We propose new families of models and algorithms for high-dimensional nonparametric learning with joint sparsity constraints. Our approach is based on a regularization method that enforces common sparsity patterns across different function components in a nonparametric additive model. The algorithms employ a coordinate descent approach that is based on a functional soft-thresholding operator. T...

We investigate in this paper the set of kadditive capacities dominating a given capacity, which we call the k-additive core. We study its structure through achievable families, which play the role of maximal chains in the classical case (k = 1), and show that associated capacities are elements (possibly a vertex) of the k-additive core when the capacity is (k+1)-monotone. As a particular case, ...

Abstract Both varying-coefficient and additive models have been studied extensively in the literature as extensions to linear models. They have also been extended to functional response data. However, existing extensions are still not sufficiently flexible to reflect the functional feature of the responses. In this paper, we extend both varying-coefficient and additive models to a much more fle...

Many large Markov decision processes (MDPs) can be represented compactly using a structured representation such as a dynamic Bayesian network. Unfortunately, the compact representation does not help standard MDP algorithms, because the value function for the MDP does not retain the structure of the process description. We argue that in many such MDPs, structure is approximately retained. That i...

pα||n α. As usual p will denote primes, pα||n means that p divides n but p does not, and a function f(n) is additive if f(mn) = f(m)+f(n) whenever (m,n) = 1. From the pioneering works of Alladi and Erdős [1]-[2], P. Erdős’s perspicacity and insight have been one of the main driving forces in the research that brought on many results on summatory functions of large additive functions and P (n). ...

1. A function is arithmetic if it is defined on the positive integers. Those arithmetic functions which assume real values and satisfy f(ab)-f(a)+f(b) for mutually prime integers a, b are classically called additive. The following examples illustrate the interest of these functions, both for themselves and for their applications. An additive function is defined by its values on the prime powers...

Discovery of additive structure is an important step towards understanding a complex multi-dimensional function, because it allows for expressing this function as the sum of lower-dimensional or otherwise simpler components. Modeling additive structure also opens up opportunities for learning better regression models. The term statistical interaction is used to describe the presence of non-addi...

The modularity is the best known and widely used quality function for community detection in graphs. We investigate approximability of maximization problem some related problems. first design a polynomial-time 0.4209-additive approximation algorithm problem, which improves current additive error 0.4672. Our theoretical analysis also demonstrates that proposed obtains nearly-optimal solution any...

Introduction: Platelets are small, anucleated cytoplasmic fragments that play an essential role in blood clotting and wound healing. Platelets are routinely stored in plasma for five days at 220C. Aim: Our objective was to assess platelet morphology and function in random donor platelet stored for seven days in platelet additive solution. Methods: The random donor platelet was prepared by PRP m...