We can then learn a latent representation of the data X as well as the kernel hyperparameters by optimizing the log-likelihood.
A quadratic optimization problem was formulated, in which optimal w was sought to optimize the log likelihood for estimating variance components in REML.
The former methods typically involve building a position-weight matrix (PWM) from sequence data, and local search techniques such as expectation maximization or Gibbs sampling are used to optimize the log likelihood ratio until convergence or a maximum number of iterations is reached.
We can use numerical methods such as the quasi-Newton algorithm to numerically optimize the log-likelihood function given in Eq. (24), to get the maximum likelihood estimates of the parameters α,λ,a,b.
The latter can be written as (3) To optimize the log-likelihood, nonlinear optimisers such as scaled conjugate gradient (Nabney, 2001) can be used after having determined the gradient of the log-likelihood with respect to the latent points and the kernel parameters.
The network structure is determined by greedily optimizing the conditional log-likelihood: where Pr[ x] is flat (i.e. Pr[ x=0]=Pr[ x=1]=0.5) since we sample foreground and background positions equally.
For optimizing the final optimal tree, we impose a much stricter constraint (log-likelihood difference = 0.0001).
As an alternative to optimizing directly the log-likelihood function (19), the EM algorithm [40] is well suited to solve optimization problems for mixture models and is simple to implement.
Beta coefficients were calculated by optimizing either the log-likelihood (NFS and CPSO) or a penalized maximum likelihood function (LASSO) through several iterations using bootstrap (NFS and CPSO) or a 10-fold cross-validation (LASSO) scheme [ 27, 28].
For θ, we follow the classical approach to derive updates by optimizing the expected complete data (observed and latent) log-likelihood, conditioning on the previous estimates of ξ.
