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Sobol’ sequences (also called LP τ sequences or (t, s) sequences in base 2) are a type of quasi-random low-discrepancy sequence.They were first introduced by the Russian mathematician Ilya M. Sobol’ (Илья Меерович Соболь) in 1967.
The algorithm thus obtained is called incremental gradient method and corresponds to an iteration = ( , ,) The main difference with the stochastic gradient method is that here a sequence is chosen to decide which training point is visited in the -th step. Such a sequence can be stochastic or deterministic.
The alternative follows from Mercer's theorem: an implicitly defined function exists whenever the space can be equipped with a suitable measure ensuring the function satisfies Mercer's condition. Mercer's theorem is similar to a generalization of the result from linear algebra that associates an inner product to any positive-definite matrix .
In contrast, the related method of maximum a posteriori estimation is formally the application of the maximum a posteriori (MAP) estimation approach. This is more complex than maximum likelihood sequence estimation and requires a known distribution (in Bayesian terms, a prior distribution) for the underlying signal.
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data.This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable.
Given a prime number q and prime power q m with positive integers m and d such that d ≤ q m − 1, a primitive narrow-sense BCH code over the finite field (or Galois field) GF(q) with code length n = q m − 1 and distance at least d is constructed by the following method.
ML involves the study and construction of algorithms that can learn from and make predictions on data. [3] These algorithms operate by building a model from a training set of example observations to make data-driven predictions or decisions expressed as outputs, rather than following strictly static program instructions.
A maximum length sequence (MLS) is a type of pseudorandom binary sequence.. They are bit sequences generated using maximal linear-feedback shift registers and are so called because they are periodic and reproduce every binary sequence (except the zero vector) that can be represented by the shift registers (i.e., for length-m registers they produce a sequence of length 2 m − 1).