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Conformal Prediction
Conformal prediction (CP) is a machine learning framework for uncertainty quantification that produces statistically valid prediction regions (prediction intervals) for any underlying point predictor (whether statistical, machine, or deep learning) only assuming exchangeability of the data. CP works by computing nonconformity scores on previously labeled data, and using these to create prediction sets on a new (unlabeled) test data point. A transductive version of CP was first proposed in 1998 by Gammerman, Vovk, and Vapnik, and since, several variants of conformal prediction have been developed with different computational complexities, formal guarantees, and practical applications. Conformal prediction requires a user-specified ''significance level'' for which the algorithm should produce its predictions. This significance level restricts the frequency of errors that the algorithm is allowed to make. For example, a significance level of 0.1 means that the algorithm can make ...
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Prediction Interval
In statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval (statistics), interval in which a future observation will fall, with a certain probability, given what has already been observed. Prediction intervals are often used in regression analysis. A simple example is given by a six-sided die with face values ranging from 1 to 6. The confidence interval for the estimated expected value of the face value will be around 3.5 and will become narrower with a larger sample size. However, the prediction interval for the next roll will approximately range from 1 to 6, even with any number of samples seen so far. Prediction intervals are used in both frequentist statistics and Bayesian statistics: a prediction interval bears the same relationship to a future observation that a frequentist confidence interval or Bayesian credible interval bears to an unobservable population parameter: prediction intervals predict the distribution of in ...
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Inductive Reasoning
Inductive reasoning refers to a variety of method of reasoning, methods of reasoning in which the conclusion of an argument is supported not with deductive certainty, but with some degree of probability. Unlike Deductive reasoning, ''deductive'' reasoning (such as mathematical induction), where the conclusion is ''certain'', given the premises are correct, inductive reasoning produces conclusions that are at best ''probable'', given the evidence provided. Types The types of inductive reasoning include generalization, prediction, statistical syllogism, argument from analogy, and causal inference. There are also differences in how their results are regarded. Inductive generalization A generalization (more accurately, an ''inductive generalization'') proceeds from premises about a Sample (statistics), sample to a conclusion about the statistical population, population. The observation obtained from this sample is projected onto the broader population. : The proportion Q of the ...
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Bootstrap Method
Bootstrapping is a self-starting process that is supposed to proceed without external input. Bootstrapping, bootstrap, or bootstraps may also refer to: * Bootstrap (front-end framework), a free collection of tools for creating websites and web applications * Bootstrap curriculum, a curriculum which uses computer programming to teach algebra to students age 12–16 * Bootstrap funding in entrepreneurship and startups * Bootstrap model, a class of theories in quantum physics * Conformal bootstrap, a mathematical method to constrain and solve models in particle physics * Bootstrapping (compilers), the process of writing a compiler in the programming language it is intended to compile * Bootstrapping (electronics), a type of circuit that employs positive feedback * Bootstrapping (finance), a method for constructing a yield curve from the prices of coupon-bearing products * Bootstrapping (law), a former rule of evidence in U.S. federal conspiracy trials * Bootstrapping (linguistics), a ...
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Calibration (statistics)
There are two main uses of the term calibration in statistics that denote special types of statistical inference problems. Calibration can mean :*a reverse process to regression, where instead of a future dependent variable being predicted from known explanatory variables, a known observation of the dependent variables is used to predict a corresponding explanatory variable; :*procedures in statistical classification to determine class membership probabilities which assess the uncertainty of a given new observation belonging to each of the already established classes. In addition, calibration is used in statistics with the usual general meaning of calibration. For example, model calibration can be also used to refer to Bayesian inference about the value of a model's parameters, given some data set, or more generally to any type of fitting of a statistical model. As Philip Dawid puts it, "a forecaster is ''well calibrated'' if, for example, of those events to which he assigns a ...
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Stroke
Stroke is a medical condition in which poor cerebral circulation, blood flow to a part of the brain causes cell death. There are two main types of stroke: brain ischemia, ischemic, due to lack of blood flow, and intracranial hemorrhage, hemorrhagic, due to bleeding. Both cause parts of the brain to stop functioning properly. Signs and symptoms of stroke may include an hemiplegia, inability to move or feel on one side of the body, receptive aphasia, problems understanding or expressive aphasia, speaking, dizziness, or homonymous hemianopsia, loss of vision to one side. Signs and symptoms often appear soon after the stroke has occurred. If symptoms last less than 24 hours, the stroke is a transient ischemic attack (TIA), also called a mini-stroke. subarachnoid hemorrhage, Hemorrhagic stroke may also be associated with a thunderclap headache, severe headache. The symptoms of stroke can be permanent. Long-term complications may include pneumonia and Urinary incontinence, loss of b ...
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