Related papers: Generalized Wick Decompositions
The problem of simultaneous decomposition of binary forms as sums of powers of linear forms is studied. For generic forms the minimal number of linear forms needed is found and the space parametrizing all the possible decompositions is…
In the framework of the generalized measure theory the decomposable probabilistic-valued set functions are introduced with triangle functions $\tau$ in an appropriate probabilistic metric space as natural candidates for the "addition",…
We derive explicit, closed-form expressions for the cumulant densities of a multivariate, self-exciting Hawkes point process, generalizing a result of Hawkes in his earlier work on the covariance density and Bartlett spectrum of such…
We obtain exact formulas for the cumulative distribution function of the variance-gamma distribution, as infinite series involving the modified Bessel function of the second kind and the modified Lommel function of the first kind. From…
The characterization of systems of differential equations admitting a superposition function allowing us to write the general solution in terms of any fundamental set of particular solutions is discussed. These systems are shown to be…
Let $w$ be a word in alphabet $\{x,D\}$ with $m$ $x$'s and $n$ $D$'s. Interpreting "$x$" as multiplication by $x$, and "$D$" as differentiation with respect to $x$, the identity $wf(x) = x^{m-n}\sum_k S_w(k) x^k D^k f(x)$, valid for any…
Symbolic data analysis has been proposed as a technique for summarising large and complex datasets into a much smaller and tractable number of distributions -- such as random rectangles or histograms -- each describing a portion of the…
In this paper we establish a new summation method by expanding $\prod_{k}(1-\frac{z}{a_{k}})^{-1}$ with two approaches: the Taylor expansion and the infinite partial fraction decomposition. Here we focus on the case when $a_{k}$ is…
A seminal technique of theoretical physics called Wick's theorem interprets the Gaussian matrix integral of the products of the trace of powers of Hermitian matrices as the number of labelled maps with a given degree sequence, sorted by…
We decompose the genealogy of a general superprocess with spatially dependent branching mechanism with respect to the last individual alive (Williams decomposition). This is a generalization of the main result of Delmas and H\'{e}nard…
We introduce the notion of generalized Weyl system, and use it to define *-products which generalize the commutation relations of Lie algebras. In particular we study in a comparative way various *-products which generalize the k-Minkowski…
The functional ANOVA, or Hoeffding decomposition, provides a principled framework for interpretability by decomposing a model prediction into main effects and higher-order interactions. For independent inputs, this classical decomposition…
When $K$ models are evaluated on the same validation set of size $n$, the selected winner's apparent performance is biased upward. Suppose $K$ models are evaluated on a shared sequence of i.i.d. observations $X_1,\dots, X_n$, where model…
The G-Wishart distribution is an essential component for the Bayesian analysis of Gaussian graphical models as the conjugate prior for the precision matrix. Evaluating the marginal likelihood of such models usually requires computing…
We define two recursive functions obtained by decomposition of a given interval into four close parts and prove two lemmas which determine features of these functions.
A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…
In earlier papers we changed the concept of the inner product to a more general one, to the so-called Minkowski product. This product changes on the tangent space hence we could investigate a more general structure than a Riemannian…
We consider two bivariate models with two-way interactions in context of risk and queueing theory. The two entities interact with each other by providing assistance but otherwise evolve independently. We focus on certain random quantities…
A unifying and generalizing approach to representations of the positive-part and absolute moments $\mathsf{E} X_+^p$ and $\mathsf{E}|X|^p$ of a random variable $X$ for real $p$ in terms of the characteristic function (c.f.) of $X$, as well…
Compositional generalization is a basic and essential intellective capability of human beings, which allows us to recombine known parts readily. However, existing neural network based models have been proven to be extremely deficient in…