梯度下降法

使用 AdaGrad 拟合 `y=wx+b` 直线

<script src="https://cdn.bootcss.com/tensorflow/0.14.1/tf.min.js"></script>

  // Generate Traning data set
  function TargetFx(x) {
    return new Array(x.length).fill().map((v,i)=>{
      return 3*x[i] + 1 + (0.1 * (2 * Math.random() - 1));
    });
  }
  const tarin_x = new Array(200).fill().map((v,i)=>+(0.01*i).toFixed(2));
  const tarin_y = TargetFx(tarin_x);

  const tensor_x = tf.tensor(tarin_x, [tarin_x.length, 1]);
  const tensor_y = tf.tensor(tarin_y, [tarin_y.length, 1]);

  // Initial variable.
  const w = tf.variable(tf.scalar(Math.random()));
  const b = tf.variable(tf.scalar(Math.random()));

  // fx = w*x + b
  const ModelFx = x => w.mul(x).add(b);

  const iterations = 200;
  const learningRate = 1;

  // https://js.tensorflow.org/api/0.14.1/#train.adagrad
  const optimizer = tf.train.adagrad(learningRate);
  // Loss = mean of sum (y-y')^2 
  const loss = (pred, label) => pred.sub(label).square().mean();

  for (let iter = 0; iter < iterations; iter++) {
    optimizer.minimize(() => {
      const loss_var = loss(ModelFx(tensor_x), tensor_y);
      // loss_var.print();
      return loss_var;
    }, true).print()
  }

使用 sgd 拟合 `y=ax²+bx+c` 曲线

  // Generate Traning data set
  function TargetFx(x) {
    return new Array(x.length).fill().map((v,i)=>{
      return Math.pow(x[i],2) + 3*x[i] + 1 + (0.1 * (2 * Math.random() - 1));
    });
  }
  const tarin_x = new Array(200).fill().map((v,i)=>+(0.01*i).toFixed(2));
  const tarin_y = TargetFx(tarin_x);

  const tensor_x = tf.tensor(tarin_x, [tarin_x.length, 1]);
  const tensor_y = tf.tensor(tarin_y, [tarin_y.length, 1]);

  // Initial variable.
  const a = tf.variable(tf.scalar(Math.random()));
  const b = tf.variable(tf.scalar(Math.random()));
  const c = tf.variable(tf.scalar(Math.random()));

  // fx = ax²+bx+c
  const ModelFx = x => tf.tidy(() =>a.mul(x.square()).add(b.mul(x)).add(c));

  const iterations = 200;
  const learningRate = 0.1;

  // https://js.tensorflow.org/api/0.14.1/#train.sgd
  const optimizer = tf.train.sgd(learningRate);
  // Loss = mean of sum (y-y')^2 
  const loss = (pred, label) => pred.sub(label).square().mean();

  for (let iter = 0; iter < iterations; iter++) {
    optimizer.minimize(() => {
      const loss_var = loss(ModelFx(tensor_x), tensor_y);
      // loss_var.print();
      return loss_var;
    }, true).print()
  }
  const test_x = tf.tensor([0.5,1,1.5],[3,1]);
  ModelFx(test_x).print();

使用tf.model拟合曲线

// Generate Traning data set
  function TargetFx(x) {
    return new Array(x.length).fill().map((v,i)=>{
      return 3*x[i] + 1 + (0.1 * (2 * Math.random() - 1));
    });
  }
  const tarin_x = new Array(200).fill().map((v,i)=>+(0.01*i).toFixed(2));
  const tarin_y = TargetFx(tarin_x);

  const tensor_x = tf.tensor(tarin_x, [tarin_x.length, 1]);
  const tensor_y = tf.tensor(tarin_y, [tarin_y.length, 1]);

  async function trainLinear() {
    const model = tf.sequential();
    model.add(tf.layers.dense({
      units: 1,
      inputShape: [1]
    }));

    model.compile({
      loss: 'meanSquaredError',
      optimizer: 'sgd'
    });
    
    await model.fit(tensor_x, tensor_y, {
      epochs: 100
    });

    model.predict(tf.tensor2d([1,2,3,4], [4, 1])).print();
  }
  
  trainLinear();
  
  /*
  当输入x为：[1,2,3,4]，输出为
  Tensor
    [[4.0171099 ],
     [6.9510436 ],
     [9.8849773 ],
     [12.8189116]]
  对比 y = 3x+1, 还是比较好地拟合到直线.
  */