The Fundamental Nature of the Log Loss Function

The standard loss functions used in the literature on probabilistic prediction are the log loss function, the Brier loss function, and the spherical loss function; however, any computable proper loss function can be used for comparison of prediction algorithms. This note shows that the log loss function is most selective in that any prediction algorithm that is optimal for a given data sequence (in the sense of the algorithmic theory of randomness) under the log loss function will be optimal under any computable proper mixable loss function; on the other hand, there is a data sequence and a prediction algorithm that is optimal for that sequence under either of the two other standard loss functions but not under the log loss function.Comment: 12 page

Technology of bot creation for wide class of logic approach-based applications

The article proposes information technology for computer-aided design and implementation of bots on the base of logical approach. The general approach to creation of bots with use of a complex of logical and linguistic models is described. The general scheme of work of the web-oriented system with use of a chat bot is developed. The model of logic of actions is presented and the theorem proving method what can be used for the formal description of process of creation of bots is described. An example of using a logical model to create a bot is described

Prediction with Expert Advice under Discounted Loss

We study prediction with expert advice in the setting where the losses are accumulated with some discounting---the impact of old losses may gradually vanish. We generalize the Aggregating Algorithm and the Aggregating Algorithm for Regression to this case, propose a suitable new variant of exponential weights algorithm, and prove respective loss bounds.Comment: 26 pages; expanded (2 remarks -> theorems), some misprints correcte