"A good estimator will be unbiased and will converge more and more closely (in the long run) on the true value as the sample size increases. Such estimators are known as consistent. But consistency is not all we can ask of an estimator. In estimating the central tendency of a distribution, we are not confined to using the arithmetic mean; we might just as well use the median. Given a choice of possible estimators, all consistent in the sense just defined, we can see whether there is anything which recommends the choice of one rather than another. The thing which at once suggests itself is the sampling variance of the different estimators, since an estimator with a small sampling variance will be less likely to differ from the true value by a large amount than an estimator whose sampling variance is large." (Michael J Moroney, "Facts from Figures", 1951)
"Sometimes the most important fit statistic you can get is ‘convergence not met’ - it can tell you something is wrong with your model." (Oliver Schabenberger, "Applied Statistics in Agriculture Conference", 2006)
"The central limit theorem differs from laws of large numbers because random variables vary and so they differ from constants such as population means. The central limit theorem says that certain independent random effects converge not to a constant population value such as the mean rate of unemployment but rather they converge to a random variable that has its own Gaussian bell-curve description." (Bart Kosko, "Noise", 2006)
"Each learning algorithm dictates a certain model that comes with a set of assumptions. This inductive bias leads to error if the assumptions do not hold for the data. Learning is an ill-posed problem and with finite data, each algorithm converges to a different solution and fails under different circumstances. The performance of a learner may be fine-tuned to get the highest possible accuracy on a validation set, but this finetuning is a complex task and still there are instances on which even the best learner is not accurate enough. The idea is that there may be another base-learner learner that is accurate on these. By suitably combining multiple base learners then, accuracy can be improved." (Ethem Alpaydin, "Introduction to Machine Learning" 2nd Ed, 2010)
"Regularization works because it is the sum of the coefficients of the predictor variables, therefore it’s important that they’re on the same scale or the regularization may find it difficult to converge, and variables with larger absolute coefficient values will greatly influence it, generating an infective regularization. It’s good practice to standardize the predictor values or bind them to a common min‐max, such as the [‐1,+1] range." (Luca Massaron & John P Mueller, "Python for Data Science For Dummies", 2015)
"Cluster analysis refers to the grouping of observations so that the objects within each cluster share similar properties, and properties of all clusters are independent of each other. Cluster algorithms usually optimize by maximizing the distance among clusters and minimizing the distance between objects in a cluster. Cluster analysis does not complete in a single iteration but goes through several iterations until the model converges. Model convergence means that the cluster memberships of all objects converge and don’t change with every new iteration." (Danish Haroon, "Python Machine Learning Case Studies", 2017)
"Theoretically, the normal distribution is most famous because many distributions converge to it, if you sample from them enough times and average the results. This applies to the binomial distribution, Poisson distribution and pretty much any other distribution you’re likely to encounter (technically, any one for which the mean and standard deviation are finite)." (Field Cady, "The Data Science Handbook", 2017)
"Early stopping and regularization can ensure network generalization when you apply them properly. [...] With early stopping, the choice of the validation set is also important. The validation set should be representative of all points in the training set. When you use Bayesian regularization, it is important to train the network until it reaches convergence. The sum-squared error, the sum-squared weights, and the effective number of parameters should reach constant values when the network has converged. With both early stopping and regularization, it is a good idea to train the network starting from several different initial conditions. It is possible for either method to fail in certain circumstances. By testing several different initial conditions, you can verify robust network performance." (Mark H Beale et al, "Neural Network Toolbox™ User's Guide", 2017)
"The high generalization error in a neural network may be caused by several reasons. First, the data itself might have a lot of noise, in which case there is little one can do in order to improve accuracy. Second, neural networks are hard to train, and the large error might be caused by the poor convergence behavior of the algorithm. The error might also be caused by high bias, which is referred to as underfitting. Finally, overfitting (i.e., high variance) may cause a large part of the generalization error. In most cases, the error is a combination of more than one of these different factors." (Charu C Aggarwal, "Neural Networks and Deep Learning: A Textbook", 2018)
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