In this section, we provide details on the toy example presented in Section 1. We used the following simple experimental setting. All covariances for the bidimensional distributions are diagonal, therefore all bidimensional Gaussian distributions are parametrised by 4 parameters (μ1, μ2, σ1, σ2) where μ, σ is a mean-variance pair on each dimension. We consider a data distribution that is a mixt...

In a (1 : b) Maker-Breaker game, one of the central questions is to find the maximal value of b that allows Maker to win the game (that is, the critical bias b∗). Erdős conjectured that the critical bias for many Maker-Breaker games played on the edge set of Kn is the same as if both players claim edges randomly. Indeed, in many Maker-Breaker games, “Erdős Paradigm” turned out to be true. There...

We consider a decision maker who can select one of a finite set of possible actions, each of which will result in one of a finite set of possible outcomes. If the decision maker has preferences over these outcomes, it will naturally prefer taking some actions to others, but may be uncertain of the result of each action. In this paper we describe how a decision maker can elicit expert prediction...

w was created in the tradition of typesetting printed pages for bound volumes. For hundreds of years, printers considered the page as a block of type surrounded by margins. As adequate margins were required for binding, practical considerations became aesthetic needs applied by strict formulas. Earlier concepts of pages, such as certain Egyptian hieroglyphs, Roman scrolls. and medieval illumina...

In a Maker-Breaker game on a graph G, Breaker and Maker alternately claim edges of G. Maker wins if, after all edges have been claimed, the graph induced by his edges has some desired property. We consider four Maker-Breaker games played on random geometric graphs. For each of our four games we show that if we add edges between n points chosen uniformly at random in the unit square by order of ...