jare用java实现了论文《Semi-Supervised Recursive Autoencoders for Predicting Sentiment Distributions》中提出的算法——基于半监督的递归自动编码机，用来预测情感分类。详情可查看论文内容，代码git地址为：https://github.com/sancha/jrae。
鸟瞰
主函数训练流程
FineTunableTheta tunedTheta = rae.train(params);// 根据参数和数据训练神经网络权重
tunedTheta.Dump(params.ModelFile); System.out.println("RAE trained. The model file is saved in "
+ params.ModelFile);
// 特征抽取器
RAEFeatureExtractor fe = new RAEFeatureExtractor(params.EmbeddingSize,
tunedTheta, params.AlphaCat, params.Beta, params.CatSize,
params.Dataset.Vocab.size(), rae.f);
// 获取训练数据
List<LabeledDatum<Double, Integer>> classifierTrainingData = fe
.extractFeaturesIntoArray(params.Dataset, params.Dataset.Data,
params.TreeDumpDir);
// 测试精度
SoftmaxClassifier<Double, Integer> classifier = new SoftmaxClassifier<Double, Integer>();
Accuracy TrainAccuracy = classifier.train(classifierTrainingData);
System.out.println("Train Accuracy :" + TrainAccuracy.toString());
几个重要的接口以及实现类
1、Minimizer<T extends DifferentiableFunction>
public interface Minimizer<T extends DifferentiableFunction> {
/**
* Attempts to find an unconstrained minimum of the objective
* <code>function</code> starting at <code>initial</code>, within
* <code>functionTolerance</code>.
*
* @param function the objective function
* @param functionTolerance a <code>double</code> value
* @param initial a initial feasible point
* @return Unconstrained minimum of function
*/
double[] minimize(T function, double functionTolerance, double[] initial);
double[] minimize(T function, double functionTolerance, double[] initial, int maxIterations);
}
如其所述，该接口用来找到给定目标函数的最小化极值，目标函数必须是处处可微的，并实现DifferentiableFunction接口。functionTolerance是最小误差，initial是初始点，maxIterations是最大迭代次数。
public interface DifferentiableFunction extends Function {
double[] derivativeAt(double[] x);
}
public interface Function {
int dimension();
double valueAt(double[] x);
}
QNMinimizer类实现了该接口，利用L-BFGS优化算法对目标函数进行优化，下面是算法的注释：
/**
* This code is part of the Stanford NLP Toolkit.
*
*
* An implementation of L-BFGS for Quasi Newton unconstrained minimization.
*
* The general outline of the algorithm is taken from: <blockquote> <i>Numerical
* Optimization</i> (second edition) 2006 Jorge Nocedal and Stephen J. Wright
* </blockquote> A variety of different options are available.
*
* <h3>LINESEARCHES</h3>
*
* BACKTRACKING: This routine simply starts with a guess for step size of 1. If
* the step size doesn't supply a sufficient decrease in the function value the
* step is updated through step = 0.1*step. This method is certainly simpler,
* but doesn't allow for an increase in step size, and isn't well suited for
* Quasi Newton methods.
*
* MINPACK: This routine is based off of the implementation used in MINPACK.
* This routine finds a point satisfying the Wolfe conditions, which state that
* a point must have a sufficiently smaller function value, and a gradient of
* smaller magnitude. This provides enough to prove theoretically quadratic
* convergence. In order to find such a point the linesearch first finds an
* interval which must contain a satisfying point, and then progressively
* reduces that interval all using cubic or quadratic interpolation.
*
*
* SCALING: L-BFGS allows the initial guess at the hessian to be updated at each
* step. Standard BFGS does this by approximating the hessian as a scaled
* identity matrix. To use this method set the scaleOpt to SCALAR. A better way
* of approximate the hessian is by using a scaling diagonal matrix. The
* diagonal can then be updated as more information comes in. This method can be
* used by setting scaleOpt to DIAGONAL.
*
*
* CONVERGENCE: Previously convergence was gauged by looking at the average
* decrease per step dividing that by the current value and terminating when
* that value because smaller than TOL. This method fails when the function
* value approaches zero, so two other convergence criteria are used. The first
* stores the initial gradient norm |g0|, then terminates when the new gradient
* norm, |g| is sufficiently smaller: i.e., |g| < eps*|g0| the second checks
* if |g| < eps*max( 1 , |x| ) which is essentially checking to see if the
* gradient is numerically zero.
*
* Each of these convergence criteria can be turned on or off by setting the
* flags: <blockquote><code>
* private boolean useAveImprovement = true;
* private boolean useRelativeNorm = true;
* private boolean useNumericalZero = true;
* </code></blockquote>
*
* To use the QNMinimizer first construct it using <blockquote><code>
* QNMinimizer qn = new QNMinimizer(mem, true)
* </code>
* </blockquote> mem - the number of previous estimate vector pairs to store,
* generally 15 is plenty. true - this tells the QN to use the MINPACK
* linesearch with DIAGONAL scaling. false would lead to the use of the criteria
* used in the old QNMinimizer class.
*/
OK，可以结合我前面文章，了解L-BFGS算法的原理，然后该类实现了这个算法，并且在某些细节上做了一些修改。具体的实现算法先略去不议，日后再说。
2、DifferentiableFunction
DifferentiableFunction定义上面已经给出，对应一个可微的函数。抽象类MemoizedDifferentiableFunction实现了这个接口，封装了一些通用的代码：
public abstract class MemoizedDifferentiableFunction implements DifferentiableFunction {
protected double[] prevQuery, gradient;
protected double value;
protected int evalCount;
protected void initPrevQuery()
{
prevQuery = new double[ dimension() ];
}
protected boolean requiresEvaluation(double[] x)
{
if(DoubleArrays.equals(x,prevQuery))
return false;
System.arraycopy(x, 0, prevQuery, 0, x.length);
evalCount++;
return true;
}
@Override
public double[] derivativeAt(double[] x){
if(DoubleArrays.equals(x,prevQuery))
return gradient;
valueAt(x);
return gradient;
}
}
封装的通用方法为，保存了上次请求的参数，如果传入参数已经被请求过，直接返回结果即可；保存了执行请求的次数；实现了求导流程，首先调用valueAt求得当前值$f(x)$，然后返回梯度（导数），valueAt由子类实现，即约定子类在计算$f(x)$的时候顺便计算好了$f'(x)$，然后保存到gradient变量中。
两个子类分别为RAECost和SoftmaxCost。
SoftmaxCost类表示，在给定样本的情况下，计算出给定权重的误差，导数指明减小误差的梯度。对应的是一个2层的网络，输入层为features(特征），输出层为label，并且转换函数为softmax（能量函数）。
RAECost类表示，在给定样本的情况下，计算出给定权重的误差，误差包括生成递归树的误差与label分类的误差只和，导数指明梯度，也是两者梯度之和。
在调用Minimizer接口进行优化时，传入的第一个参数即是RAECost对象，优化完毕时即是训练完毕时。
参考文献：
http://www.socher.org/index.php/Main/Semi-SupervisedRecursiveAutoencodersForPredictingSentimentDistributions