We study the differential properties of higher-order statistical probabilistic programs with recursion and conditioning. Our starting point is an open problem posed by Hongseok Yang: what class have densities that are differentiable almost everywhere? To formalise problem, we consider Statistical PCF (SPCF), extension call-by-value real numbers, constructs for sampling give SPCF a sampling-styl...

Information-neutral recommender systems aim to make recommendations whose neutrality from the specified viewpoint is guaranteed. Such systems are developed for dissolving a filter bubble problem, which is the bias or restriction that provided to people by the influence of personalization technologies. Our previously developed system was not scalable because efficient optimization techniques cou...

As we shall see later, Thomae’s function is not differentiable on the irrationals. In this note, we address whether there is a modification of Thomae’s function which is differentiable on a subset of the irrationals. In Section 2, we prove that Thomae’s function is not differentiable on the irrationals and define modified versions of Thomae’s function. In Section 3, we show that for each of our...

We establish a solution to the Monge problem in N , with an asymmetric, strictly convex norm cost function, when the initial measure is absolutely continuous. We focus on the strategy, based on disintegration of measures, initially proposed by Sudakov. As known, there is a gap to fill. The missing step is completed when the unit ball is strictly convex, but not necessarily differentiable nor un...