Transcription of Parametric vs Nonparametric Models
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Parametric vs Nonparametric Models
Parametric vs Nonparametric Models Parametric modelsassume somefinite set of parameters .Giventheparameters,future predictions,x, are independent of the observed data,D:P(x| ,D)=P(x| )therefore capture everything there is to know about the data. So the complexity of the model is bounded even if the amount of data isunbounded. This makes them not very flexible. Non- Parametric modelsassume that the data distribution cannot be defined interms of such a finite set of parameters. But they can often be defined byassuming aninfinite dimensional . Usually we think of as afunction. The amount of information that can capture about the dataDcan grow asthe amount of data grows. This makes them more nonparametricsA simple framework for modelling complex Models can be viewed as having infinitely many parametersExamples of non- Parametric Models :ParametricNon-parametricApplicati onpolynomial regressionGaussian processesfunction regressionGaussian process classifiersclassificationmixture Models , k-meansDirichlet process mixturesclusteringhidden Markov modelsinfinite HMMstime seriesfactor analysis / pPCA / PMFinfinite latent factor modelsfeature regression and Gaussian processesConsider the problem ofnonlinear regression:You want to learn afunctionfwitherror barsfromdataD={X,y}xyAGaussian processdefines a distribution over functionsp(f)whi
Parametric vs Nonparametric Models • Parametric models assume some finite set of parameters .Giventheparameters, future predictions, x, are independent of the observed data, D:
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