Differential privacy has recently emerged in private statistical data release as one of the strongest privacy guarantees. Most of the existing techniques that generate differentially private histograms or synthetic data only work well for single dimensional or low-dimensional histograms. They become problematic for high dimensional and large domain data due to increased perturbation error and c...

Understanding and measuring uncertainty is central in risk analysis. Uncertainty emerges when there is less information than the total information required to describe a system and environment. Uncertainty and information are so closely associated that information provided by an experiment for instance is equal to the amount of uncertainty removed. Uncertainty prevails in several forms and vari...

By a theorem due to Sklar, a multivariate distribution can be represented in terms of its underlying margins by binding them together using a copula function. By exploiting this representation, the “copula approach” to modelling proceeds by specifying distributions for each margin, and a copula function. In this article, a number of copula functions are given, with attention focusing on members...

We tackle the problem of multi-task learning with copula process. Multivariable prediction in spatial and spatialtemporal processes such as natural resource estimation and pollution monitoring have been typically addressed using techniques based on Gaussian processes and co-Kriging. While the Gaussian prior assumption is convenient from analytical and computational perspectives, nature is domin...

We propose a copula based statistical method of fitting joint cumulative returns between a market index and a stock from the index family to daily data. Modifying the method of inference functions for margins (IFM method), we perform two separate maximum likelihood estimations of the univariate marginal distributions, assumed to be normal inverse gamma mixtures with kurtosis parameter equal to ...

We introduce a general approach to nonlinear quantile regression modelling that is based on the specification of the copula function that defines the dependency structure between the variables of interest. Hence we extend Koenker and Bassett’s [1978] original statement of the quantile regression problem by determining a distribution for the dependent variable Y conditional on the regressors X a...

This paper sets out the puzzle of the polyfunctionality of copula sentences in Japanese, and proposes a principled solution from the viewpoint of Semantic Incrementality. Some copula sentences have specificational and identity functions, and they display different behaviours in terms of connotation and anaphora. It is proposed that the single item no as a pronominal nominaliser captures the two...

Although there exists a large variety of copula functions, only a few are practically manageable, and often the choice in dependence modeling falls on the Gaussian copula. Further, most copulas are exchangeable, thus implying symmetric dependence. We introduce a way to construct copulas based on periodic functions. We study the two-dimensional case based on one dependence parameter and then pro...