**Restricted Maximum Likelihood (REML)**

In statistics, the restricted (or residual, or reduced) maximum likelihood (REML) approach is a particular form of maximum likelihood estimation which does not base estimates on a maximum likelihood fit of all the information, but instead uses a likelihood function calculated from a transformed set of data, so that nuisance parameters have no effect. In the case of variance component estimation, the original data set is replaced by a set of contrasts calculated from the data, and the likelihood function is calculated from the probability distribution of these contrasts, according to the model for the complete data set. In particular, REML is used as a method for fitting linear mixed models. In contrast to the earlier maximum likelihood estimation, REML can produce unbiased estimates of variance and covariance parameters. The idea underlying REML estimation was put forward by M. S. Bartlett in 1937. The first description of the approach applied to estimating components of variance in unbalanced data was by Desmond Patterson and Robin Thompson of the University of Edinburgh, although they did not use the term REML. A review of the early literature was given by Harville. REML estimation is available in a number of general-purpose statistical software packages, including Genstat (the REML directive), SAS (the MIXED procedure), SPSS (the MIXED command), Stata (the mixed command), and R (the lme4 and older nlme packages), as well as in more specialist packages such as MLwiN, HLM, ASReml, Statistical Parametric Mapping and CropStat. … **Machine Reasoning**

Imagine that the toddler who was once pushing the glass off the table now understands the physics of movement and gravity. Even without having encountered this situation before, the toddler can surmise what will inevitably happen. The toddler can apply the same logic to another object on the table – adapting that knowledge and applying it to a TV remote on the same table – because he knows why it happens. That’s machine reasoning. Machine reasoning is a more human-like approach within the AI spectrum that’s highly relevant to big data investigations, therefore it allows for more flexible adaptation than machine learning. However, machine reasoning requires heuristics and curation, which is usually done by knowledgeable domain experts. This process is where machine reasoning may be difficult for companies to scale – it requires a great deal of expert human effort for this curation to take place. Machine reasoning is best applied in deterministic scenarios – that is, determining whether something is true or not, or whether something will happen or not. Knowing this, it’s clear why machine learning and machine reasoning work well together. … **directional Bat Algorithm (dBA)**

Bat algorithm (BA) is a recent optimization algorithm based on swarm intelligence and inspiration from the echolocation behavior of bats. One of the issues in the standard bat algorithm is the premature convergence that can occur due to the low exploration ability of the algorithm under some conditions. To overcome this deficiency, directional echolocation is introduced to the standard bat algorithm to enhance its exploration and exploitation capabilities. In addition to such directional echolocation, three other improvements have been embedded into the standard bat algorithm to enhance its performance. The new proposed approach, namely the directional Bat Algorithm (dBA), has been then tested using several standard and non-standard benchmarks from the CEC’2005 benchmark suite. The performance of dBA has been compared with ten other algorithms and BA variants using non-parametric statistical tests. The statistical test results show the superiority of the directional bat algorithm. …

# If you did not already know

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Sep 2018

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