This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general enough to include cases in which no minimum exists, as occurs typically, for instance, with standard boosting algorithms. Concretely, we first show that any...

Empirical evidence shows that entrepreneurs hold a large fraction of wealth, have higher saving rates than workers, and face substantial uninsurable entrepreneurial and investment risks. This paper constructs a heterogeneous-agent general equilibrium model with uninsurable entrepreneurial risk and capital-market imperfections to explore the implications of uninsurable entrepreneurial risk for w...

Let (X ,μ) be a probability space, set X to be distributed according to μ and put Y to be an unknown target random variable. In the usual setup in learning theory, one observes N independent couples (Xi, Yi)Ni=1 in X × R, distributed according to the joint distribution of X and Y . The goal is to construct a real-valued function f which is a good guess/prediction of Y . A standard way of measur...

We consider embeddings of planar graphs in R where vertices map to points and edges map to polylines. We refer to such an embedding as a polyline drawing, and ask how few bends are required to form such a drawing for an arbitrary planar graph. It has long been known that even when the vertex locations are completely fixed, a planar graph admits a polyline drawing where edges bend a total of O(n...

The atoms of a regular language are non-empty intersections of complemented and uncomplemented quotients of the language. Tight upper bounds on the number of atoms of a language and on the quotient complexities of atoms are known. We introduce a new class of regular languages, called the maximally atomic languages, consisting of all languages meeting these bounds. We prove the following result:...

Methodological norms in economic theorising are interpreted as rational strategies to optimise some epistemic utility functions. A definition of ‘empirical verisimilitude’ is defended as a plausible interpretation of the epistemic preferences of researchers. Some salient differences between the scientific strategies of physics and of economics are derived from the comparison of the relative cos...

We study drawings of graphs of maximum degree six on the hexagonal (triangular) grid, with the main focus of keeping the number of bends small. We give algorithms that achieve 3.5n + 3.5 bends for all simple graphs. We also prove optimal lower bounds on the number of bends for K7, and give asymptotic lower bounds for graph classes of varying connectivity.