Competitive Regret

	Competitive Regret In decision theory, competitive regret is the relative regret compared to an oracle with limited or unlimited power in the process of distribution estimation. Competitive regret to the oracle with full power Consider estimating a discrete probability distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon i ... p on a discrete set \mathcal based on data X, the regret of an estimator q is defined as : \max_ r_n (q,p). where \mathcal is the set of all possible probability distribution, and : r_n(q,p) = \mathbb (D(p , , q(X))). where D(p , , q) is the Kullback–Leibler divergence between p and q. Competitive regret to the oracle with limited power Oracle with partial information The oracle is restricted to have access to partial information of the true distribution p by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Decision Theory Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical consequences to the outcome. There are three branches of decision theory: # Normative decision theory: Concerned with the identification of optimal decisions, where optimality is often determined by considering an ideal decision-maker who is able to calculate with perfect accuracy and is in some sense fully rational. # Prescriptive decision theory: Concerned with describing observed behaviors through the use of conceptual models, under the assumption that those making the decisions are behaving under some consistent rules. # Descriptive decision theory: Analyzes how individuals actually make the decisions that they do. Decision theory is closely related to the field of game theory and is an interdisciplinary topic, studied by ec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Regret (decision Theory) In decision theory, on making decisions under uncertainty—should information about the best course of action arrive ''after'' taking a fixed decision—the human emotional response of regret is often experienced, and can be measured as the value of difference between a made decision and the optimal decision. The theory of regret aversion or anticipated regret proposes that when facing a decision, individuals might ''anticipate'' regret and thus incorporate in their choice their desire to eliminate or reduce this possibility. Regret is a negative emotion with a powerful social and reputational component, and is central to how humans learn from experience and to the human psychology of risk aversion. Conscious anticipation of regret creates a feedback loop that transcends regret from the emotional realm—often modeled as mere human behavior—into the realm of the rational choice behavior that is modeled in decision theory. Description Regret theory is a model in theoretical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Probability Distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Kullback–Leibler Divergence In mathematical statistics, the Kullback–Leibler divergence (also called relative entropy and I-divergence), denoted D_\text(P \parallel Q), is a type of statistical distance: a measure of how one probability distribution ''P'' is different from a second, reference probability distribution ''Q''. A simple interpretation of the KL divergence of ''P'' from ''Q'' is the expected excess surprise from using ''Q'' as a model when the actual distribution is ''P''. While it is a distance, it is not a metric, the most familiar type of distance: it is not symmetric in the two distributions (in contrast to variation of information), and does not satisfy the triangle inequality. Instead, in terms of information geometry, it is a type of divergence, a generalization of squared distance, and for certain classes of distributions (notably an exponential family), it satisfies a generalized Pythagorean theorem (which applies to squared distances). In the simple case, a relative entropy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]