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Deterministic vs. probabilistic (stochastic). A deterministic model is one in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables; therefore, a deterministic model always performs the same way for a given set of initial conditions.
A deterministic algorithm is an algorithm which, given a particular input, will always produce the same output, with the underlying machine always passing through the same sequence of states. There may be non-deterministic algorithms that run on a deterministic machine, for example, an algorithm that relies on random choices.
This is useful because it puts deterministic variables and random variables in the same formalism. The discrete uniform distribution , where all elements of a finite set are equally likely. This is the theoretical distribution model for a balanced coin, an unbiased die, a casino roulette, or the first card of a well-shuffled deck.
Thus, in a statistical model specified via mathematical equations, some of the variables do not have specific values, but instead have probability distributions; i.e. some of the variables are stochastic. In the above example with children's heights, ε is a stochastic variable; without that stochastic variable, the model would be deterministic.
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations , probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms .
Deterministic algorithms are by far the most studied and familiar kind of algorithm, as well as one of the most practical, since they can be run on real machines efficiently. Formally, a deterministic algorithm computes a mathematical function ; a function has a unique value for any input in its domain , and the algorithm is a process that ...
Finally, there is a need to specify each event's likelihood of happening; this is done using the probability measure function, P. Once an experiment is designed and established, ω from the sample space Ω, all the events in F {\displaystyle \scriptstyle {\mathcal {F}}} that contain the selected outcome ω (recall that each event is a subset of ...
Standard examples of each, all of which are linear classifiers, are: generative classifiers: naive Bayes classifier and; linear discriminant analysis; discriminative model: logistic regression; In application to classification, one wishes to go from an observation x to a label y (or probability distribution on labels