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Classification Test
Given a population whose members each belong to one of a number of different sets or classes, a classification rule or classifier is a procedure by which the elements of the population set are each predicted to belong to one of the classes. A perfect classification is one for which every element in the population is assigned to the class it really belongs to. An imperfect classification is one in which some errors appear, and then statistical analysis must be applied to analyse the classification. A special kind of classification rule is binary classification, for problems in which there are only two classes. Testing classification rules Given a data set consisting of pairs ''x'' and ''y'', where ''x'' denotes an element of the population and ''y'' the class it belongs to, a classification rule ''h''(''x'') is a function that assigns each element ''x'' to a predicted class \hat=h(x). A binary classification is such that the label ''y'' can take only one of two values. The tru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Class (set Theory)
In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share. Classes act as a way to have set-like collections while differing from sets so as to avoid Russell's paradox (see ). The precise definition of "class" depends on foundational context. In work on Zermelo–Fraenkel set theory, the notion of class is informal, whereas other set theories, such as von Neumann–Bernays–Gödel set theory, axiomatize the notion of "proper class", e.g., as entities that are not members of another entity. A class that is not a set (informally in Zermelo–Fraenkel) is called a proper class, and a class that is a set is sometimes called a small class. For instance, the class of all ordinal numbers, and the class of all sets, are proper classes in many formal systems. In Quine's set-theoretical writing, the phrase "ultimate class" is often used in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayes' Theorem
In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to an individual of a known age to be assessed more accurately (by conditioning it on their age) than simply assuming that the individual is typical of the population as a whole. One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference. When applied, the probabilities involved in the theorem may have different probability interpretations. With Bayesian probability interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence. Bayesian inference is fundamental to Bayesia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sensitivity And Specificity
''Sensitivity'' and ''specificity'' mathematically describe the accuracy of a test which reports the presence or absence of a condition. Individuals for which the condition is satisfied are considered "positive" and those for which it is not are considered "negative". *Sensitivity (true positive rate) refers to the probability of a positive test, conditioned on truly being positive. *Specificity (true negative rate) refers to the probability of a negative test, conditioned on truly being negative. If the true condition can not be known, a " gold standard test" is assumed to be correct. In a diagnostic test, sensitivity is a measure of how well a test can identify true positives and specificity is a measure of how well a test can identify true negatives. For all testing, both diagnostic and screening, there is usually a trade-off between sensitivity and specificity, such that higher sensitivities will mean lower specificities and vice versa. If the goal is to return the ratio at w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Medical Test
A medical test is a medical procedure performed to detect, diagnose, or monitor diseases, disease processes, susceptibility, or to determine a course of treatment. Medical tests such as, physical and visual exams, diagnostic imaging, genetic testing, chemical and cellular analysis, relating to clinical chemistry and molecular diagnostics, are typically performed in a medical setting. Types of tests By purpose Medical tests can be classified by their purposes, the most common of which are diagnosis, screening and evaluation. Diagnostic A diagnostic test is a procedure performed to confirm or determine the presence of disease in an individual suspected of having a disease, usually following the report of symptoms, or based on other medical test results. This includes posthumous diagnosis. Examples of such tests are: * Using nuclear medicine to examine a patient suspected of having a lymphoma. * Measuring the blood sugar in a person suspected of having diabetes mellitus after ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loss Functions For Classification
In machine learning and mathematical optimization, loss functions for classification are computationally feasible loss functions representing the price paid for inaccuracy of predictions in classification problems (problems of identifying which category a particular observation belongs to). Given \mathcal as the space of all possible inputs (usually \mathcal \subset \mathbb^d), and \mathcal = \ as the set of labels (possible outputs), a typical goal of classification algorithms is to find a function f: \mathcal \to \mathcal which best predicts a label y for a given input \vec. However, because of incomplete information, noise in the measurement, or probabilistic components in the underlying process, it is possible for the same \vec to generate different y. As a result, the goal of the learning problem is to minimize expected loss (also known as the risk), defined as :I = \displaystyle \int_ V(f(\vec),y) \, p(\vec,y) \, d\vec \, dy where V(f(\vec),y) is a given loss function, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gold Standard (test)
In medicine and statistics, a gold standard test is usually the diagnostic test or benchmark that is the best available under reasonable conditions. In other words, a gold standard is the most accurate test possible without restrictions. Both meanings are different because for example, in medicine, dealing with conditions that would require an autopsy to have a perfect diagnosis, the gold standard test would be the best one that keeps the patient alive instead of the autopsy. In medicine "Gold standard" can refer to the criteria by which scientific evidence is evaluated. For example, in resuscitation research, the "gold standard" test of a medication or procedure is whether or not it leads to an increase in the number of neurologically intact survivors that walk out of the hospital.''ACLS: Principles and Practice''. p. 62. Dallas: American Heart Association, 2003. . Other types of medical research might regard a significant decrease in 30-day mortality as the gold standard. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diagnostic Test
A medical test is a medical procedure performed to detect, diagnose, or monitor diseases, disease processes, susceptibility, or to determine a course of treatment. Medical tests such as, physical and visual exams, diagnostic imaging, genetic testing, chemical and cellular analysis, relating to clinical chemistry and molecular diagnostics, are typically performed in a medical setting. Types of tests By purpose Medical tests can be classified by their purposes, the most common of which are diagnosis, screening and evaluation. Diagnostic A diagnostic test is a procedure performed to confirm or determine the presence of disease in an individual suspected of having a disease, usually following the report of symptoms, or based on other medical test results. This includes posthumous diagnosis. Examples of such tests are: * Using nuclear medicine to examine a patient suspected of having a lymphoma. * Measuring the blood sugar in a person suspected of having diabetes mellitus af ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision Rule
In decision theory, a decision rule is a function which maps an observation to an appropriate action. Decision rules play an important role in the theory of statistics and economics, and are closely related to the concept of a strategy (game theory), strategy in game theory. In order to evaluate the usefulness of a decision rule, it is necessary to have a loss function detailing the outcome of each action under different states. Formal definition Given an observable random variable ''X'' over the probability space \scriptstyle (\mathcal,\Sigma, P_\theta), determined by a parameter ''θ'' ∈ ''Θ'', and a set ''A'' of possible actions, a (deterministic) decision rule is a function ''δ'' : \scriptstyle\mathcal→ ''A''. Examples of decision rules * An estimator is a decision rule used for estimating a parameter. In this case the set of actions is the parameter space, and a loss function details the cost of the discrepancy between the true value of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Classification
Binary classification is the task of classifying the elements of a set into two groups (each called ''class'') on the basis of a classification rule. Typical binary classification problems include: * Medical testing to determine if a patient has certain disease or not; * Quality control in industry, deciding whether a specification has been met; * In information retrieval, deciding whether a page should be in the result set of a search or not. Binary classification is dichotomization applied to a practical situation. In many practical binary classification problems, the two groups are not symmetric, and rather than overall accuracy, the relative proportion of different types of errors is of interest. For example, in medical testing, detecting a disease when it is not present (a ''false positive'') is considered differently from not detecting a disease when it is present (a ''false negative''). Statistical binary classification Statistical classification is a problem studied in ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Inference
Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability". Introduction to Bayes' rule Formal explanation Bayesian inference derives the posterior probability as a consequence of two antecedents: a prior probability and a "likelihood function" derived from a statistical model for the observed data. Bayesian inference computes the posterior probability according to Bayes' theorem: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayes Classifier
In statistical classification, the Bayes classifier minimizes the probability of misclassification. Definition Suppose a pair (X,Y) takes values in \mathbb^d \times \, where Y is the class label of X. Assume that the conditional distribution of ''X'', given that the label ''Y'' takes the value ''r'' is given by :(X\mid Y=r) \sim P_r for r=1,2,\dots,K where "\sim" means "is distributed as", and where P_r denotes a probability distribution. A classifier is a rule that assigns to an observation ''X''=''x'' a guess or estimate of what the unobserved label ''Y''=''r'' actually was. In theoretical terms, a classifier is a measurable function C: \mathbb^d \to \, with the interpretation that ''C'' classifies the point ''x'' to the class ''C''(''x''). The probability of misclassification, or risk, of a classifier ''C'' is defined as :\mathcal(C) = \operatorname\. The Bayes classifier is :C^\text(x) = \underset \operatorname(Y=r \mid X=x). In practice, as in most of statistics, the d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Confusion Matrix
In the field of machine learning and specifically the problem of statistical classification, a confusion matrix, also known as an error matrix, is a specific table layout that allows visualization of the performance of an algorithm, typically a supervised learning one (in unsupervised learning it is usually called a matching matrix). Each row of the matrix represents the instances in an actual class while each column represents the instances in a predicted class, or vice versa – both variants are found in the literature. The name stems from the fact that it makes it easy to see whether the system is confusing two classes (i.e. commonly mislabeling one as another). It is a special kind of contingency table, with two dimensions ("actual" and "predicted"), and identical sets of "classes" in both dimensions (each combination of dimension and class is a variable in the contingency table). __TOC__ Example Given a sample of 12 individuals, 8 that have been diagnosed with cancer an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
