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Given the statistical model which generates a set of observed data, a set of unobserved latent data or missing values, and a vector of unknown parameters , along with a likelihood function (;,) = (,), the maximum likelihood estimate (MLE) of the unknown parameters is determined by maximizing the marginal likelihood of the observed data
The EM algorithm consists of two steps: the E-step and the M-step. Firstly, the model parameters and the () can be randomly initialized. In the E-step, the algorithm tries to guess the value of () based on the parameters, while in the M-step, the algorithm updates the value of the model parameters based on the guess of () of the E-step.
where are the input samples and () is the kernel function (or Parzen window). is the only parameter in the algorithm and is called the bandwidth. This approach is known as kernel density estimation or the Parzen window technique. Once we have computed () from the equation above, we can find its local maxima using gradient ascent or some other optimization technique. The problem with this ...
The probability distribution for the sex of the sample can now be determined: = = (()), where = and = are the parameters of normal distribution which have been previously determined from the training set. Note that a value greater than 1 is OK here – it is a probability density rather than a probability, because height is a continuous ...
It is believed that the data become more linearly separable in the feature space, and hence, linear algorithms can be applied on the data with a higher success. The kernel matrix can thus be analyzed in order to find the optimal number of clusters. [12] The method proceeds by the eigenvalue decomposition of the kernel matrix.
Random sample consensus (RANSAC) is an iterative method to estimate parameters of a mathematical model from a set of observed data that contains outliers, when outliers are to be accorded no influence [clarify] on the values of the estimates. Therefore, it also can be interpreted as an outlier detection method. [1]
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Global optimization is a branch of applied mathematics and numerical analysis that attempts to find the global minima or maxima of a function or a set of functions on a given set. It is usually described as a minimization problem because the maximization of the real-valued function g ( x ) {\displaystyle g(x)} is equivalent to the minimization ...