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| -rw-r--r-- | docs/mllib-linear-methods.md | 10 | ||||
| -rw-r--r-- | docs/mllib-optimization.md | 17 |
2 files changed, 18 insertions, 9 deletions
diff --git a/docs/mllib-linear-methods.md b/docs/mllib-linear-methods.md index bc914a1899..44b7f67c57 100644 --- a/docs/mllib-linear-methods.md +++ b/docs/mllib-linear-methods.md @@ -110,12 +110,16 @@ However, L1 regularization can help promote sparsity in weights leading to small It is not recommended to train models without any regularization, especially when the number of training examples is small. +### Optimization + +Under the hood, linear methods use convex optimization methods to optimize the objective functions. MLlib uses two methods, SGD and L-BFGS, described in the [optimization section](mllib-optimization.html). Currently, most algorithm APIs support Stochastic Gradient Descent (SGD), and a few support L-BFGS. Refer to [this optimization section](mllib-optimization.html#Choosing-an-Optimization-Method) for guidelines on choosing between optimization methods. + ## Binary classification [Binary classification](http://en.wikipedia.org/wiki/Binary_classification) aims to divide items into two categories: positive and negative. MLlib -supports two linear methods for binary classification: linear support vector -machines (SVMs) and logistic regression. For both methods, MLlib supports +supports two linear methods for binary classification: linear Support Vector +Machines (SVMs) and logistic regression. For both methods, MLlib supports L1 and L2 regularized variants. The training data set is represented by an RDD of [LabeledPoint](mllib-data-types.html) in MLlib. Note that, in the mathematical formulation in this guide, a training label $y$ is denoted as @@ -123,7 +127,7 @@ either $+1$ (positive) or $-1$ (negative), which is convenient for the formulation. *However*, the negative label is represented by $0$ in MLlib instead of $-1$, to be consistent with multiclass labeling. -### Linear support vector machines (SVMs) +### Linear Support Vector Machines (SVMs) The [linear SVM](http://en.wikipedia.org/wiki/Support_vector_machine#Linear_SVM) is a standard method for large-scale classification tasks. It is a linear method as described above in equation `$\eqref{eq:regPrimal}$`, with the loss function in the formulation given by the hinge loss: diff --git a/docs/mllib-optimization.md b/docs/mllib-optimization.md index 45141c235b..4d101afca2 100644 --- a/docs/mllib-optimization.md +++ b/docs/mllib-optimization.md @@ -138,6 +138,12 @@ vertical scalability issue (the number of training features) when computing the explicitly in Newton's method. As a result, L-BFGS often achieves rapider convergence compared with other first-order optimization. +### Choosing an Optimization Method + +[Linear methods](mllib-linear-methods.html) use optimization internally, and some linear methods in MLlib support both SGD and L-BFGS. +Different optimization methods can have different convergence guarantees depending on the properties of the objective function, and we cannot cover the literature here. +In general, when L-BFGS is available, we recommend using it instead of SGD since L-BFGS tends to converge faster (in fewer iterations). + ## Implementation in MLlib ### Gradient descent and stochastic gradient descent @@ -168,10 +174,7 @@ descent. All updaters in MLlib use a step size at the t-th step equal to * `regParam` is the regularization parameter when using L1 or L2 regularization. * `miniBatchFraction` is the fraction of the total data that is sampled in each iteration, to compute the gradient direction. - -Available algorithms for gradient descent: - -* [GradientDescent](api/scala/index.html#org.apache.spark.mllib.optimization.GradientDescent) + * Sampling still requires a pass over the entire RDD, so decreasing `miniBatchFraction` may not speed up optimization much. Users will see the greatest speedup when the gradient is expensive to compute, for only the chosen samples are used for computing the gradient. ### L-BFGS L-BFGS is currently only a low-level optimization primitive in `MLlib`. If you want to use L-BFGS in various @@ -359,13 +362,15 @@ public class LBFGSExample { {% endhighlight %} </div> </div> -#### Developer's note + +## Developer's notes + Since the Hessian is constructed approximately from previous gradient evaluations, the objective function can not be changed during the optimization process. As a result, Stochastic L-BFGS will not work naively by just using miniBatch; therefore, we don't provide this until we have better understanding. -* `Updater` is a class originally designed for gradient decent which computes +`Updater` is a class originally designed for gradient decent which computes the actual gradient descent step. However, we're able to take the gradient and loss of objective function of regularization for L-BFGS by ignoring the part of logic only for gradient decent such as adaptive step size stuff. We will refactorize |