This paper uses multivariate probability models to assess financial system risks.
problem Assessing systemic risk in financial systems.
method Computes multivariate conditional probability distributions for elliptical distributions, focusing on Student-t and Normal models.
result Proposes measures of stress impact and systemic risk.
The paper calculates moments and conditional risks for skewed elliptical distributions.
problem Estimating moments and tail conditional risks for skewed elliptical distributions.
method Derives explicit expressions for multivariate doubly truncated moments and conditional risks for generalized skew-elliptical distributions.
result Explicit formulas for multivariate doubly truncated moments and conditional risks are derived for various skewed elliptical distributions.
The paper provides exact multivariate amplitude distributions for non-stationary Gaussian or algebraic fluctuations.
problem Capturing the statistical properties of fluctuating correlations in non-stationary systems.
method Developed a random matrix model to average multivariate amplitude distributions from short time scales to large time scales.
result Explicit multivariate distributions for non-stationary correlation systems are provided, capturing the degree of non-stationarity.
The paper uses Fourier integral theorem for estimating multivariate distributions.
problem Estimating multivariate distributions and conditional distribution functions.
method Natural Monte Carlo and fully nonparametric estimators based on Fourier integral theorem.
result Explicit Monte Carlo estimators without estimated covariance matrix.
In this paper, we consider the multivariate Bernoulli distribution as a model to estimate the structure of graphs with binary nodes. This distribution is discussed in the framework of the exponential family, and its statistical properties regarding independence of the nodes are demonstrated. Importantly the model can e…
The univariate piecing-together approach (PT) fits a univariate generalized Pareto distribution (GPD) to the upper tail of a given distribution function in a continuous manner. We propose a multivariate extension. First it is shown that an arbitrary copula is in the domain of attraction of a multivariate extreme value …
The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world high-dimensional count-valued data found in word counts, genomics, and crime statis…
Study analyzes stock market correlations using multivariate distributions.
problem Capturing the correlation structure of complex, non-stationary systems.
method Applied Random Matrix Model to empirical data of 479 US stocks.
result Described and quantified changes in empirical distributions due to non-stationarity.
A new random forest method for multivariate distributions.
problem Estimating complex multivariate distributions with heterogeneity.
method A novel splitting criterion based on MMD for multivariate responses.
result Estimates full conditional distribution for arbitrary targets.
Characterizes symmetric Bernoulli distributions with minimal convex sums.
problem Understanding minimal dependence among Bernoulli random vectors.
method Geometric and algebraic representations of multivariate symmetric Bernoulli distributions.
result Characterizes extremal negative dependence and builds minimal dependence copulas.
Regularizes ML algorithms for robust multivariate analysis against distribution shifts.
problem Ensuring robustness of multivariate analysis algorithms against distribution shifts.
method Integrates a causal regularisation term into the loss function of multivariate analysis algorithms.
result Demonstrates improved out-of-distribution generalisation with reduced-rank regression and partial least squares.
New algorithms for multivariate RL improve decision-making in complex systems.
problem Complex multi-objective decision-making in reinforcement learning.
method Oracle-free and computationally-tractable algorithms for multivariate distributional RL.
result Convergence rates match scalar reward settings and provide insights into reward dimensionality.
Method estimates multivariate counterfactual distributions efficiently and accurately.
problem Estimating multivariate counterfactual distributions in causal models with correlation structures.
method Proposes a method leveraging a one-dimensional subspace to capture correlation structures and efficiently estimate multivariate counterfactual distributions.
result Demonstrates superior performance over existing methods on synthetic and real-world data.
An analytic solution for asset allocation with Laplace distribution.
problem Asset allocation with multivariate Laplace distribution.
method Specialization of elliptically symmetric distribution theory to Laplace distribution, accounting for dimensionality and variance rescaling.
result A result consistent with conjecture but with differences due to omitted term and rescaling.
We exploit the link between the transport equation and derivatives of expectations to construct efficient pathwise gradient estimators for multivariate distributions. We focus on two main threads. First, we use null solutions of the transport equation to construct adaptive control variates that can be used to construct…
Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by extending some standard probabilistic modelling tools to the circular domain. First w…
The paper defines MTCov for skewed elliptical distributions.
problem No specific problem stated, but dealing with skewed elliptical distributions.
method Defined MTCov for generalized skew-elliptical distributions and compared with skewed and non-skewed normal distributions.
result Special formula for MTCov of generalized skew-elliptical distributions.
Forecasts of multivariate probability distributions are required for a variety of applications. Scoring rules enable the evaluation of forecast accuracy, and comparison between forecasting methods. We propose a theoretical framework for scoring rules for multivariate distributions, which encompasses the existing quadra…
Bayesian DDR models complex multivariate distributions.
problem Modeling relationships between multivariate distributions with differing dimensions.
method Generalized Bayesian framework using sliced Wasserstein distance and MALA for inference.
result Posterior consistency and robust fits demonstrated in simulations and real data.
Characterizes connections on multivariate normal distributions.
problem Characterizing connections on statistical manifold of multivariate normal distributions.
method Analyzes statistical manifold (N,gF,ablaA,ablaA∗) of multivariate normal distributions. result The Amari-Chentsov connection ablaA is characterized by conjugate symmetry. Process capability index (PCI) is a commonly used statistic to measure ability of a process to operate within the given specifications or to produce products which meet the required quality specifications. PCI can be univariate or multivariate depending upon the number of process specifications or quality characteristi…
Combines MCTM and NF for flexible multivariate density regression with interpretable marginals.
problem Difficult interpretation of flexible NF models and limitations of MCTM in flexibility.
method Hybrid approach combining MCTM for interpretable marginals and NF for complex joint distributions.
result Demonstrates versatility and improved performance compared to MCTM and other NF models.
New method for multivariate distribution regression using NPT metric.
problem Regression with multivariate distributional responses and Euclidean predictors.
method Fréchet regression with nonparanormal transport (NPT) metric.
result Efficient estimation and granular interpretation of predictor effects.
TSRGA scales multivariate linear regression for feature-distributed data.
problem Multivariate linear regression for feature-distributed data with high dimensions and many computing nodes.
method Two-stage relaxed greedy algorithm (TSRGA) for multivariate linear regression.
result TSRGA is highly scalable and can yield low-rank coefficient estimates.
Proposes MVG-CRPS for robust multivariate forecasting.
problem Outliers in multivariate forecasting lead to significant errors.
method Integrates CRPS for MVG distributions, optimizing with MVG-CRPS.
result Improves robustness, accuracy, and uncertainty quantification.
Matrix H-theory models stock market fluctuations using hierarchical multivariate distributions.
problem Understanding collective behavior in stock market fluctuations.
method Matrix H-theory framework for multivariate stochastic processes with hierarchical structure.
result Matrix H-theory effectively describes stock market fluctuations using Meijer G-functions.
The paper analyzes heavy-tailed multivariate distributions in non-stationary systems using random matrix theory.
problem Risk assessment for rare events in complex, non-stationary systems.
method Generalized scalar product between correlation matrices, model for non-stationary fluctuations.
result Formulae for multivariate distributions with reduced parameters, facilitating applications.
COMET Flows model multivariate extremes with heavy tails and asymmetric dependence.
problem Normalizing flows struggle with multivariate extremes and asymmetric tail dependence.
method COMET Flows decomposes modeling into marginal and copula parts; uses tail belief and kernel density for marginals, and low-dimensional manifold for tail dependence.
result COMET Flows outperform other models in capturing heavy-tailed marginals and asymmetric tail dependence.
The paper proposes a method to learn evolving multivariate distributions from sample paths.
problem Learning the temporal evolution of multivariate densities from sample data.
method Normalizing flows to construct time-dependent mappings.
result The method can approximate evolving probability density functions from observed data.
Cluster GARCH model improves multivariate GARCH for high-dimensional asset returns.
problem Modeling high-dimensional asset returns with flexible tail dependencies and cluster structures.
method Introduced a novel multivariate GARCH model with flexible convolution-t distributions, tractable likelihood and derivatives for dynamic correlation structure.
result Cluster GARCH model outperforms existing models in daily returns of 100 assets, both in-sample and out-of-sample.
A new notion of stochastic ordering is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of ordering conditions on the spectral measures, which allows for analytical or numerical…
A new clustering method for functional data using skewed distributions.
problem Clustering functional data with skewed distributions.
method Mixtures of functional linear regression models and three skewed multivariate distributions (variance-gamma, skew-t, normal-inverse Gaussian).
result The proposed method funWeightClustSkew performs well on simulated and real data.
Let X and X be two n-dimensional elliptical random vectors, we establish an identity for E[f(Y)]−E[f(X)], where f:Rn→R fulfilling some regularity conditions. Using this identity we provide a unified derivation of sufficient and necessary conditions for classif…
In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk portfolio. The lower-orthant VaR is constructed from level sets of multivariate di…
New method for geodesics of multivariate normals, derived from a Toda lattice.
problem Computing geodesics of multivariate normal distributions.
method Using block Cholesky decomposition and a natural Riemannian submersion, a new Toda lattice type Lax pair is derived.
result A new Toda lattice type Lax pair derived from geodesics and block Cholesky decomposition.
The paper introduces MRVaR and MRCov for elliptical and log-elliptical distributions.
problem Risk management of regulation and investment purposes.
method Proposes MRVaR and MRCov as risk measures for elliptical and log-elliptical distributions.
result Explicit expressions of MRVaR and MRCov derived for multivariate (log-)elliptical distributions.
Modified Metropolis algorithm ensures convergence for multivariate binary distributions with fixed-order updates.
problem Infeasibility of standard Metropolis algorithm for multivariate binary distributions with fixed-order updates.
method Proposed a modified Metropolis transition operator ensuring irreducibility and convergence.
result Ensures convergence to the limiting distribution in multivariate binary case with fixed-order updates.
Study invariant connections on multivariate Gaussian distributions.
problem Understanding statistical connections on multivariate Gaussian distributions.
method Investigate invariant connections on N0n with the Fisher metric. result Explicitly determined invariant connections and their moduli spaces.
Neural optimal transport improves multivariate conformal prediction.
problem Multivariate quantile regression challenges and existing methods ignore joint distribution geometry.
method Combines neural optimal transport with amortized optimization for efficient training and faster inference.
result Constructs tighter and more informative predictive regions for multivariate conformal prediction.
Gaussian process model for vector-valued function has been shown to be useful for multi-output prediction. The existing method for this model is to re-formulate the matrix-variate Gaussian distribution as a multivariate normal distribution. Although it is effective in many cases, re-formulation is not always workable a…
This paper improves PPCA robustness using t-distributions.
problem Improving robustness of probabilistic PCA.
method Using multivariate t-distributions and a hierarchical model. result Clarified the correct correspondence between the multivariate t-PPCA framework and the hierarchical model. Extends geostatistical simulation method to handle multiple variables and large grids.
problem Scalability and handling of multiple variables in geostatistical simulation.
method Uses Sinkhorn optimal transport with sparse matcher and FFT-MA Gaussian backbone.
result MST-Direct reproduces joint distribution with zero histogram error and accurately preserves spatial correlation.
The paper explores solutions to the distributional Bellman equation in reinforcement learning.
problem Distributional reinforcement learning considers complete return distributions, not just expected returns.
method Study existence and uniqueness of solutions to general distributional Bellman equations, linking them to multivariate affine equations.
result Any solution to a distributional Bellman equation can be derived from a multivariate affine distributional equation.
The paper analyzes multivariate Hawkes processes and their induced population processes.
problem Analyzing the time-dependent joint probability distribution of multivariate Hawkes processes.
method Exact and asymptotic analysis of general multivariate Hawkes processes and their induced population processes.
result Full characterization of the time-dependent joint transform of the multivariate population process and its intensity process.
The multivariate version of the Mixed Tempered Stable is proposed. It is a generalization of the Normal Variance Mean Mixtures. Characteristics of this new distribution and its capacity in fitting tails and capturing dependence structure between components are investigated. We discuss a random number generating procedu…
Paper relaxes triangle inequality for KL divergence between Gaussian distributions.
problem KL divergence does not satisfy triangle inequality for Gaussian distributions.
method Investigates relaxed triangle inequality and finds supremum.
result Supremum of KL divergence is found and conditions for attaining it are determined.
Generative moment matching networks (GMMNs) are introduced for generating quasi-random samples from multivariate models with any underlying copula in order to compute estimates under variance reduction. So far, quasi-random sampling for multivariate distributions required a careful design, exploiting specific propertie…
TQF models multivariate uncertainty by learning conditional quantiles.
problem Challenges in fully nonparametric estimation of multivariate conditional distributions.
method Tomographic Quantile Forests (TQF) learns conditional quantiles of directional projections.
result TQF reconstructs multivariate conditional distribution efficiently without convexity restrictions.