Algorithmic Inference

	Algorithmic Inference Algorithmic inference gathers new developments in the statistical inference methods made feasible by the powerful computing devices widely available to any data analyst. Cornerstones in this field are computational learning theory, granular computing, bioinformatics, and, long ago, structural probability . The main focus is on the algorithms which compute statistics rooting the study of a random phenomenon, along with the amount of data they must feed on to produce reliable results. This shifts the interest of mathematicians from the study of the distribution laws to the functional properties of the statistics, and the interest of computer scientists from the algorithms for processing data to the information they process. The Fisher parametric inference problem Concerning the identification of the parameters of a distribution law, the mature reader may recall lengthy disputes in the mid 20th century about the interpretation of their variability in terms of fiducial distribution , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Statistical Inference Statistical inference is the process of using data analysis to infer properties of an underlying probability distribution.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population. In machine learning, the term ''inference'' is sometimes used instead to mean "make a prediction, by evaluating an already trained model"; in this context inferring properties of the model is referred to as ''training'' or ''learning'' (rather than ''inference''), and using a model for prediction is referred to as ''inference'' (instead of ''prediction''); se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Complexity Complexity characterizes the behavior of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity, randomness, collective dynamics, hierarchy, and emergence. The term is generally used to characterize something with many parts where those parts interact with each other in multiple ways, culminating in a higher order of emergence greater than the sum of its parts. The study of these complex linkages at various scales is the main goal of complex systems theory. The intuitive criterion of complexity can be formulated as follows: a system would be more complex if more parts could be distinguished, and if more connections between them existed. , a number of approaches to characterizing complexity have been used in science; Zayed ''et al.'' reflect many of these. Neil Johnson states that "even among scientists, there is no unique definition of complexity – and the scientific notion has traditionally been conveyed using partic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Twisting Properties Twisting properties in general terms are associated with the properties of samples that identify with statistics that are suitable for exchange. Description Starting with a sample \ observed from a random variable ''X'' having a given distribution law with a non-set parameter, a parametric inference problem consists of computing suitable values – call them estimates – of this parameter precisely on the basis of the sample. An estimate is suitable if replacing it with the unknown parameter does not cause major damage in next computations. In algorithmic inference, suitability of an estimate reads in terms of compatibility with the observed sample. In turn, parameter compatibility is a probability measure that we derive from the probability distribution of the random variable to which the parameter refers. In this way we identify a random parameter Θ compatible with an observed sample. Given a sampling mechanism M_X=(g_\theta,Z), the rationale of this operation lies in us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Bootstrapping Populations Bootstrapping populations in statistics and mathematics starts with a Statistical sample, sample \ observed from a random variable. When ''X'' has a given cumulative distribution function, distribution law with a set of non fixed parameters, we denote with a vector \boldsymbol\theta, a Parametric statistics, parametric inference problem consists of computing suitable values – call them estimator, estimates – of these parameters precisely on the basis of the sample. An estimate is suitable if replacing it with the unknown parameter does not cause major damage in next computations. In Algorithmic inference, suitability of an estimate reads in terms of Algorithmic inference#compatible distribution, compatibility with the observed sample. In this framework, Resampling (statistics), resampling methods are aimed at generating a set of candidate values to replace the unknown parameters that we read as compatible replicas of them. They represent a population of specifications of a ran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]