New private identity testers for high-dimensional distributions with improved sample complexity.
problem Testing goodness-of-fit for high-dimensional product distributions under differential privacy.
method Developed novel differentially private testers for multivariate product distributions, including Gaussians and binary product distributions.
result Achieved sample complexity matching the minimax sample complexity of O(d1/2/α2) in many parameter regimes. 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…
Study identifies regions where scoring rules reliably detect forecast errors.
problem Insufficient reliability of scoring rules in evaluating multivariate probabilistic forecasts.
method Systematic finite-sample analysis of proper scoring rules on synthetic and real-world data.
result Identified regions of reliability for scoring rules in time-series forecasting.
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.
Study learns mixtures of smooth product distributions from samples.
problem Learning mixtures of non-parametric product distributions.
method Two-stage approach using identifiability properties of tensor decomposition and signal processing techniques.
result Recovery of component distributions under a smoothness condition.
Geometric estimator calculates dependency between multivariate samples.
problem Estimating dependency between multivariate samples.
method Randomly permuted minimal spanning tree over multivariate samples.
result Geometric Mutual Information (GMI) converges to a quantity equivalent to Henze-Penrose divergence.
Researchers derived formulas for joint moments of elliptical distributions.
problem Calculating joint moments of elliptical distributions.
method Used Stein's lemma and two different methods to derive expressions.
result New formulae for expectations of product of normally distributed random variables and simplified expressions for other distributions.
A new method uses a product of experts with Dirichlet variables to approximate complex distributions.
problem Approximating complex distributions with tractable models.
method A product of experts with auxiliary Dirichlet variables, using a Feynman identity to sample and optimize.
result The method efficiently approximates complex distributions using a product of experts and Dirichlet variables.
Paper presents forecasting models for platelet demand.
problem Managing platelet demand and supply is challenging due to variability and short shelf life.
method Utilized ARIMA, Prophet, lasso regression, and LSTM networks on a clinical dataset.
result Multivariate approaches generally have higher accuracy, but simpler ARIMA can suffice with sufficient data.
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.
Manifold calculus of functors, due to M. Weiss, studies contravariant functors from the poset of open subsets of a smooth manifold to topological spaces. We introduce "multivariable" manifold calculus of functors which is a generalization of this theory to functors whose domain is a product of categories of open sets. …
The paper analyzes multivariate payments in multi-state life insurance using Markovian state processes.
problem Analyzing joint effects of life annuities and death benefits in a multi-state framework.
method Introduces multivariate present value of future payments, derives differential equations and moment generating functions, and focuses on pair-wise covariances.
result Derives Hattendorff type results for pair-wise covariances in a disability model.
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.
We prove a central limit theorem for the components of the eigenvectors corresponding to the d largest eigenvalues of the normalized Laplacian matrix of a finite dimensional random dot product graph. As a corollary, we show that for stochastic blockmodel graphs, the rows of the spectral embedding of the normalized La…
A new method uses Gram matrix for efficient multivariate functional principal components.
problem Efficiently estimating eigencomponents of multidimensional functional datasets.
method Proposes using inner-product matrix to estimate eigenelements of multivariate and multidimensional functional datasets.
result Established relationship between eigenelements of covariance operator and inner-product matrix.
A justification of the Basel liquidity formula for risk capital in the trading book is given under the assumption that market risk-factor changes form a Gaussian white noise process over 10-day time steps and changes to P&L are linear in the risk-factor changes. A generalization of the formula is derived under the more…
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…
Multivariate binary distributions can be decomposed into products of univariate conditional distributions. Recently popular approaches have modeled these conditionals through neural networks with sophisticated weight-sharing structures. It is shown that state-of-the-art performance on several standard benchmark dataset…
One approach for constructing copula functions is by multiplication. Given that products of cumulative distribution functions (CDFs) are also CDFs, an adjustment to this multiplication will result in a copula model, as discussed by Liebscher (J Mult Analysis, 2008). Parameterizing models via products of CDFs has some a…
New scoring rules for multivariate distributions and level sets.
problem Evaluating forecast accuracy for multivariate distributions and level sets.
method Theoretical framework for scoring rules, decomposition of multivariate scoring functions, numerical algorithm for computation.
result New scoring functions for multivariate distributions and level sets, including density and cumulative distribution level sets.
Unified derivation of stochastic order conditions for elliptical distributions.
problem Classifying multivariate elliptical distributions based on stochastic orders.
method Established an identity for comparing expectations of functions of elliptical vectors and used it to derive conditions for stochastic orders.
result Unified derivation of conditions for various stochastic orders in multivariate elliptical distributions.
In this paper we introduce a new multivariate dependence measure based on comonotonicity by means of product moment which motivated by the recent papers of Koch and Schepper (ASTIN Bulletin 41 (2011) 191-213) and Dhaene et al. (Journal of Computational and Applied Mathematics 263 (2014) 78-87). Some differences and rel…
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 …
We consider an application involving a financial quadratic portfolio of options, when the joint underlying log-returns changes with multivariate elliptic distribution. This motivates the needs for methods for the approximation of multiple integrals over hyperboloids. A transformation is used to reduce the hyperboloid i…
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.
New algorithms test independence with fewer samples by using predictive information.
problem Testing independence of distributions with limited samples.
method Augmented distribution testing framework that incorporates predictive information.
result Optimal sample complexity achieved, matching lower bounds.
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.
The paper introduces new processes for modeling multivariate volatility.
problem Developing new stochastic processes for multivariate volatility modeling.
method Introducing Volterra Wishart and Volterra pure jump processes with fractional kernels.
result Affine covariance processes for multivariate volatility modeling.
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.
Copulas model cross-product effects in intraday power markets.
problem Intraday power markets' cross-product effects are not adequately addressed by existing univariate approaches.
method Copulas and latent beta regression for modeling high-dimensional intraday price return vector, with time-varying dependence parameter.
result Modeling cross-product effects improves forecasting performance.
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 present novel, computationally efficient, and differentially private algorithms for two fundamental high-dimensional learning problems: learning a multivariate Gaussian and learning a product distribution over the Boolean hypercube in total variation distance. The sample complexity of our algorithms nearly matches t…
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.
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.
Access to a large variety of data across a massive population has made it possible to predict customer purchase patterns and responses to marketing campaigns. In particular, accurate demand forecasts for popular products with frequent repeat purchases are essential since these products are one of the main drivers of pr…
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. 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 …
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 model captures time and mark inter-dependence in TPPs.
problem Limited predictive performance of conditionally independent TPP models on entangled time and mark interactions.
method Developed a multivariate TPP that models conditional inter-dependence of time and mark, using both intensity-based and intensity-free models.
result Proposed TPP models outperform conditionally independent and dependent models in standard prediction tasks.
The covariance matrix is formulated in the framework of a linear multivariate ARCH process with long memory, where the natural cross product structure of the covariance is generalized by adding two linear terms with their respective parameter. The residuals of the linear ARCH process are computed using historical data …