Universal Prediction for Indexed Classes of Sources
نویسندگان
چکیده
We study universal prediction w.r.t. an indexed class of sources (e.g., parametric families) and general loss functions. We explore the centrality of the self-information loss function (log-loss) in the theory of universal prediction by showing that under certain assumptions, the feasibility of universal prediction w.r.t. the log-loss function, over an indexed class of sources (that is, universal data compression), is a necessary and su cient condition for its feasibility w.r.t. other loss functions.
منابع مشابه
Water erosion prediction using Revised Universal Soil Loss Equation and GIS: A case study of Gorganrud Basin
Soil erosion and sedimentation processes can be considered as serious eco-environmentalproblems. This study aimed to estimate the basin-wide erosion using the Revised UniversalSoil Loss Equation (RUSLE). The soil erosion parameters included rainfall erosivity mapgenerated from the rainfall data, soil erodibility extracted from the soil map, land cover andmanagement map produced from supervised ...
متن کاملApplication of soil properties, auxiliary parameters, and their combination for prediction of soil classes using decision tree model
Soil classification systems are very useful for a simple and fast summarization of soil properties. These systems indicate the method for data summarization and facilitate connections among researchers, engineers, and other users. One of the practical systems for soil classification is Soil Taxonomy (ST). As determining soil classes for an entire area is expensive, time-consuming, and almost ...
متن کاملUniversal prediction and universal coding
Although prediction schemes which are named \universal" are now abundant, very little has been addressed as to the de nition of universal prediction. This paper addresses for -nary ( 2) sequences the criteria of successful universal prediction and the prediction schemes which achieve the goals. We propose the following criteria: for any probability measures in a given measure class, the error p...
متن کاملHierarchical universal coding
In an earlier paper, we proved a strong version of the redundancy-capacity converse theorem of universal coding, stating that for `most' sources in a given class, the universal coding redundancy is essentially lower bounded by the capacity of the channel induced by this class. Since this result holds for general classes of sources, it extends Rissanen's strong converse theorem for parametric fa...
متن کاملRecent Results in Universal and Non-Universal Induction
We present and relate recent results in prediction based on countable classes of either probability (semi-)distributions or base predictors. Learning by Bayes, MDL, and stochastic model selection will be considered as instances of the first category. In particular, we will show how analog assertions to Solomonoff’s universal induction result can be obtained for MDL and stochastic model selectio...
متن کامل