instruction:
In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
question:
We study the classic online learning problem of predicting with expert advice, and propose a truly parameter-free and adaptive algorithm that achieves several objectives simultaneously without using any prior information. The main component of this work is an improved version of the NormalHedge.DT algorithm [Luo and Schapire, 2014], called AdaNormalHedge. On one hand, this new algorithm ensures small regret when the competitor has small loss and almost constant regret when the losses are stochastic. On the other hand, the algorithm is able to compete with any convex combination of the experts simultaneously, with a regret in terms of the relative entropy of the prior and the competitor. This resolves an open problem proposed by Chaudhuri et al. [2009] and Chernov and Vovk [2010]. Moreover, we extend the results to the sleeping expert setting and provide two applications to illustrate the power of AdaNormalHedge: 1) competing with time-varying unknown competitors and 2) predicting almost as well as the best pruning tree. Our results on these applications significantly improve previous work from different aspects, and a special case of the first application resolves another open problem proposed by Warmuth and Koolen [2014] on whether one can simultaneously achieve optimal shifting regret for both adversarial and stochastic losses.
answer:
Achieving All with No Parameters: Adaptive NormalHedge

question:
Rough set theory, a mathematical tool to deal with vague concepts, has originally described the indiscernibility of elements by equivalence relations. Covering rough sets are a natural extension of classical rough sets by relaxing the partitions arising from equivalence relations to covers. Recently, some topological concepts such as neighborhood have been applied to covering rough sets. In this paper, we further investigate the covering rough sets based on neighborhoods by approximation operations. We show that the upper approximation based on neighborhoods can be defined equivalently without using neighborhoods. To analyze the covers themselves, we introduce unary and composition operations on covers. A notion of homomorphism is provided to relate two covering approximation spaces. We also examine the properties of approximations preserved by the operations and homomorphisms, respectively.
answer:
Covering rough sets based on neighborhoods

question:
This paper is about reducing influence dia gram (ID) evaluation into Bayesian network (BN) inference problems. Such reduction is interesting because it enables one to read ily use one's favorite BN inference algorithm to efficiently evaluate IDs. Two such reduc tion methods have been proposed previously (Cooper 1988, Shachter and Peot 1992). This paper proposes a new method. The BN in ference problems induced by the mew method are much easier to solve than those induced by the two previous methods.
answer:
Probabilistic Inference in Influence Diagrams