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.
The paper proposes a new method for modeling and quantifying uncertainty in multiple closed curves.
problem Modeling and uncertainty quantification of multiple closed curves.
method A multiple-output, multi-dimensional Gaussian process modeling framework.
result The proposed method provides meaningful uncertainty quantification for curve and shape-related tasks.
Bayesian nonparametric method partitions shapes using curves.
problem Capturing complex shapes in multi-dimensional data.
method Proposes a novel spline partitioning approach using curves.
result Demonstrates improved shape modeling compared to existing methods.
Study compares geometric approaches for shape and deformation statistics.
problem Characterizing statistical models of shapes and deformations.
method Information geometry and Wasserstein geometry.
result Wasserstein estimator is robust against waveform perturbation.
ESPRESSO segments time-series data for better human activity recognition.
problem Segmenting high-dimensional time-series data for applications like HAR.
method ESPRESSO combines entropy and shape analysis for multi-dimensional time-series segmentation.
result ESPRESSO outperforms four state-of-the-art methods across seven datasets.
In this paper we complete and extend our previous work on stochastic control applied to high frequency market-making with inventory constraints and directional bets. Our new model admits several state variables (e.g. market spread, stochastic volatility and intensities of market orders) provided the full system is Mark…
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.
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…
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.
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.
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.
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.
Many signals on Cartesian product graphs appear in the real world, such as digital images, sensor observation time series, and movie ratings on Netflix. These signals are "multi-dimensional" and have directional characteristics along each factor graph. However, the existing graph Fourier transform does not distinguish …
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.
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.
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…
We derive deterministic criteria for the existence and non-existence of equivalent (local) martingale measures for financial markets driven by multi-dimensional time-inhomogeneous diffusions. Our conditions can be used to construct financial markets in which the \emph{no unbounded profit with bounded risk} condition ho…
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.
How is popularity gained online? Is being successful strictly related to rapidly becoming viral in an online platform or is it possible to acquire popularity in a steady and disciplined fashion? What are other temporal characteristics that can unveil the popularity of online content? To answer these questions, we lever…
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.
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…
Intersectionality is a framework that analyzes how interlocking systems of power and oppression affect individuals along overlapping dimensions including race, gender, sexual orientation, class, and disability. Intersectionality theory therefore implies it is important that fairness in artificial intelligence systems b…
We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data. We propose a novel algorithmic framework that is tractable, asymptotically consistent, and superior to comparable methods on example problems. O…
We present a new algorithm for boosting generalized additive models for location, scale and shape (GAMLSS) that allows to incorporate stability selection, an increasingly popular way to obtain stable sets of covariates while controlling the per-family error rate (PFER). The model is fitted repeatedly to subsampled data…
The first widely used financial model is linked to dynamical Hamilton jacobi model
This paper improves the scalability of sparse neural network compression.
problem Sparse neural network compression for diverse data modalities.
method State-of-the-art sparsification techniques and meta-learning.
result Meta-learning sparse compression networks achieve new state-of-the-art results.
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.
New scalarizing functions improve multi-objective Bayesian optimisation.
problem Improving multi-objective Bayesian optimisation efficiency.
method Comparing two infill criteria based on hypervolume improvement.
result Effective scalarizing functions enhance hypervolume maximisation.
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.
Research on manifold learning within a density ridge estimation framework has shown great potential in recent work for both estimation and de-noising of manifolds, building on the intuitive and well-defined notion of principal curves and surfaces. However, the problem of unwrapping or unfolding manifolds has received r…
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.
Promising federated learning coupled with Mobile Edge Computing (MEC) is considered as one of the most promising solutions to the AI-driven service provision. Plenty of studies focus on federated learning from the performance and security aspects, but they neglect the incentive mechanism. In MEC, edge nodes would not l…
The paper investigates learning conditional distributions on multi-dimensional spaces using clustering and neural networks.
problem Learning conditional distributions on multi-dimensional spaces with varying dimensions.
method The approach involves clustering data near varying query points in the feature space to create empirical measures in the target space using two clustering schemes: fixed-radius ball and nearest neighbors. The convergence rates of both methods are analyzed, and the nearest neighbors method is incorporated into neural network training.
result The empirical analysis shows that the nearest neighbors method has better performance in practice and can adapt to a suitable level of Lipschitz continuity locally.
The increasing use of multiple sensors, which produce a large amount of multi-dimensional data, requires efficient representation and classification methods. In this paper, we present a new method for multi-dimensional data classification that relies on two premises: 1) multi-dimensional data are usually represented by…
The paper defines and solves time-inconsistent stopping control problems in multi-dimensional diffusion models.
problem Time-inconsistent problems in control and stopping strategies.
method Formal definition of weak equilibria, extended HJB system, and verification methodology.
result Explicit equilibrium solutions and existence of non-constant equilibria.
The paper solves the skewness problem in high-dimensional basket options.
problem Inconsistent skewness between individual stock options and basket options on an index.
method Developed an effective local volatility model and calibrated the basket to the index smile using a jump-diffusion model.
result The method resolves the skewness issue, matching the index smile in basket option prices.