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Then, "independent and identically distributed" implies that an element in the sequence is independent of the random variables that came before it. In this way, an i.i.d. sequence is different from a Markov sequence , where the probability distribution for the n th random variable is a function of the previous random variable in the sequence ...
The data has to conform to some standards, such as data being exchangeable (a slightly weaker assumption than the standard IID imposed in standard machine learning). For conformal prediction, a n% prediction region is said to be valid if the truth is in the output n% of the time. [3]
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:
The notation AR(p) refers to the autoregressive model of order p.The AR(p) model is written as = = + where , …, are parameters and the random variable is white noise, usually independent and identically distributed (i.i.d.) normal random variables.
Most machine learning techniques are mostly designed to work on specific problem sets, under the assumption that the training and test data are generated from the same statistical distribution . However, this assumption is often dangerously violated in practical high-stake applications, where users may intentionally supply fabricated data that ...
The estimation method requires that the data are independent and identically distributed (iid). It performs well even when the distribution is asymmetric or censored . [ 1 ] EL methods can also handle constraints and prior information on parameters.
Within bayesian statistics for machine learning, kernel methods arise from the assumption of an inner product space or similarity structure on inputs. For some such methods, such as support vector machines (SVMs), the original formulation and its regularization were not Bayesian in nature.
In probability theory, a Chernoff bound is an exponentially decreasing upper bound on the tail of a random variable based on its moment generating function.The minimum of all such exponential bounds forms the Chernoff or Chernoff-Cramér bound, which may decay faster than exponential (e.g. sub-Gaussian).