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We present the new Orthogonal Polynomials Approximation Algorithm (OPAA), a parallelizable algorithm that estimates probability distributions using functional analytic approach: first, it finds a smooth functional estimate of the…
Operator regular variation of a multivariate distribution can be decomposed into the operator tail dependence of the underlying copula and the regular variation of the univariate marginals. In this paper, we introduce operator tail…
The study of loss function distributions is critical to characterize a model's behaviour on a given machine learning problem. For example, while the quality of a model is commonly determined by the average loss assessed on a testing set,…
In this paper, we study large losses arising from defaults of a credit portfolio. We assume that the portfolio dependence structure is modelled by the Archimedean copula family as opposed to the widely used Gaussian copula. The resulting…
Over-the-air (OTA) computation has emerged as a promising technique for efficiently aggregating data from massive numbers of wireless devices. OTA computations can be performed by analog or digital communications. Analog OTA systems are…
Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts,…
This paper considers over-the-air federated learning (OTA-FL). OTA-FL exploits the superposition property of the wireless medium, and performs model aggregation over the air for free. Thus, it can greatly reduce the communication cost…
We review the main "omnibus procedures" for goodness-of-fit testing for copulas: tests based on the empirical copula process, on probability integral transformations, on Kendall's dependence function, etc, and some corresponding reductions…
Vine copulas are a type of multivariate dependence model, composed of a collection of bivariate copulas that are combined according to a specific underlying graphical structure. Their flexibility and practicality in moderate and high…
The performance of correlated optimized effective potential (OEP) functionals based on the spin-resolved second-order correlation energy is analyzed. The relative importance of singly- and doubly- excited contributions as well as the effect…
We develop factor copula models for analysing the dependence among mixed continuous and discrete responses. Factor copula models are canonical vine copulas that involve both observed and latent variables, hence they allow tail, asymmetric…
A statistical field theory is developed to explore the density of states and spatial profile of `tail states' at the edge of the spectral support of a general class of disordered non-Hermitian operators. These states, which are identified…
Heavy-tailed fluctuations and power law statistics pervade physics, finance, and economics, yet their origin is often ascribed to systems poised near criticality. Here we show that such behavior can emerge far from instability through a…
Data Collaboration (DC) enables multiple parties to jointly train a model by sharing only linear projections of their private datasets. The core challenge in DC is to align the bases of these projections without revealing each party's…
Ordinal Patterns are a time-series data analysis tool used as a preliminary step to construct the Permutation Entropy which itself allows the same characterization of dynamics as chaotic or regular as more theoretical constructs such as the…
We develop a new statistical procedure to test whether the dependence structure is identical between two groups. Rather than relying on a single index such as Pearson's correlation coefficient or Kendall's Tau, we consider the entire…
The existence of an exactly marginal deformation in a conformal field theory is very special, but it is not well understood how this is reflected in the allowed dimensions and OPE coefficients of local operators. To shed light on this…
We consider off-policy evaluation (OPE), which evaluates the performance of a new policy from observed data collected from previous experiments, without requiring the execution of the new policy. This finds important applications in areas…
Experimental extraction of $\beta$-shape functions, C(W), is challenging. Comparing different experimental $\beta$-shapes to each other and to those predicted by theory in a consistent manner is difficult. This difficulty is compounded when…
In the wind energy industry, it is of great importance to develop models that accurately forecast the power output of a wind turbine, as such predictions are used for wind farm location assessment or power pricing and bidding, monitoring,…