arXiv research

The paper explores multidimensional critic output in GANs, improving convergence and diversity.

Whitney type examples of maps $f\in C^k(\real^m,\real^n)$ for a maximal possible real $k$, and multidimensional space-filling curves with special properties are constructed.

A method for accurate pricing of multidimensional derivatives under uncertain volatility.

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…

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…

Bayesian Complementary Kernelized Learning models complex spatiotemporal data.

The problem of estimation error in portfolio optimization is discussed, in the limit where the portfolio size N and the sample size T go to infinity such that their ratio is fixed. The estimation error strongly depends on the ratio N/T and diverges for a critical value of this parameter. This divergence is the manifest…

This paper improves conditional multidimensional scaling for incomplete data.

Improved algorithm for multidimensional scaling reduces stress.

A method to visualize multidimensional local subspaces using implicit differentiation.

Although shill bidding is a common auction fraud, it is however very tough to detect. Due to the unavailability and lack of training data, in this study, we build a high-quality labeled shill bidding dataset based on recently collected auctions from eBay. Labeling shill biding instances with multidimensional features i…

Global minima found for multidimensional scaling with penalties.

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…

New RL algorithm tackles complex discrete action spaces.

Study uses multidimensional SE-NBD process to analyze default portfolios and identify shock amplification.

To any positive number $\varepsilon$ and any nonnegative even Schwartz function $w:\mathbb{R}\to\mathbb{R}$ we associate the random function $u^\varepsilon$ on the $m$-torus $T^m_\varepsilon:=\mathbb{R}^m/(\varepsilon^{-1}\mathbb{Z})^m$ defined as the real part of the random Fourier series $$ \sum_{ν\in\mathbb{Z}^m} X_…

Efficiently recovers piecewise linear functions from noisy samples.

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…

Novel method for multiclass ROC curves using multidimensional Gini index.

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…

Extends Morse-Forman theory to vector-valued functions for multiparameter persistence.

A novel online framework for analyzing 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.

Recurrent neural networks (RNNs) have drawn interest from machine learning researchers because of their effectiveness at preserving past inputs for time-varying data processing tasks. To understand the success and limitations of RNNs, it is critical that we advance our analysis of their fundamental memory properties. W…

Paper presents adaptive minimax risk classifiers for multidimensional concept drift.

sWk-means clusters multidimensional financial time series into distinct market regimes.

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…

New method simulates sticky boundaries in multidimensional diffusions.

Extends Carathéodory's theorem to multidimensional domains with constant curvature.

A new tensor regression model preserves multidimensional data structure.

New method for learning multidimensional CDFs using Archimedean copulas.

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.

New method identifies cause and effect using complexity of autoencoders.

Develops statistical confidence sets for multidimensional scaling.

Generalizations of the Weierstrass formulae to generic surface immersed into $R^4$, $S^4$ 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…

A new method reduces memory requirements for sorting high-dimensional data.

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 …

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.

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.

Paper analyzes multidimensional PIDEs for financial modeling, proving existence and uniqueness in Bessel spaces.

Extends multidimensional scaling to analyze three-way asymmetric proximities.

A new model captures multifractal volatility in stock returns.

Some aspects of the relation between differential geometry of curves and surfaces and multidimensional soliton equations is discussed. The connection between multidimensional soliton equations and Self-dual Yang-Mills equation is studied.

UAPCA projects uncertain data to low dimensions using GMMs.

A method for multidimensional probabilistic electricity market forecasting is proposed.