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.
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.
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.
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 …
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.
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.
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.
This is a detailed tutorial paper which explains the Fisher discriminant Analysis (FDA) and kernel FDA. We start with projection and reconstruction. Then, one- and multi-dimensional FDA subspaces are covered. Scatters in two- and then multi-classes are explained in FDA. Then, we discuss on the rank of the scatters and …
Paper introduces a method to assess liquidity risk in meme tokens using entity-linked address analysis.
problem High market volatility and vulnerability to manipulation in meme tokens.
method Multi-dimensional approach integrating fund flow analysis, behavioral similarity, and anomalous transaction detection.
result Significant disparities between apparent and actual liquidity in meme token markets.
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.
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.
We study the problem of detecting change points (CPs) that are characterized by a subset of dimensions in a multi-dimensional sequence. A method for detecting those CPs can be formulated as a two-stage method: one for selecting relevant dimensions, and another for selecting CPs. It has been difficult to properly contro…
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.
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…
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.
Leveraging the intrinsic symmetries in data for clear and efficient analysis is an important theme in signal processing and other data-driven sciences. A basic example of this is the ubiquity of the discrete Fourier transform which arises from translational symmetry (i.e. time-delay/phase-shift). Particularly important…
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.
New method handles indirect mediators in CMA for complex scenarios.
problem Handling indirect and multi-dimensional mediators in causal mediation analysis.
method Identifiable Variational Autoencoder (iVAE) architecture for multi-dimensional, indirectly observed mediators.
result Accurate estimation of direct and mediated effects in synthetic and semi-synthetic experiments.
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.
Optimal sampling reduces power grid data analysis costs.
problem Efficient online analysis of high-speed, correlated IoT data.
method D-optimality criterion-based sampling methods combining Bernoulli and leverage score sampling.
result Leverage score sampling improves computational efficiency and outperforms benchmarks.
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.
MCD offers a complete model understanding for high-stake decisions.
problem Local model understanding in XAI methods is not sufficient for high-stake decisions.
method MCD extends concept-based methods to ensure global model understanding via multi-dimensional subspaces.
result MCD provides a complete model understanding, ensuring the model reasoning is related to the actual model.
The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff funct…
New framework for regression trees with multivariate response and dynamic mean vectors.
problem Characterizing and implementing regression trees for multivariate responses.
method High dimensional model with dynamic mean vectors over multi-dimensional change axes.
result Optimal rate of convergence and asymptotic valid confidence intervals for change points.
Objective: A median of 14.4% of patient undergone at least one adverse event during surgery and a third of them are preventable. The occurrence of adverse events forces surgeons to implement corrective strategies and, thus, deviate from the standard surgical process. Therefore, it is clear that the automatic identifica…
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.
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.
We introduce an extension to Merton's famous continuous time model of optimal consumption and investment, in the spirit of previous works by Pliska and Ye, to allow for a wage earner to have a random lifetime and to use a portion of the income to purchase life insurance in order to provide for his estate, while investi…
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.
New framework for data-driven hyperparameter tuning with structured loss.
problem Statistical foundations for multi-dimensional hyperparameter tuning remain limited.
method General framework using real algebraic geometry for semi-algebraic function classes.
result First general guarantees for multi-dimensional hyperparameter tuning.
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…
Non-Gaussian component analysis (NGCA) is an unsupervised linear dimension reduction method that extracts low-dimensional non-Gaussian "signals" from high-dimensional data contaminated with Gaussian noise. NGCA can be regarded as a generalization of projection pursuit (PP) and independent component analysis (ICA) to mu…
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 analyze large, multi-dimensional, sparse counting data sets, finding unsupervised groups to provide unique insights into genetic data. We create gene and biological pathway groups based on patients' variants to find common risk factors for four common types of cancer (breast, lung, prostate, and colorectal) and auti…
Paper improves tensor approximation for streaming data.
problem Challenges in finding accurate low-tubal-rank tensor approximations in streaming settings.
method Extends Frequent Directions for efficient low-tubal-rank tensor approximation.
result The new algorithm achieves arbitrarily small approximation error with linear sketch size growth.
Cryptos remained resilient after SVB's collapse, contrary to expectations.
problem Impact of SVB collapse on crypto markets.
method Factual summary, sentiment analysis, and market performance examination.
result Cryptocurrencies showed resilience after SVB's collapse.
The paper optimizes model selection and parameter estimation for multi-dimensional Gaussian Mixture Models.
problem Learning and distinguishing multi-dimensional Gaussian Mixture Models with reliable model order selection and efficient estimation.
method The paper establishes an information-theoretic lower bound and proposes a thresholding-based estimation algorithm with a time complexity of O(k^2 n). It also introduces a gradient-based minimization method with PCA for high-dimensional cases.
result The proposed method matches the established lower bound in sample complexity and achieves optimal parametric convergence rate.
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…
The first widely used financial model is linked to dynamical Hamilton jacobi model