Transcription of Maximum Likelihood, Logistic Regression, and Stochastic ...
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Maximum Likelihood, Logistic Regression, and Stochastic ...
Maximum likelihood , Logistic Regression, and Stochastic Gradient TrainingCharles 10, 20141 Principle of Maximum likelihoodConsider a family of probability distributions defined by a set of parameters .The distributions may be either probability mass functions (pmfs) or probabilitydensity functions (pdfs). Suppose that we have a random sample drawn froma fixed but unknown member of this family. The random sample is a trainingset ofnexamplesx1toxn. An example may also be called an observation, anoutcome, an instance, or a data point. In general eachxjis a vector of values, and is a vector of real-valued parameters. For example, for a Gaussian distribution = , 2.
The distributions may be either probability mass functions (pmfs) or probability density functions (pdfs). Suppose that we have a random sample drawn from a fixed but unknown member of this family. The random sample is a training set of nexamples x 1 to x n. An example may also be called an observation, an outcome, an instance, or a data point.
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