A popular solution to the computational problem is to use some form of stochastic gradient descent, such as that provided by the back-propagation algrorithm.Trevor Hastie
During the course of fitting by least squares, the residuals can sometimes develop marked patterns.Trevor Hastie
For any fixed size training set, an optimal model complexity can be determined by cross-validation or using a test set.Trevor Hastie
The general prediction problem assumes that we have a measurement ( X = X1, X2...Xp) of a real valued random input vector X, and we wish to predict the value of a random output variable Y.Trevor Hastie
Conceptually, this bias-variance tradeoff appears to be a necessary aspect of any induction scheme.Trevor Hastie
In summary, with many predictors, especially with highly correlated predictors, there is a lot of sampling variability in the least squares fit, resulting in overfitting and consequently poor predictions on future data.Trevor Hastie
The success of learning with deep networks is attributed to many factors, and still not fully understood.Trevor Hastie
It turns out that with least squares estimation, simple formulas exist for these quantities, and to our knowledge these formulas are used almost exclusively in practice.Trevor Hastie
Percentile bootstrap works well when the sampling distribution of θ̂ is skewed or when its variability depends on the point estimate itself.Trevor Hastie
High-dimensional data have their own special characteristics and challenges, requiring somewhat different tools.Trevor Hastie
Some of the more promising and popular methods include artificial neural networks, decision trees, random forests, and gradient boosting.Trevor Hastie
For real-valued outputs, common choices of loss function include squared error loss and absolute error.Trevor Hastie