We present a dimension adaptive sparse grid combination technique for the machine learning problem of regression. A function over a d-dimensional space, which assumedly describes the relationship between the features and the response variable, is reconstructed using a linear combination of partial functions; these may depend only on a subset of all features. The partial functions, which are pie...

A quantitative structure-activity relationship (QSAR) modeling of the antimalarial activity of two diverse sets of compounds for each of two strains D6 and NF54 of Plasmodium falciparum is presented. The molecular structural features of compounds are presented by molecular descriptors (geometrical, topological, quantum mechanical, and electronic) calculated using the CODESSA PRO software. Satis...

We give a short proof of a slightly weaker version of the multilinear Kakeya inequality proven by Bennett, Carbery, and Tao. The multilinear Kakeya inequality is a geometric estimate about the overlap pattern of cylindrical tubes in R pointing in different directions. This estimate was first proven by Bennett, Carbery, and Tao in [BCT]. Recently it has had some striking applications in harmonic...

Disjointly constrained multilinear programming concerns the problem of maximizing a multilinear function on the product of finitely many disjoint polyhedra. While maximizing a linear function on a polytope (linear programming) is known to be solvable in polynomial time, even bilinear programming is NP-hard. Based on a reformulation of the problem in terms of sum-of-squares polynomials, we study...

In this paper, we present some general as well as explicit characterizations of the convex envelope of multilinear functions defined over a unit hypercube. A new approach is used to derive this characterization via a related convex hull representation obtained by applying the Reformulation-Linearization Technique (RLT) of Sherali and Adams (1990, 1994). For the special cases of multilinear func...

Higher order tensor inversion is possible for even order. This is due to the fact that a tensor group endowed with the contracted product is isomorphic to the general linear group of degree n. With these isomorphic group structures, we derive a tensor SVD which we have shown to be equivalent to well-known canonical polyadic decomposition and multilinear SVD provided that some constraints are sa...

We characterize the infinite words determined by one-way stack automata. An infinite language L determines an infinite word α if every string in L is a prefix of α. If L is regular or context-free, it is known that α must be ultimately periodic. We extend this result to the class of languages recognized by one-way nondeterministic checking stack automata (1-NCSA). We then consider stronger clas...

We deene a Boolean circuit to be multilinear if the formal polynomial associated with it is multilinear as well. We consider the problem of computing the connectiv-ity function using circuits that are monotone and multilinear. Our main result is that monotone multilinear circuits for this function require exponential size. Since connectivity can be computed by monotone Boolean circuits within s...

Multilinear algebra, the algebra of higher-order tensors, offers a potent mathematical framework for analyzing ensembles of images resulting from the interaction of any number of underlying factors. We present a dimensionality reduction algorithm that enables subspace analysis within the multilinear framework. This N -mode orthogonal iteration algorithm is based on a tensor decomposition known ...

Let f(x) = f(x1, . . . , xn) = ∑ |S|≤k aS ∏ i∈S xi be an n-variate real multilinear polynomial of degree at most k, where S ⊆ [n] = {1, 2, . . . , n}. For its one-block decoupled version,