Learning (sr-DDL) and LSTM-ANN block.
result Framework outperforms state-of-the-art approaches in clinical outcome prediction.
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.
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.
Two new feature selection algorithms improve on RFE.
problem Optimal feature selection for faster and more accurate models.
method Fibonacci and k-Subsecting Recursive Feature Elimination.
result Faster feature selection with comparable predictive performance.
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…
Optimizes kernel density ratios for better predictions and information measures.
problem Improving accuracy of kernel density estimates for density ratios.
method Derives an optimal weight function using calculus of variations.
result Reduces bias in kernel density estimates, leading to improved prediction posteriors and information-theoretic measures.
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.
New method for learning multidimensional CDFs using Archimedean copulas.
problem Learning multidimensional CDFs in high dimensions.
method Generative modeling technique using Archimedean copulas as mixture models with latent variables from neural networks.
result Efficacy and computational efficiency compared to existing methods.
We investigate the use of Malliavin calculus in order to calculate the Greeks of multidimensional complex path-dependent options by simulation. For this purpose, we extend the formulas employed by Montero and Kohatsu-Higa to the multidimensional case. The multidimensional setting shows the convenience of the Malliavin …
DPI quantifies phase differences in 1D and multidimensional signals using Riesz transform.
problem Quantifying phase differences in signals of varying dimensions.
method Riesz transform framework for harmonic analysis.
result DPI detects hypersynchronization and subtle changes in images and artworks.
We present a method for a wine recommendation system that employs multidimensional clustering and unsupervised learning methods. Our algorithm first performs clustering on a large corpus of wine reviews. It then uses the resulting wine clusters as an approximation of the most common flavor palates, recommending a user …
Develops statistical confidence sets for multidimensional scaling.
problem Statistical uncertainty in multidimensional scaling of noisy data.
method Formal statistical framework, distributional convergence results, uniform confidence sets, bootstrap procedures.
result Construction of reliable confidence sets for latent configurations in multidimensional scaling.
Generalizations of the Weierstrass formulae to generic surface immersed into R4, S4 and into multidimensional Riemann spaces are proposed. Integrable deformations of surfaces in these spaces via the modified Veselov-Novikov equation are discussed.
Optimal B-robust estimate is constructed for multidimensional parameter in drift coefficient of diffusion type process with small noise. Optimal mean-variance robust (optimal V -robust) trading strategy is find to hedge in mean-variance sense the contingent claim in incomplete financial market with arbitrary informatio…
In this paper, we study optimal switching problems under ambiguity. To characterize the optimal switching under ambiguity in the finite horizon, we use multidimensional reflected backward stochastic differential equations (multidimensional RBSDEs) and show that a value function of the optimal switching under ambiguity …
Machine learning often needs to model density from a multidimensional data sample, including correlations between coordinates. Additionally, we often have missing data case: that data points can miss values for some of coordinates. This article adapts rapid parametric density estimation approach for this purpose: model…
In this paper the well-known Dubrovin-Novikov problem posed as long ago as 1984 in connection with the Hamiltonian theory of systems of hydrodynamic type, namely, the classification problem for multidimensional Poisson brackets of hydrodynamic type, is solved. In contrast to the one-dimensional case, in the general cas…
Efficiently analyzes multidimensional functional data using separable basis functions.
problem Curse of dimensionality in traditional functional data analysis.
method Marginal product basis systems for multidimensional data, tensor decomposition, differential operator-based penalties.
result Efficient estimation of multidimensional functional data representations.
The present contribution suggests the use of a multidimensional scaling (MDS) algorithm as a visualization tool for manifold-valued elements. A visualization tool of this kind is useful in signal processing and machine learning whenever learning/adaptation algorithms insist on high-dimensional parameter manifolds.