We study a regression problem where for some part of the data we observe both label variable (Y) and predictors (X), while other only are given. Such arises, example, when observations costly may require skilled human agent. When conditional expectation E[Y|X] is not exactly linear, one can consider best linear approximation to expectation, which be estimated consistently by least-square estima...

‎linear semi-infinite programming problem is an important class of optimization problems which deals with infinite constraints‎. ‎in this paper‎, ‎to solve this problem‎, ‎we combine a discretization method and a neural network method‎. ‎by a simple discretization of the infinite constraints,we convert the linear semi-infinite programming problem into linear programming problem‎. ‎then‎, ‎we use...

An r-uniform hypergraph H is semi-algebraic of complexity t=(d,D,m) if the vertices correspond to points in Rd and edges are determined by sign-pattern m degree-D polynomials. Semi-algebraic hypergraphs bounded provide a general framework for studying geometrically defined hypergraphs. The much-studied Ramsey number Rrt(s,n) denotes smallest N such that every t on contains either clique size s ...