New method detects change points in multi-dimensional sequences, controlling false detection.
problem Detecting change points in sequences with multiple dimensions.
method Two-stage approach: select relevant dimensions and CPs, using selective inference.
result Exact inference possible for a class of CP detection methods.
New method for valid and exact statistical inference of multi-dimensional change-points.
problem Statistical inference of change-points in multi-dimensional sequences.
method Proposes a method to guarantee the statistical reliability of both location and components of detected changes.
result Demonstrates the effectiveness of the method in genomic abnormality identification and human behavior analysis.
The abstract introduces a new concept called flagfolds to model multi-dimensional shapes.
problem Modeling multi-dimensional shapes in a way that avoids going through higher dimensional spaces.
method Interpreting covariance matrices as nested subspaces and defining a Riemannian metric on the highest dimensional stratum.
result A Riemannian metric on the highest dimensional stratum allows for geodesics between subspaces of different dimensions.
A new model captures dependencies and unique characteristics in multi-dimensional sequences.
problem Modeling high-dimensional sequential data with dependencies and unique characteristics.
method Collaborative multi-output Gaussian process dynamical system (CGPDS) with shared and private latent processes, using inducing points and stochastic variational inference.
result Captures dependencies and unique characteristics in multi-dimensional sequences.
Multi-dimensional classification (MDC) is the supervised learning problem where an instance is associated with multiple classes, rather than with a single class, as in traditional classification problems. Since these classes are often strongly correlated, modeling the dependencies between them allows MDC methods to imp…
Study efficient rebalancing strategies for portfolio tracking error.
problem Optimizing portfolio rebalancing under high-frequency asset price models.
method Discrete-time rebalancing strategies derived from continuous model.
result Asymptotically efficient sequence of simple strategies.
TEAFormers preserve multi-dimensional time series structures for better forecasting.
problem Traditional Transformers flatten multi-dimensional time series data, losing critical multi-dimensional relationships.
method Tensor-Augmented Transformer (TEAFormer) with Tensor-Augmentation (TEA) module.
result Significant performance enhancements in time series forecasting across benchmarks.
Proposes a deep neural network for multi-dimensional functional data classification.
problem Classifying multi-dimensional functional data with non-Gaussian distributions.
method Trains a deep neural network on the principle components of the training data.
result FDNN achieves minimax optimality when log density ratio has a locally connected modular structure.
A low-rank tensor model simplifies multi-dimensional Markov chains.
problem Simplifying the dynamics of multi-dimensional Markov chains.
method Low-rank tensor decomposition for multi-dimensional state spaces.
result Our tensor model requires fewer parameters and samples than conventional methods.
The paper focuses on the sparse approximation of signals using overcomplete representations, such that it preserves the (prior) structure of multi-dimensional signals. The underlying optimization problem is tackled using a multi-dimensional split Bregman optimization approach. An extensive empirical evaluation shows ho…
New graph Fourier transform distinguishes directions in multi-dimensional signals.
problem Existing graph Fourier transform fails to distinguish directions in multi-dimensional signals.
method Algebraic properties of Cartesian products rearrange 1-D spectra into multi-dimensional frequency domain.
result Solves multi-valuedness of spectra and enables directional frequency analysis.
Study optimal stopping times for multi-dimensional processes with non-exponential discounting.
problem Optimal stopping in multi-dimensional processes with non-exponential discounting.
method Probabilistic potential theory to establish existence of optimal equilibria.
result Existence of optimal equilibria for multi-dimensional stopping problems.
pLSTM tackles long-range language modeling and computer vision tasks with parallelizable linear source transition mark networks.
problem Challenges of existing recurrent architectures in handling sequences and multi-dimensional data.
method Introduces pLSTM, a parallelizable linear source transition mark network for linear graphs and DAGs, addressing vanishing/exploding activation/gradient issues.
result pLSTM outperforms Transformers in long-range tasks like arrow-pointing extrapolation and image size extrapolation.
Paper solves robust multi-dimensional scaling with accelerated projections.
problem Localize point locations from noisy pairwise distances.
method Alternating projections with tangent space acceleration.
result Linear convergence of reconstructed points to original points.
Paper defines multi-dimensional fractional Brownian motion under volatility uncertainty.
problem Volatility uncertainty in fractional Brownian motion.
method Definition and study of multi-dimensional fractional Brownian motion (G-fBm) with Hurst index.
result First results on stochastic calculus for G-fBm with Hurst index > 0.5.
Paper formalizes multi-dimensional FSD using geometric methods.
problem Complex measure theory and calculus barriers to formalization in proof assistants.
method Geometric framework for first-order stochastic dominance in N dimensions.
result Geometric approach bypasses complex integration theory for direct comparison of survival probabilities.
Robust deep neural networks estimate multi-dimensional functional data robustly.
problem Estimating location function from multi-dimensional functional data robustly.
method Deep neural networks with ReLU activation, robust to outliers and model misspecification.
result Uniform convergence rates for robust deep neural network estimators.
Generative model combines multi-dimensional annotations for more accurate ground truth estimation.
problem Inaccurate ground truth estimation from naive annotators' multi-dimensional annotations.
method Proposes a joint multi-dimensional model for global and time-series annotation fusion using Expectation-Maximization algorithm.
result More accurate ground truth estimates through joint modeling of multiple dimensions.
A new method estimates multi-dimensional value distributions using Hilbert space embeddings.
problem Estimating value distributions in complex, multi-dimensional reinforcement learning settings.
method Hilbert space mappings and kernel mean embeddings to estimate the kernel mean embedding of multi-dimensional value distributions.
result Uniform convergence guarantees and robust off-policy evaluation demonstrated in simulations.
New method for handling multi-dimensional singular controls with jump costs in mean-field problems.
problem Handling jump costs in multi-dimensional singular controls.
method Introducing two-layer parametrisations to interpolate jumps on both distributional and pathwise levels.
result Derivation of a DPP and characterisation of the value function as a minimal super-solution to a quasi-variational inequality.
Two spherical and flat periscopes are analyzed in multi-dimensional space.
problem Understanding the wave fronts of periscopes in various dimensions.
method Local diffeomorphisms of wave fronts induced by 2-mirror systems are described.
result Local diffeomorphisms of wave fronts are characterized for spherical and flat periscopes.
Delay Pruning regularizes DyBM for better learning of temporal sequences.
problem Improving DyBM's generalization in learning high-dimensional temporal sequences.
method Delay Pruning: setting some FIFO queue lengths to one with fixed probability.
result Delay Pruning enhances DyBM's performance in learning high-dimensional temporal sequences.
Paper solves multi-dimensional passport option pricing problem using machine learning.
problem Pricing multi-dimensional passport options in correlated markets remains unsolved.
method Discrete-time solution for multi-dimensional BS markets with uncorrelated assets; machine learning approaches.
result Machine learning-powered approaches successfully price passport options in both 1D and multi-dimensional uncorrelated BS markets.
Principal binets generalize curvature line surfaces to square lattices and are a discrete integrable system.
problem Discretizing curvature line surfaces on square lattices.
method Showed principal binets as a multi-dimensional consistent system.
result Principal binets generalize to higher-dimensional square lattices and are integrable.
A new tensor-based method improves multi-dimensional data classification accuracy.
problem Efficient representation and classification of multi-dimensional data from multiple sensors.
method n-mode generalized difference subspace (n-mode GDS) for tensor data, with improved metric based on geodesic distance.
result The proposed method outperforms existing methods in gesture and action recognition.
We study a method of reducing space dimension in multi-dimensional Black-Scholes partial differential equations as well as in multi-dimensional parabolic equations. We prove that a multiplicative transformation of space variables in the Black-Scholes partial differential equation reserves the form of Black-Scholes part…
Random Tessellation Process improves multi-dimensional data analysis.
problem Axis-aligned cuts limit flexibility in space partitioning methods.
method Proposes Random Tessellation Process (RTP) for non-axis aligned cuts.
result Improved accuracies in gene expression data analysis.
Paper proves stability of multi-dimensional rarefaction waves in gas dynamics.
problem Challenges in constructing multi-dimensional rarefaction waves in gas dynamics.
method Geometric Weighted Energy Method (GWEM) to overcome derivative losses.
result Established nonlinear stability of multi-dimensional rarefaction waves for compressible Euler equations.
SPP improves partitioning of sparse regions in multi-dimensional arrays.
problem Existing partition models cause unnecessary dissections in sparse regions.
method SPP uses an 'enclosing' strategy to attach patches to dense regions, making it self-consistent for infinite arrays.
result SPP outperforms state-of-the-arts in relational modeling.
Contrast uses normalizing flows to create precise prediction regions for multi-dimensional outputs.
problem Generating reliable prediction regions for multi-dimensional outputs in supervised and unsupervised learning.
method Contrast uses normalizing flows to define nonconformity scores based on distances in latent space, creating sharp prediction regions.
result Contrast maintains guaranteed coverage probability and outperforms existing methods in generating accurate prediction regions.
MTL improves multi-dimensional regression in luminescence sensing.
problem Challenges in modeling multi-dimensional regression problems with classical methods.
method Multi-task learning (MTL) with feed-forward neural networks (FFNNs).
result MTL allows predicting multiple parameters from a single set of measurements.
A new framework using kernel packets overcomes limitations of state space models for multi-dimensional data.
problem Computational limitations of Gaussian process regression in large-scale applications.
method Kernel packet approach, identifying KPs via forward and backward state space representations.
result Exact, memory-efficient inference with linear-time training and logarithmic/predictive time.
Improved crude oil price forecasting using multi-dimensional LLM sentiment signals.
problem Challenges in predicting crude oil prices due to unstructured news.
method Extracted five sentiment dimensions from GPT-4o, Llama 3.2-3b, and FinBERT models on energy-sector news articles.
result Combining GPT-4o and FinBERT yields the best predictive performance for weekly WTI crude oil futures returns.
A method for predicting human locomotion using sensor correlations.
problem Predicting missing signals in human locomotion data.
method Coregionalised Locomotion Envelopes - multi-dimensional manifold regression.
result Developed a qualitative method for robust control of rehabilitation robots.
We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the volatility terms of the state process. Under appropriate conditions, we show that t…
Determines conditions for arbitrage in complex financial markets.
problem Identifying markets without arbitrage opportunities.
method Derives deterministic criteria for equivalent martingale measures.
result Constructs financial markets with specific risk conditions.
Bayesian model tackles intersectional fairness in AI.
problem Statistical challenges in measuring fairness for multi-dimensional protected attributes.
method Bayesian probabilistic modeling approach for reliable, data-efficient estimation of fairness.
result Bayesian methods improve fairness measurement in intersectional contexts.
Framework learns asymmetric and local features in multi-dimensional data.
problem Learning features in multi-dimensional data, especially images.
method Bayesian hierarchical modeling with recursive wavelet transforms.
result Framework achieves high computational scalability and adaptivity.
QRNN and QLSTM improve speech recognition with fewer parameters.
problem Speech recognition with multi-dimensional input features.
method Quaternion algebra for modeling internal and external dependencies.
result QRNN and QLSTM achieve better performance with fewer parameters.
Probability Density Estimation (PDE) is a multivariate discrimination technique based on sampling signal and background densities defined by event samples from data or Monte-Carlo (MC) simulations in a multi-dimensional phase space. In this paper, we present a modification of the PDE method that uses a self-adapting bi…
New method for time series prediction with uncertainty quantification.
problem Uncertainty quantification for multi-dimensional time series predictions.
method Flow-based conformal prediction for time series.
result Significantly smaller prediction sets with target coverage.
NEWMA detects changes in multi-dimensional data streams efficiently.
problem Detecting abrupt changes in multi-dimensional time series with limited resources.
method A simple, model-free online change-point detection method using two EWMA statistics with different forgetting factors and Random Features.
result The method is significantly faster than usual non-parametric methods for a given accuracy.
New framework exploits edge features in graph neural networks for improved performance.
problem Insufficient utilization of edge features in current graph neural networks.
method Proposes a new framework with doubly stochastic normalization and multi-dimensional edge feature handling.
result Improves performance on graph node classification and regression tasks.
Introduces tensor bandits for multi-dimensional online decision making.
problem Optimal decision making in multi-dimensional online scenarios.
method Stochastic low-rank tensor bandits, tensor elimination, tensor epoch-greedy, tensor ensemble sampling.
result Tensor elimination and tensor epoch-greedy algorithms outperform existing methods.
Optimizes decisions from observational data with a novel algorithm.
problem Optimizing uncertain objectives over continuous, multi-dimensional spaces with limited data.
method Proposes a novel algorithm that combines predictive machine learning with uncertainty information.
result Demonstrates superior performance compared to existing methods on various data sets.
Rectangular Bounding Process (RBP) improves partitioning efficiency in multi-dimensional spaces.
problem Creating many unnecessary divisions in sparse regions when describing dense regions.
method Introduces Rectangular Bounding Process (RBP) to efficiently partition multi-dimensional spaces using a bounding strategy.
result The RBP is self-consistent and can be extended to infinite space, offering rich yet parsimonious expressiveness.
This paper considers multi-dimensional affine processes with continuous sample paths. By analyzing the Riccati system, which is associated with affine processes via the transform formula, we fully characterize the regions of exponents in which exponential moments of a given process do not explode at any time or explode…
TRACE improves conformal prediction for multi-dimensional outputs.
problem Challenges in constructing valid and informative conformal prediction regions for multi-dimensional outputs.
method TRACE uses transport alignment in diffusion and flow matching models to define nonconformity scores.
result TRACE yields valid and adaptive conformal prediction regions for multimodal and non-convex distributions.