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There are two major types of problems in uncertainty quantification: one is the forward propagation of uncertainty (where the various sources of uncertainty are propagated through the model to predict the overall uncertainty in the system response) and the other is the inverse assessment of model uncertainty and parameter uncertainty (where the ...
Identify the model output to be analysed (the target of interest should ideally have a direct relation to the problem tackled by the model). Run the model a number of times using some design of experiments, [15] dictated by the method of choice and the input uncertainty. Using the resulting model outputs, calculate the sensitivity measures of ...
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 ...
Machine learning techniques arise largely from statistics and also information theory. In general, entropy is a measure of uncertainty and the objective of machine learning is to minimize uncertainty. Decision tree learning algorithms use relative entropy to determine the decision rules that govern the data at each node. [34]
Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. They can also be used to model phenomena with significant uncertainty in inputs, such as calculating the risk of a nuclear power plant failure.
In statistics and machine learning, the bias–variance tradeoff describes the relationship between a model's complexity, the accuracy of its predictions, and how well it can make predictions on previously unseen data that were not used to train the model. In general, as we increase the number of tunable parameters in a model, it becomes more ...
Model selection may also refer to the problem of selecting a few representative models from a large set of computational models for the purpose of decision making or optimization under uncertainty. [2] In machine learning, algorithmic approaches to model selection include feature selection, hyperparameter optimization, and statistical learning ...
A model of an unknown probability distribution p, may be proposed based on a training sample that was drawn from p. Given a proposed probability model q, one may evaluate q by asking how well it predicts a separate test sample x 1, x 2, ..., x N also drawn from p. The perplexity of the model q is defined as