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**Probability matching** is a decision strategy in which predictions of class membership are proportional to the class base rates. Thus, if in the training set positive examples are observed 60% of the time, and negative examples are observed 40% of the time, then the observer using a *probability-matching* strategy will predict (for unlabeled examples) a class label of "positive" on 60% of instances, and a class label of "negative" on 40% of instances.

The optimal Bayesian decision strategy (to maximize the number of correct predictions, see Duda, Hart & Stork (2001)) in such a case is to always predict "positive" (i.e., predict the majority category in the absence of other information), which has 60% chance of winning rather than matching which has 52% of winning (where *p* is the probability of positive realization, the result of matching would be , here ). The probability-matching strategy is of psychological interest because it is frequently employed by human subjects in decision and classification studies (where it may be related to Thompson sampling).

In artificial intelligence, **Thompson sampling**, named after William R. Thompson, is a heuristic for choosing actions that addresses the exploration-exploitation dilemma in the multi-armed bandit problem. It consists in choosing the action that maximizes the expected reward with respect to a randomly drawn belief.

The only case when probability matching will yield same results as Bayesian decision strategy mentioned above is when all class base rates are the same. So, if in the training set positive examples are observed 50% of the time, then the Bayesian strategy would yield 50% accuracy (1 × .5), just as probability matching (.5 ×.5 + .5 × .5).

**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".

In machine learning, **naive Bayes classifiers** are a family of simple "probabilistic classifiers" based on applying Bayes' theorem with strong (naive) independence assumptions between the features.

**Pattern recognition** is the automated recognition of patterns and regularities in data. Pattern recognition is closely related to artificial intelligence and machine learning, together with applications such as data mining and knowledge discovery in databases (KDD), and is often used interchangeably with these terms. However, these are distinguished: machine learning is one approach to pattern recognition, while other approaches include hand-crafted rules or heuristics; and pattern recognition is one approach to artificial intelligence, while other approaches include symbolic artificial intelligence. A modern definition of pattern recognition is:

The field of pattern recognition is concerned with the automatic discovery of regularities in data through the use of computer algorithms and with the use of these regularities to take actions such as classifying the data into different categories.

A **Bayesian network**, **Bayes network**, **belief network**, **decision network**, **Bayes(ian) model** or **probabilistic directed acyclic graphical model** is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). Bayesian networks are ideal for taking an event that occurred and predicting the likelihood that any one of several possible known causes was the contributing factor. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases.

**Binary** or **binomial classification** is the task of classifying the elements of a given set into two groups on the basis of a classification rule. Contexts requiring a decision as to whether or not an item has some qualitative property, some specified characteristic, or some typical binary classification include:

In Bayesian statistics, the **posterior probability** of a random event or an uncertain proposition is the conditional probability that is assigned after the relevant evidence or background is taken into account. Similarly, the **posterior probability distribution** is the probability distribution of an unknown quantity, treated as a random variable, conditional on the evidence obtained from an experiment or survey. "Posterior", in this context, means after taking into account the relevant evidence related to the particular case being examined. For instance, there is a ("non-posterior") probability of a person finding buried treasure if they dig in a random spot, and a posterior probability of finding buried treasure if they dig in a spot where their metal detector rings.

In statistical inference, specifically predictive inference, a **prediction interval** is an estimate of an interval in which a future observation will fall, with a certain probability, given what has already been observed. Prediction intervals are often used in regression analysis.

In computer science, **Decision tree learning** uses a decision tree to go from observations about an item to conclusions about the item's target value. It is one of the predictive modeling approaches used in statistics, data mining and machine learning. Tree models where the target variable can take a discrete set of values are called **classification trees**; in these tree structures, leaves represent class labels and branches represent conjunctions of features that lead to those class labels. Decision trees where the target variable can take continuous values are called **regression trees**.

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. Each row of the matrix represents the instances in a predicted class while each column represents the instances in an actual class. The name stems from the fact that it makes it easy to see if the system is confusing two classes.

A **receiver operating characteristic curve**, or **ROC curve**, is a graphical plot that illustrates the diagnostic ability of a binary classifier system as its discrimination threshold is varied.

In machine learning and statistics, **classification** is the problem of identifying to which of a set of categories (sub-populations) a new observation belongs, on the basis of a training set of data containing observations whose category membership is known. Examples are assigning a given email to the "spam" or "non-spam" class, and assigning a diagnosis to a given patient based on observed characteristics of the patient. Classification is an example of pattern recognition.

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.

In decision theory, a **score function**, or **scoring rule**, measures the accuracy of probabilistic predictions. It is applicable to tasks in which predictions must assign probabilities to a set of mutually exclusive outcomes. The set of possible outcomes can be either binary or categorical in nature, and the probabilities assigned to this set of outcomes must sum to one. A score can be thought of as either a measure of the "calibration" of a set of probabilistic predictions, or as a "cost function" or "loss function".

In machine learning, **multi-label classification** and the strongly related problem of **multi-output classification** are variants of the classification problem where multiple labels may be assigned to each instance. Multi-label classification is a generalization of multiclass classification, which is the single-label problem of categorizing instances into precisely one of more than two classes; in the multi-label problem there is no constraint on how many of the classes the instance can be assigned to.

The **Matthews correlation coefficient** is used in machine learning as a measure of the quality of binary (two-class) classifications, introduced by biochemist Brian W. Matthews in 1975. It takes into account true and false positives and negatives and is generally regarded as a balanced measure which can be used even if the classes are of very different sizes. The MCC is in essence a correlation coefficient between the observed and predicted binary classifications; it returns a value between −1 and +1. A coefficient of +1 represents a perfect prediction, 0 no better than random prediction and −1 indicates total disagreement between prediction and observation. The statistic is also known as the phi coefficient. MCC is related to the chi-square statistic for a 2×2 contingency table

In pattern recognition, information retrieval and binary classification, **precision** is the fraction of relevant instances among the retrieved instances, while **recall** is the fraction of relevant instances that have been retrieved over the total amount of relevant instances. Both precision and recall are therefore based on an understanding and measure of relevance.

*Not to be confused with multi-label classification.*

The **evaluation of binary classifiers** compares two methods of assigning a binary attribute, one of which is usually a standard method and the other is being investigated. There are many metrics that can be used to measure the performance of a classifier or predictor; different fields have different preferences for specific metrics due to different goals. For example, in medicine sensitivity and specificity are often used, while in computer science precision and recall are preferred. An important distinction is between metrics that are independent on the prevalence, and metrics that depend on the prevalence – both types are useful, but they have very different properties.

In machine learning, **multiple-instance learning** (MIL) is a type of supervised learning. Instead of receiving a set of instances which are individually labeled, the learner receives a set of labeled *bags*, each containing many instances. In the simple case of multiple-instance binary classification, a bag may be labeled negative if all the instances in it are negative. On the other hand, a bag is labeled positive if there is at least one instance in it which is positive. From a collection of labeled bags, the learner tries to either (i) induce a concept that will label individual instances correctly or (ii) learn how to label bags without inducing the concept.

- Duda, Richard O.; Hart, Peter E.; Stork, David G. (2001),
*Pattern Classification*(2nd ed.), New York: John Wiley & Sons

The **City of New York**, usually called either **New York City** (**NYC**) or simply **New York** (**NY**), is the most populous city in the United States. With an estimated 2018 population of 8,398,748 distributed over a land area of about 302.6 square miles (784 km^{2}), New York is also the most densely populated major city in the United States. Located at the southern tip of the state of New York, the city is the center of the New York metropolitan area, the largest metropolitan area in the world by urban landmass and one of the world's most populous megacities, with an estimated 20,320,876 people in its 2017 Metropolitan Statistical Area and 23,876,155 residents in its Combined Statistical Area. A global power city, New York City has been described as the cultural, financial, and media capital of the world, and exerts a significant impact upon commerce, entertainment, research, technology, education, politics, tourism, art, fashion, and sports. The city's fast pace has inspired the term *New York minute*. Home to the headquarters of the United Nations, New York is an important center for international diplomacy.

- Shanks, D. R., Tunney, R. J., & McCarthy, J. D. (2002). A re‐examination of probability matching and rational choice.
*Journal of Behavioral Decision Making*, 15(3), 233-250.

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