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Statistical learning theory is a framework for machine learning drawing from the fields of statistics and functional analysis. [ 1 ] [ 2 ] [ 3 ] Statistical learning theory deals with the statistical inference problem of finding a predictive function based on data.
Statistics education is the practice of teaching and learning of statistics, along with the associated scholarly research. Statistics is both a formal science and a practical theory of scientific inquiry , and both aspects are considered in statistics education.
Usually, the researcher has a certain theory regarding the topic under investigation. Based on this theory, statements or hypotheses will be proposed (e.g., "Listening to vocal music has a negative effect on learning a word list."). From these hypotheses, predictions about specific events are derived (e.g., "People who study a word list while ...
In general, the risk () cannot be computed because the distribution (,) is unknown to the learning algorithm. However, given a sample of iid training data points, we can compute an estimate, called the empirical risk, by computing the average of the loss function over the training set; more formally, computing the expectation with respect to the empirical measure:
During the course of history, one theory has succeeded another, and some have suggested further work while others have seemed content just to explain the phenomena. The reasons why one theory has replaced another are not always obvious or simple. The philosophy of science includes the question: What criteria are satisfied by a 'good' theory ...
Within arts and humanities departments there are ongoing debates about how to define this emerging research phenomenon, and there are a variety of models of practice research (practice-as-research, practice-based, practice-led, mixed-mode research practice and practice through research), see for example screen media practice research.
Statistical inference makes propositions about a population, using data drawn from the population with some form of sampling.Given a hypothesis about a population, for which we wish to draw inferences, statistical inference consists of (first) selecting a statistical model of the process that generates the data and (second) deducing propositions from the model.
The above image shows a table with some of the most common test statistics and their corresponding tests or models. A statistical hypothesis test is a method of statistical inference used to decide whether the data sufficiently supports a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic.