public void Demo_010_Liner_Regression()
{
Console.WriteLine("線形回帰のデモンストレーションです");
Console.WriteLine("y = ax + bはとても素朴ですが、工夫するとニューラルネットワークに匹敵する性能を得られます。\n\n");
Console.WriteLine("今回の入力と答えの関係は下記のとおりです。");
double[,] X = new double[6, 1];
double[,] t_vec = new double[6, 1];
Console.WriteLine("\t" + "教師t\t" + "入力x");
for (int j = 0; j < 6; j++)
{
X[j, 0] = j;
if (j < 2 || 3 < j)
{
t_vec[j, 0] = -1;
}
else
{
t_vec[j, 0] = 1;
}
Console.WriteLine("\t" + t_vec[j, 0] + "\t" + X[j, 0]);
}
Console.WriteLine("\n\n" + "今回の例は明らかに y = ax + b では解けないです。");
Console.WriteLine("そこで、入力xの代わりに、ベクトルφ(x)^Tを計画行列とします。");
Console.WriteLine("ベクトルφ(x)^T = ( exp(-(x-0.5)^2/2 )/√2π , exp(-(x-2.5)^2/2 )/√2π , exp(-(x-4.5)^2/2 )/√2π )");
double[,] phi_X = new double[6, 3];
Console.WriteLine("\t" + "教師t" + "\t" + "exp(-(x-0.5)^2/2 )/√2π" + "\t" + "exp(-(x-2.5)^2/2 )/√2π" + "\t" + "exp(-(x-4.5)^2/2 )/√2π");
for (int j = 0; j < 6; j++)
{
phi_X[j, 0] = Math.Exp(-(X[j, 0] - 0.5) * (X[j, 0] - 0.5) / 2.0) / Math.Sqrt(2 * Math.PI);
phi_X[j, 1] = Math.Exp(-(X[j, 0] - 1.5) * (X[j, 0] - 2.5) / 2.0) / Math.Sqrt(2 * Math.PI);
phi_X[j, 2] = Math.Exp(-(X[j, 0] - 2.5) * (X[j, 0] - 4.5) / 2.0) / Math.Sqrt(2 * Math.PI);
Console.WriteLine("\t" + t_vec[j, 0] + "\t" + phi_X[j, 0].ToString("G2") + "\t\t\t\t" + phi_X[j, 1].ToString("G2") + "\t\t\t\t" + phi_X[j, 2].ToString("G2"));
}
Console.WriteLine("\n\n");
Console.WriteLine("学習結果を表示します。");
Console.WriteLine("ニューラルネットワークに比べて精度よく推定できていると言えます。");
double[,] w = Liner_Regression.Learning_parameter_w_column_vector(phi_X, t_vec);
double[,] y = Liner_Regression.Regression_Design_Matrix(phi_X, w);
Console.WriteLine("\t" + "教師t\t" + "予想y");
for (int j = 0; j < 6; j++)
{
Console.WriteLine("\t" + t_vec[j, 0] + "\t" + y[j, 0].ToString("G2"));
}
}
public void Demo_011_Compare_NN_SVM_LR()
{
Console.WriteLine("ニューラルネットワーク、サポートベクトルマシン、線形回帰を比較します。");
Console.WriteLine("WriteLineはPCの処理能力を使うので、裏ですべて計算してから、結果をお見せします。");
//計算時間
DateTime start_NN;
DateTime finish_NN;
TimeSpan span_NN_epoch_100k;
DateTime start_SVM;
DateTime finish_SVM;
TimeSpan span_SVM;
DateTime start_LR;
DateTime finish_LR;
TimeSpan span_LR;
List <double[, ]> list_x = new List <double[, ]>();
List <double[, ]> list_t = new List <double[, ]>();
for (int j = 0; j < 9; j++)
{
double[,] x = new double[1, 1];
x[0, 0] = j;
list_x.Add(x);
double[,] t = new double[1, 1];
if (j < 3 || 5 < j)
{
t[0, 0] = -1;
}
else
{
t[0, 0] = 1;
}
list_t.Add(t);
}
//Console.WriteLine("次は、2層のNeural Networkで試してみます");
//Console.WriteLine("第1層の計数行列はwは2行1列の行列とします");
//Console.WriteLine("活性化関数はSigmoid関数とします");
double[,] w_1 = new double[2, 1];
w_1[0, 0] = 10;
w_1[1, 0] = -10;
//Console.WriteLine("第1層の計数行列 w");
//this.Show_Matrix_Element(w_1);
double[,] b_1 = new double[2, 1];
b_1[0, 0] = -35;
b_1[1, 0] = 55;
//Console.WriteLine("第1層のバイアスベクトル b");
//this.Show_Matrix_Element(b_1);
//第一層は隠れ層なので、別のクラスです
Hidden_Layer hd_1 = new Hidden_Layer();
hd_1.Preset_1_4th_Set_w(w_1);
hd_1.Preset_2_4th_Set_b(b_1);
hd_1.Preset_3_4th_Set_Hyper_Parameter(0.01, 0, 0, 0);
hd_1.Preset_4_4th_Set_activation_Function(new Sigmoid_IFunction());
//Console.WriteLine("\n");
//Console.WriteLine("第2層の計数行列はwは1行2列の行列とします");
//Console.WriteLine("活性化関数は、第2層はHyperbolic_Tangent関数とします");
double[,] w_2 = new double[1, 2];
w_2[0, 0] = 20;
w_2[0, 1] = 20;
//Console.WriteLine("第2層の計数行列 w");
//this.Show_Matrix_Element(w_2);
double[,] b_2 = new double[1, 1];
b_2[0, 0] = -30;
//Console.WriteLine("第2層のバイアスベクトル b");
//this.Show_Matrix_Element(b_2);
//Console.WriteLine("\n\n");
Regression_Final_Layer rfl_2 = new Regression_Final_Layer();
rfl_2.Preset_1_4th_Set_w(w_2);
rfl_2.Preset_2_4th_Set_b(b_2);
rfl_2.Preset_3_4th_Set_Hyper_Parameter(0.001, 0, 0, 0);
rfl_2.Preset_4_4th_Set_activation_Function(new Hyperbolic_Tangent_IFunction());
//Console.WriteLine("\n\n");
int epoch = 1000;
double[] error = new double[list_x.Count];
//double max_error = 0;
//int max_k = 0;
start_NN = DateTime.Now;
for (int j = 0; j < list_x.Count * epoch; j++)
{
/*
* //Console.WriteLine("epoch" + "\t" + j);
* for (int k = 0; k < list_x.Count; k++)
* {
* hd_1.Step_1_3rd_Forward_Propagation(list_x[k]);
* rfl_2.Step_1_3rd_Forward_Propagation(hd_1.Get_f_wx_plus_b());
* error[k] = Math.Abs(rfl_2.Get_f_wx_plus_b()[0, 0] - list_t[k][0, 0]);
* //Console.WriteLine(k + "\t" + error[k].ToString("G3") + "\t" + list_t[k][0, 0] + "\t" + rfl_2.Get_f_wx_plus_b()[0, 0].ToString("G3") + "\t" + hd_1.Get_f_wx_plus_b()[0, 0].ToString("G3") + "\t" + hd_1.Get_f_wx_plus_b()[1, 0].ToString("G3"));
* }
*
* max_k = 0;
* max_error = error[0];
* for (int k = 1; k < list_x.Count; k++)
* {
* if (max_error < error[k])
* {
* max_error = error[k];
* max_k = k;
* }
* }
* //Console.WriteLine("Max error is No." + max_k);
* //Console.WriteLine(" ");
*/
//順伝搬
hd_1.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl_2.Step_1_3rd_Forward_Propagation(hd_1.Get_f_wx_plus_b());
//逆伝搬
rfl_2.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_t.Count]);
//hd_1.Step_2_3rd_Calculate_Delta(rfl_2.Get_w(), rfl_2.Get_delta());
//パラメータの更新
rfl_2.Step_3_3rd_Update();
//hd_1.Step_3_3rd_Update();
}
finish_NN = DateTime.Now;
span_NN_epoch_100k = finish_NN - start_NN;
double[,] y_NN = new double[list_x.Count, 1];
for (int j = 0; j < 9; j++)
{
//順伝搬
hd_1.Step_1_3rd_Forward_Propagation(list_x[j]);
rfl_2.Step_1_3rd_Forward_Propagation(hd_1.Get_f_wx_plus_b());
y_NN[j, 0] = rfl_2.Get_f_wx_plus_b()[0, 0];
}
//SVM、線形回帰の計画行列を定義します。
double[,] X = new double[9, 1];
double[,] t_vec = new double[9, 1];
//Console.WriteLine("\t" + "入力x\t" + "教師t");
for (int j = 0; j < 9; j++)
{
X[j, 0] = j;
if (j < 3 || 5 < j)
{
t_vec[j, 0] = -1;
}
else
{
t_vec[j, 0] = 1;
}
//Console.WriteLine("\t" + X[j, 0] + "\t" + t_vec[j, 0] + "");
}
//SVMの学習です
start_SVM = DateTime.Now;
double[,] variance_covariance = Design_Matrix.Variance_Covariance_Matrix(X);
//係数Aを学習する
double[,] Coefficient_A = Support_Vector_Machine.Learned_Coefficient_A(t_vec, X, new Power_of_10_IKernel(), variance_covariance);
finish_SVM = DateTime.Now;
span_SVM = finish_SVM - start_SVM;
double[,] classified = Support_Vector_Machine.Classification_Design_Matrix(t_vec, X, new Power_of_10_IKernel(), variance_covariance, Coefficient_A, X);
//線形回帰用の計画行列です。
double[,] phi_X = new double[9, 3];
//Console.WriteLine("\t" + "教師t" + "\t" + "exp(-(x-0.5)^2/2 )/√2π" + "\t" + "exp(-(x-2.5)^2/2 )/√2π" + "\t" + "exp(-(x-4.5)^2/2 )/√2π");
for (int j = 0; j < 9; j++)
{
phi_X[j, 0] = Math.Exp(-(X[j, 0] - 1) * (X[j, 0] - 1) / 2.0) / Math.Sqrt(2 * Math.PI);
phi_X[j, 1] = Math.Exp(-(X[j, 0] - 4) * (X[j, 0] - 4) / 2.0) / Math.Sqrt(2 * Math.PI);
phi_X[j, 2] = Math.Exp(-(X[j, 0] - 7) * (X[j, 0] - 7) / 2.0) / Math.Sqrt(2 * Math.PI);
//Console.WriteLine("\t" + t_vec[j, 0] + "\t" + phi_X[j, 0].ToString("G2") + "\t\t\t\t" + phi_X[j, 1].ToString("G2") + "\t\t\t\t" + phi_X[j, 2].ToString("G2"));
}
start_LR = DateTime.Now;
double[,] w = Liner_Regression.Learning_parameter_w_column_vector(phi_X, t_vec);
finish_LR = DateTime.Now;
span_LR = finish_LR - start_LR;
double[,] y_LR = Liner_Regression.Regression_Design_Matrix(phi_X, w);
Console.WriteLine("入力x" + "\t" + "答えt" + "\t" + "NN" + "\t" + "SVM" + "\t" + "LR");
for (int j = 0; j < 9; j++)
{
Console.Write(X[j, 0] + "\t");
Console.Write(t_vec[j, 0] + "\t");
Console.Write(y_NN[j, 0].ToString("G2") + "\t");
Console.Write(classified[j, 0].ToString("G2") + "\t");
Console.Write(y_LR[j, 0].ToString("G2") + "\t");
Console.WriteLine(" ");
}
Console.WriteLine(" ");
Console.WriteLine("NNの計算時間\t\t" + span_NN_epoch_100k.Minutes + "分" + span_NN_epoch_100k.Seconds + "秒");
Console.WriteLine("SVMの計算時間\t\t" + span_SVM.Minutes + "分" + span_SVM.Seconds + "秒");
Console.WriteLine("LRの計算時間\t\t" + span_LR.Minutes + "分" + span_LR.Seconds + "秒");
Console.WriteLine("\n\n" + "NNの精度が良くないですね。");
Console.WriteLine("計数行列wの初期値や、学習回数、ハイパーパラメータなどを調整したのですが、これが限界でした。");
}