In a dramatic production, an ensemble cast is one that comprises many principal actors and performers who are typically assigned roughly equal amounts of screen time.[1] The term is also used interchangeably to refer to a production (typically film) with a large cast or a cast with several prominent performers.[2]

Ensemble casts in film were introduced as early as September 1916, with D. W. Griffith's silent epic film Intolerance, featuring four separate though parallel plots.[4] The film follows the lives of several characters over hundreds of years, across different cultures and time periods.[5] The unification of different plot lines and character arcs is a key characteristic of ensemble casting in film; whether it is a location, event, or an overarching theme that ties the film and characters together.[4]


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Films that feature ensembles tend to emphasize the interconnectivity of the characters, even when the characters are strangers to one another.[6] The interconnectivity is often shown to the audience through examples of the "six degrees of separation" theory, and allows them to navigate through plot lines using cognitive mapping.[6] Examples of this method, where the six degrees of separation is evident in films with an ensemble cast, are in productions such as Love Actually, Crash, and Babel, which all have strong underlying themes interwoven within the plots that unify each film.[4]

The Avengers, X-Men, and Justice League are three examples of ensemble casts in the superhero genre.[7] In The Avengers, there is no need for a single central protagonist as each character shares equal importance in the narrative, successfully balancing the ensemble cast.[8] Referential acting is a key factor in executing this balance, as ensemble cast members "play off each other rather than off reality".[3]

Hollywood movies with ensemble casts tend to use numerous actors of high renown and/or prestige, instead of one or two "big stars" and a lesser-known supporting cast.[citation needed] Filmmakers known for their use of ensemble casts include Quentin Tarantino, Wes Anderson, and Paul Thomas Anderson among others.

Ensemble casting also became more popular in television series because it allows flexibility for writers to focus on different characters in different episodes. In addition, the departure of players is less disruptive than would be the case with a regularly structured cast. The television series The Golden Girls and Friends are archetypal examples of ensemble casts in American sitcoms. The science-fiction mystery drama Lost features an ensemble cast. Ensemble casts of 20 or more actors are common in soap operas, a genre that relies heavily on the character development of the ensemble.[9] The genre also requires continuous expansion of the cast as the series progresses, with soap operas such as General Hospital, Days of Our Lives, The Young and The Restless, and The Bold and the Beautiful staying on air for decades.[10]

An example of a success for television in ensemble casting is the Emmy Award-winning HBO series Game of Thrones. The fantasy series features one of the largest ensemble casts on the small screen.[11] The series is notorious for major character deaths, resulting in constant changes within the ensemble.[12]

In statistics and machine learning, ensemble methods use multiple learning algorithms to obtain better predictive performance than could be obtained from any of the constituent learning algorithms alone.[1][2][3]Unlike a statistical ensemble in statistical mechanics, which is usually infinite, a machine learning ensemble consists of only a concrete finite set of alternative models, but typically allows for much more flexible structure to exist among those alternatives.

Supervised learning algorithms perform the task of searching through a hypothesis space to find a suitable hypothesis that will make good predictions with a particular problem.[4] Even if the hypothesis space contains hypotheses that are very well-suited for a particular problem, it may be very difficult to find a good one. Ensembles combine multiple hypotheses to form a (hopefully) better hypothesis. The term ensemble is usually reserved for methods that generate multiple hypotheses using the same base learner.[according to whom?]The broader term of multiple classifier systems also covers hybridization of hypotheses that are not induced by the same base learner.[citation needed]

Evaluating the prediction of an ensemble typically requires more computation than evaluating the prediction of a single model. In one sense, ensemble learning may be thought of as a way to compensate for poor learning algorithms by performing a lot of extra computation. On the other hand, the alternative is to do a lot more learning on one non-ensemble system. An ensemble system may be more efficient at improving overall accuracy for the same increase in compute, storage, or communication resources by using that increase on two or more methods, than would have been improved by increasing resource use for a single method. Fast algorithms such as decision trees are commonly used in ensemble methods (for example, random forests), although slower algorithms can benefit from ensemble techniques as well.

Empirically, ensembles tend to yield better results when there is a significant diversity among the models.[5][6] Many ensemble methods, therefore, seek to promote diversity among the models they combine.[7][8] Although perhaps non-intuitive, more random algorithms (like random decision trees) can be used to produce a stronger ensemble than very deliberate algorithms (like entropy-reducing decision trees).[9] Using a variety of strong learning algorithms, however, has been shown to be more effective than using techniques that attempt to dumb-down the models in order to promote diversity.[10] It is possible to increase diversity in the training stage of the model using correlation for regression tasks [11] or using information measures such as cross entropy for classification tasks.[12]

While the number of component classifiers of an ensemble has a great impact on the accuracy of prediction, there is a limited number of studies addressing this problem. A priori determining of ensemble size and the volume and velocity of big data streams make this even more crucial for online ensemble classifiers. Mostly statistical tests were used for determining the proper number of components. More recently, a theoretical framework suggested that there is an ideal number of component classifiers for an ensemble such that having more or less than this number of classifiers would deteriorate the accuracy. It is called "the law of diminishing returns in ensemble construction." Their theoretical framework shows that using the same number of independent component classifiers as class labels gives the highest accuracy.[14][15]

The Bayes optimal classifier is a classification technique. It is an ensemble of all the hypotheses in the hypothesis space. On average, no other ensemble can outperform it.[16] The Naive Bayes classifier is a version of this that assumes that the data is conditionally independent on the class and makes the computation more feasible. Each hypothesis is given a vote proportional to the likelihood that the training dataset would be sampled from a system if that hypothesis were true. To facilitate training data of finite size, the vote of each hypothesis is also multiplied by the prior probability of that hypothesis. The Bayes optimal classifier can be expressed with the following equation:

where y {\displaystyle y} is the predicted class, C {\displaystyle C} is the set of all possible classes, H {\displaystyle H} is the hypothesis space, P {\displaystyle P} refers to a probability, and T {\displaystyle T} is the training data. As an ensemble, the Bayes optimal classifier represents a hypothesis that is not necessarily in H {\displaystyle H} . The hypothesis represented by the Bayes optimal classifier, however, is the optimal hypothesis in ensemble space (the space of all possible ensembles consisting only of hypotheses in H {\displaystyle H} ).

Bootstrap aggregation (bagging) involves training an ensemble on bootstrapped data sets. A bootstrapped set is created by selecting from original training data set with replacement. Thus, a bootstrap set may contain a given example zero, one, or multiple times. Ensemble members can also have limits on the features (e.g., nodes of a decision tree), to encourage exploring of diverse features.[17] The variance of local information in the bootstrap sets and feature considerations promote diversity in the ensemble, and can strengthen the ensemble.[18] To reduce overfitting, a member can be validated using the out-of-bag set (the examples that are not in its bootstrap set).[19]

Inference is done by voting of predictions of ensemble members, called aggregation. It is illustrated below with an ensemble of four decision trees. The query example is classified by each tree. Because three of the four predict the positive class, the ensemble's overall classification is positive. Random forests like the one shown are a common application of bagging.

The question with any use of Bayes' theorem is the prior, i.e., the probability (perhaps subjective) that each model is the best to use for a given purpose. Conceptually, BMA can be used with any prior. R packages ensembleBMA[21] and BMA[22] use the prior implied by the Bayesian information criterion, (BIC), following Raftery (1995).[23] R package BAS supports the use of the priors implied by Akaike information criterion (AIC) and other criteria over the alternative models as well as priors over the coefficients.[24]

Bayesian model combination (BMC) is an algorithmic correction to Bayesian model averaging (BMA). Instead of sampling each model in the ensemble individually, it samples from the space of possible ensembles (with model weights drawn randomly from a Dirichlet distribution having uniform parameters). This modification overcomes the tendency of BMA to converge toward giving all the weight to a single model. Although BMC is somewhat more computationally expensive than BMA, it tends to yield dramatically better results. BMC has been shown to be better on average (with statistical significance) than BMA and bagging.[29] 006ab0faaa

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