Was ist der Unterschied zwischen "regulärer" linearer Regression und linearer Deep-Learning-Regression?

Ich möchte den Unterschied zwischen der linearen Regression in einer regulären Analyse des maschinellen Lernens und der linearen Regression in der Einstellung "Deep Learning" kennen. Welche Algorithmen werden für die lineare Regression in Deep-Learning-Umgebungen verwendet?

Unter der Annahme, dass Sie mit Deep Learning genauere neuronale Netze gemeint haben: Ein vollständig verbundenes neuronales Vanilla-Feedforward-Netz mit nur linearen Aktivierungsfunktionen führt eine lineare Regression durch, unabhängig davon, wie viele Schichten es hat. Ein Unterschied besteht darin, dass bei einem neuronalen Netzwerk normalerweise ein Gradientenabstieg verwendet wird, während bei einer "normalen" linearen Regression nach Möglichkeit die normale Gleichung verwendet wird (wenn die Anzahl der Merkmale nicht zu groß ist).

Beispiel eines vollständig verbundenen neuronalen Feedforward-Netzwerks ohne verborgene Schicht und unter Verwendung einer linearen Aktivierungsfunktion (nämlich der Identitätsaktivierungsfunktion):

Wenn Sie die Aktivierungsfunktion der Ausgabeschicht durch eine Sigmoidfunktion ersetzen, führt das neuronale Netzwerk eine logistische Regression durch. Wenn Sie die Aktivierungsfunktion der Ausgabeebene durch eine Softmax-Funktion ersetzen und einige Ausgabeeinheiten hinzufügen, führt das neuronale Netzwerk eine logistische Regression mit mehreren Klassen durch: Unterschied zwischen logistischer Regression und neuronalen Netzwerken . Wenn Sie die Kostenfunktion durch den Scharnierverlust ersetzen , ist das neuronale Netzwerk eine SVM, die in ihrer ursprünglichen Form optimiert wurde: http://cs231n.github.io/linear-classify/ .

Hier ist das in dem oben in TensorFlow programmierte Bild gezeigte Beispiel:

""" Linear Regression Example """
# https://github.com/tflearn/tflearn/blob/master/examples/basics/linear_regression.py

from __future__ import absolute_import, division, print_function

import tflearn

# Regression data
X = [3.3,4.4,5.5,6.71,6.93,4.168,9.779,6.182,7.59,2.167,7.042,10.791,5.313,7.997,5.654,9.27,3.1]
Y = [1.7,2.76,2.09,3.19,1.694,1.573,3.366,2.596,2.53,1.221,2.827,3.465,1.65,2.904,2.42,2.94,1.3]

# Linear Regression graph
input_ = tflearn.input_data(shape=[None])
linear = tflearn.single_unit(input_)
regression = tflearn.regression(linear, optimizer='sgd', loss='mean_square',
                                metric='R2', learning_rate=0.01)
m = tflearn.DNN(regression)
m.fit(X, Y, n_epoch=1000, show_metric=True, snapshot_epoch=False)

print("\nRegression result:")
print("Y = " + str(m.get_weights(linear.W)) +
      "*X + " + str(m.get_weights(linear.b)))

print("\nTest prediction for x = 3.2, 3.3, 3.4:")
print(m.predict([3.2, 3.3, 3.4]))
# should output (close, not exact) y = [1.5315033197402954, 1.5585315227508545, 1.5855598449707031]

Hier ist ein Code-Snippet, das keine neuronalen Netzwerkbibliotheken verwendet:

# From http://briandolhansky.com/blog/artificial-neural-networks-linear-regression-part-1
import matplotlib.pyplot as plt
import numpy as np

# Load the data and create the data matrices X and Y
# This creates a feature vector X with a column of ones (bias)
# and a column of car weights.
# The target vector Y is a column of MPG values for each car.
X_file = np.genfromtxt('mpg.csv', delimiter=',', skip_header=1)
N = np.shape(X_file)[0]
X = np.hstack((np.ones(N).reshape(N, 1), X_file[:, 4].reshape(N, 1)))
Y = X_file[:, 0]

# Standardize the input 
X[:, 1] = (X[:, 1]-np.mean(X[:, 1]))/np.std(X[:, 1])

# There are two weights, the bias weight and the feature weight
w = np.array([0, 0])

# Start batch gradient descent, it will run for max_iter epochs and have a step
# size eta
max_iter = 100
eta = 1E-3
for t in range(0, max_iter):
    # We need to iterate over each data point for one epoch
    grad_t = np.array([0., 0.])
    for i in range(0, N):
        x_i = X[i, :]
        y_i = Y[i]
        # Dot product, computes h(x_i, w)
        h = np.dot(w, x_i)-y_i
        grad_t += 2*x_i*h

    # Update the weights
    w = w - eta*grad_t
print "Weights found:",w

# Plot the data and best fit line
tt = np.linspace(np.min(X[:, 1]), np.max(X[:, 1]), 10)
bf_line = w[0]+w[1]*tt

plt.plot(X[:, 1], Y, 'kx', tt, bf_line, 'r-')
plt.xlabel('Weight (Normalized)')
plt.ylabel('MPG')
plt.title('ANN Regression on 1D MPG Data')

plt.savefig('mpg.png')

plt.show()

Datendatei mpg.csv(~ 50% aufgrund der Beschränkung der Stack Exchange-Antwortgröße gekürzt):

mpg (n),cylinders (n),displacement (n),horsepower (n),weight (n),acceleration (n),year (n),origin (n), name (s)
18.000000,8.000000,307.000000,130.000000,3504.000000,12.000000,70.000000,1.000000
15.000000,8.000000,350.000000,165.000000,3693.000000,11.500000,70.000000,1.000000
18.000000,8.000000,318.000000,150.000000,3436.000000,11.000000,70.000000,1.000000
16.000000,8.000000,304.000000,150.000000,3433.000000,12.000000,70.000000,1.000000
17.000000,8.000000,302.000000,140.000000,3449.000000,10.500000,70.000000,1.000000
15.000000,8.000000,429.000000,198.000000,4341.000000,10.000000,70.000000,1.000000
14.000000,8.000000,454.000000,220.000000,4354.000000,9.000000,70.000000,1.000000
14.000000,8.000000,440.000000,215.000000,4312.000000,8.500000,70.000000,1.000000
14.000000,8.000000,455.000000,225.000000,4425.000000,10.000000,70.000000,1.000000
15.000000,8.000000,390.000000,190.000000,3850.000000,8.500000,70.000000,1.000000
15.000000,8.000000,383.000000,170.000000,3563.000000,10.000000,70.000000,1.000000
14.000000,8.000000,340.000000,160.000000,3609.000000,8.000000,70.000000,1.000000
15.000000,8.000000,400.000000,150.000000,3761.000000,9.500000,70.000000,1.000000
14.000000,8.000000,455.000000,225.000000,3086.000000,10.000000,70.000000,1.000000
24.000000,4.000000,113.000000,95.000000,2372.000000,15.000000,70.000000,3.000000
22.000000,6.000000,198.000000,95.000000,2833.000000,15.500000,70.000000,1.000000
18.000000,6.000000,199.000000,97.000000,2774.000000,15.500000,70.000000,1.000000
21.000000,6.000000,200.000000,85.000000,2587.000000,16.000000,70.000000,1.000000
27.000000,4.000000,97.000000,88.000000,2130.000000,14.500000,70.000000,3.000000
26.000000,4.000000,97.000000,46.000000,1835.000000,20.500000,70.000000,2.000000
25.000000,4.000000,110.000000,87.000000,2672.000000,17.500000,70.000000,2.000000
24.000000,4.000000,107.000000,90.000000,2430.000000,14.500000,70.000000,2.000000
25.000000,4.000000,104.000000,95.000000,2375.000000,17.500000,70.000000,2.000000
26.000000,4.000000,121.000000,113.000000,2234.000000,12.500000,70.000000,2.000000
21.000000,6.000000,199.000000,90.000000,2648.000000,15.000000,70.000000,1.000000
10.000000,8.000000,360.000000,215.000000,4615.000000,14.000000,70.000000,1.000000
10.000000,8.000000,307.000000,200.000000,4376.000000,15.000000,70.000000,1.000000
11.000000,8.000000,318.000000,210.000000,4382.000000,13.500000,70.000000,1.000000
9.000000,8.000000,304.000000,193.000000,4732.000000,18.500000,70.000000,1.000000
27.000000,4.000000,97.000000,88.000000,2130.000000,14.500000,71.000000,3.000000
28.000000,4.000000,140.000000,90.000000,2264.000000,15.500000,71.000000,1.000000
25.000000,4.000000,113.000000,95.000000,2228.000000,14.000000,71.000000,3.000000
19.000000,6.000000,232.000000,100.000000,2634.000000,13.000000,71.000000,1.000000
16.000000,6.000000,225.000000,105.000000,3439.000000,15.500000,71.000000,1.000000
17.000000,6.000000,250.000000,100.000000,3329.000000,15.500000,71.000000,1.000000
19.000000,6.000000,250.000000,88.000000,3302.000000,15.500000,71.000000,1.000000
18.000000,6.000000,232.000000,100.000000,3288.000000,15.500000,71.000000,1.000000
14.000000,8.000000,350.000000,165.000000,4209.000000,12.000000,71.000000,1.000000
14.000000,8.000000,400.000000,175.000000,4464.000000,11.500000,71.000000,1.000000
14.000000,8.000000,351.000000,153.000000,4154.000000,13.500000,71.000000,1.000000
14.000000,8.000000,318.000000,150.000000,4096.000000,13.000000,71.000000,1.000000
12.000000,8.000000,383.000000,180.000000,4955.000000,11.500000,71.000000,1.000000
13.000000,8.000000,400.000000,170.000000,4746.000000,12.000000,71.000000,1.000000
13.000000,8.000000,400.000000,175.000000,5140.000000,12.000000,71.000000,1.000000
18.000000,6.000000,258.000000,110.000000,2962.000000,13.500000,71.000000,1.000000
22.000000,4.000000,140.000000,72.000000,2408.000000,19.000000,71.000000,1.000000
19.000000,6.000000,250.000000,100.000000,3282.000000,15.000000,71.000000,1.000000
18.000000,6.000000,250.000000,88.000000,3139.000000,14.500000,71.000000,1.000000
23.000000,4.000000,122.000000,86.000000,2220.000000,14.000000,71.000000,1.000000
28.000000,4.000000,116.000000,90.000000,2123.000000,14.000000,71.000000,2.000000
30.000000,4.000000,79.000000,70.000000,2074.000000,19.500000,71.000000,2.000000
30.000000,4.000000,88.000000,76.000000,2065.000000,14.500000,71.000000,2.000000
31.000000,4.000000,71.000000,65.000000,1773.000000,19.000000,71.000000,3.000000
35.000000,4.000000,72.000000,69.000000,1613.000000,18.000000,71.000000,3.000000
27.000000,4.000000,97.000000,60.000000,1834.000000,19.000000,71.000000,2.000000
26.000000,4.000000,91.000000,70.000000,1955.000000,20.500000,71.000000,1.000000
24.000000,4.000000,113.000000,95.000000,2278.000000,15.500000,72.000000,3.000000
25.000000,4.000000,97.500000,80.000000,2126.000000,17.000000,72.000000,1.000000
23.000000,4.000000,97.000000,54.000000,2254.000000,23.500000,72.000000,2.000000
20.000000,4.000000,140.000000,90.000000,2408.000000,19.500000,72.000000,1.000000
21.000000,4.000000,122.000000,86.000000,2226.000000,16.500000,72.000000,1.000000
13.000000,8.000000,350.000000,165.000000,4274.000000,12.000000,72.000000,1.000000
14.000000,8.000000,400.000000,175.000000,4385.000000,12.000000,72.000000,1.000000
15.000000,8.000000,318.000000,150.000000,4135.000000,13.500000,72.000000,1.000000
14.000000,8.000000,351.000000,153.000000,4129.000000,13.000000,72.000000,1.000000
17.000000,8.000000,304.000000,150.000000,3672.000000,11.500000,72.000000,1.000000
11.000000,8.000000,429.000000,208.000000,4633.000000,11.000000,72.000000,1.000000
13.000000,8.000000,350.000000,155.000000,4502.000000,13.500000,72.000000,1.000000
12.000000,8.000000,350.000000,160.000000,4456.000000,13.500000,72.000000,1.000000
13.000000,8.000000,400.000000,190.000000,4422.000000,12.500000,72.000000,1.000000
19.000000,3.000000,70.000000,97.000000,2330.000000,13.500000,72.000000,3.000000
15.000000,8.000000,304.000000,150.000000,3892.000000,12.500000,72.000000,1.000000
13.000000,8.000000,307.000000,130.000000,4098.000000,14.000000,72.000000,1.000000
13.000000,8.000000,302.000000,140.000000,4294.000000,16.000000,72.000000,1.000000
14.000000,8.000000,318.000000,150.000000,4077.000000,14.000000,72.000000,1.000000
18.000000,4.000000,121.000000,112.000000,2933.000000,14.500000,72.000000,2.000000
22.000000,4.000000,121.000000,76.000000,2511.000000,18.000000,72.000000,2.000000
21.000000,4.000000,120.000000,87.000000,2979.000000,19.500000,72.000000,2.000000
26.000000,4.000000,96.000000,69.000000,2189.000000,18.000000,72.000000,2.000000
22.000000,4.000000,122.000000,86.000000,2395.000000,16.000000,72.000000,1.000000
28.000000,4.000000,97.000000,92.000000,2288.000000,17.000000,72.000000,3.000000
23.000000,4.000000,120.000000,97.000000,2506.000000,14.500000,72.000000,3.000000
28.000000,4.000000,98.000000,80.000000,2164.000000,15.000000,72.000000,1.000000
27.000000,4.000000,97.000000,88.000000,2100.000000,16.500000,72.000000,3.000000
13.000000,8.000000,350.000000,175.000000,4100.000000,13.000000,73.000000,1.000000
14.000000,8.000000,304.000000,150.000000,3672.000000,11.500000,73.000000,1.000000
13.000000,8.000000,350.000000,145.000000,3988.000000,13.000000,73.000000,1.000000
14.000000,8.000000,302.000000,137.000000,4042.000000,14.500000,73.000000,1.000000
15.000000,8.000000,318.000000,150.000000,3777.000000,12.500000,73.000000,1.000000
12.000000,8.000000,429.000000,198.000000,4952.000000,11.500000,73.000000,1.000000
13.000000,8.000000,400.000000,150.000000,4464.000000,12.000000,73.000000,1.000000
13.000000,8.000000,351.000000,158.000000,4363.000000,13.000000,73.000000,1.000000
14.000000,8.000000,318.000000,150.000000,4237.000000,14.500000,73.000000,1.000000
13.000000,8.000000,440.000000,215.000000,4735.000000,11.000000,73.000000,1.000000
12.000000,8.000000,455.000000,225.000000,4951.000000,11.000000,73.000000,1.000000
13.000000,8.000000,360.000000,175.000000,3821.000000,11.000000,73.000000,1.000000
18.000000,6.000000,225.000000,105.000000,3121.000000,16.500000,73.000000,1.000000
16.000000,6.000000,250.000000,100.000000,3278.000000,18.000000,73.000000,1.000000
18.000000,6.000000,232.000000,100.000000,2945.000000,16.000000,73.000000,1.000000
18.000000,6.000000,250.000000,88.000000,3021.000000,16.500000,73.000000,1.000000
23.000000,6.000000,198.000000,95.000000,2904.000000,16.000000,73.000000,1.000000
26.000000,4.000000,97.000000,46.000000,1950.000000,21.000000,73.000000,2.000000
11.000000,8.000000,400.000000,150.000000,4997.000000,14.000000,73.000000,1.000000
12.000000,8.000000,400.000000,167.000000,4906.000000,12.500000,73.000000,1.000000
13.000000,8.000000,360.000000,170.000000,4654.000000,13.000000,73.000000,1.000000
12.000000,8.000000,350.000000,180.000000,4499.000000,12.500000,73.000000,1.000000
18.000000,6.000000,232.000000,100.000000,2789.000000,15.000000,73.000000,1.000000
20.000000,4.000000,97.000000,88.000000,2279.000000,19.000000,73.000000,3.000000
21.000000,4.000000,140.000000,72.000000,2401.000000,19.500000,73.000000,1.000000
22.000000,4.000000,108.000000,94.000000,2379.000000,16.500000,73.000000,3.000000
18.000000,3.000000,70.000000,90.000000,2124.000000,13.500000,73.000000,3.000000
19.000000,4.000000,122.000000,85.000000,2310.000000,18.500000,73.000000,1.000000
21.000000,6.000000,155.000000,107.000000,2472.000000,14.000000,73.000000,1.000000
26.000000,4.000000,98.000000,90.000000,2265.000000,15.500000,73.000000,2.000000
15.000000,8.000000,350.000000,145.000000,4082.000000,13.000000,73.000000,1.000000
16.000000,8.000000,400.000000,230.000000,4278.000000,9.500000,73.000000,1.000000
29.000000,4.000000,68.000000,49.000000,1867.000000,19.500000,73.000000,2.000000
24.000000,4.000000,116.000000,75.000000,2158.000000,15.500000,73.000000,2.000000
20.000000,4.000000,114.000000,91.000000,2582.000000,14.000000,73.000000,2.000000
19.000000,4.000000,121.000000,112.000000,2868.000000,15.500000,73.000000,2.000000
15.000000,8.000000,318.000000,150.000000,3399.000000,11.000000,73.000000,1.000000
24.000000,4.000000,121.000000,110.000000,2660.000000,14.000000,73.000000,2.000000
20.000000,6.000000,156.000000,122.000000,2807.000000,13.500000,73.000000,3.000000
11.000000,8.000000,350.000000,180.000000,3664.000000,11.000000,73.000000,1.000000
20.000000,6.000000,198.000000,95.000000,3102.000000,16.500000,74.000000,1.000000
19.000000,6.000000,232.000000,100.000000,2901.000000,16.000000,74.000000,1.000000
15.000000,6.000000,250.000000,100.000000,3336.000000,17.000000,74.000000,1.000000
31.000000,4.000000,79.000000,67.000000,1950.000000,19.000000,74.000000,3.000000
26.000000,4.000000,122.000000,80.000000,2451.000000,16.500000,74.000000,1.000000
32.000000,4.000000,71.000000,65.000000,1836.000000,21.000000,74.000000,3.000000
25.000000,4.000000,140.000000,75.000000,2542.000000,17.000000,74.000000,1.000000
16.000000,6.000000,250.000000,100.000000,3781.000000,17.000000,74.000000,1.000000
16.000000,6.000000,258.000000,110.000000,3632.000000,18.000000,74.000000,1.000000
18.000000,6.000000,225.000000,105.000000,3613.000000,16.500000,74.000000,1.000000
16.000000,8.000000,302.000000,140.000000,4141.000000,14.000000,74.000000,1.000000
13.000000,8.000000,350.000000,150.000000,4699.000000,14.500000,74.000000,1.000000
14.000000,8.000000,318.000000,150.000000,4457.000000,13.500000,74.000000,1.000000
14.000000,8.000000,302.000000,140.000000,4638.000000,16.000000,74.000000,1.000000
14.000000,8.000000,304.000000,150.000000,4257.000000,15.500000,74.000000,1.000000
29.000000,4.000000,98.000000,83.000000,2219.000000,16.500000,74.000000,2.000000
26.000000,4.000000,79.000000,67.000000,1963.000000,15.500000,74.000000,2.000000
26.000000,4.000000,97.000000,78.000000,2300.000000,14.500000,74.000000,2.000000
31.000000,4.000000,76.000000,52.000000,1649.000000,16.500000,74.000000,3.000000
32.000000,4.000000,83.000000,61.000000,2003.000000,19.000000,74.000000,3.000000
28.000000,4.000000,90.000000,75.000000,2125.000000,14.500000,74.000000,1.000000
24.000000,4.000000,90.000000,75.000000,2108.000000,15.500000,74.000000,2.000000
26.000000,4.000000,116.000000,75.000000,2246.000000,14.000000,74.000000,2.000000
24.000000,4.000000,120.000000,97.000000,2489.000000,15.000000,74.000000,3.000000
26.000000,4.000000,108.000000,93.000000,2391.000000,15.500000,74.000000,3.000000
31.000000,4.000000,79.000000,67.000000,2000.000000,16.000000,74.000000,2.000000
19.000000,6.000000,225.000000,95.000000,3264.000000,16.000000,75.000000,1.000000
18.000000,6.000000,250.000000,105.000000,3459.000000,16.000000,75.000000,1.000000
15.000000,6.000000,250.000000,72.000000,3432.000000,21.000000,75.000000,1.000000
15.000000,6.000000,250.000000,72.000000,3158.000000,19.500000,75.000000,1.000000
16.000000,8.000000,400.000000,170.000000,4668.000000,11.500000,75.000000,1.000000
15.000000,8.000000,350.000000,145.000000,4440.000000,14.000000,75.000000,1.000000
16.000000,8.000000,318.000000,150.000000,4498.000000,14.500000,75.000000,1.000000
14.000000,8.000000,351.000000,148.000000,4657.000000,13.500000,75.000000,1.000000
17.000000,6.000000,231.000000,110.000000,3907.000000,21.000000,75.000000,1.000000
16.000000,6.000000,250.000000,105.000000,3897.000000,18.500000,75.000000,1.000000
15.000000,6.000000,258.000000,110.000000,3730.000000,19.000000,75.000000,1.000000
18.000000,6.000000,225.000000,95.000000,3785.000000,19.000000,75.000000,1.000000
21.000000,6.000000,231.000000,110.000000,3039.000000,15.000000,75.000000,1.000000
20.000000,8.000000,262.000000,110.000000,3221.000000,13.500000,75.000000,1.000000
13.000000,8.000000,302.000000,129.000000,3169.000000,12.000000,75.000000,1.000000
29.000000,4.000000,97.000000,75.000000,2171.000000,16.000000,75.000000,3.000000
23.000000,4.000000,140.000000,83.000000,2639.000000,17.000000,75.000000,1.000000
20.000000,6.000000,232.000000,100.000000,2914.000000,16.000000,75.000000,1.000000
23.000000,4.000000,140.000000,78.000000,2592.000000,18.500000,75.000000,1.000000
24.000000,4.000000,134.000000,96.000000,2702.000000,13.500000,75.000000,3.000000
25.000000,4.000000,90.000000,71.000000,2223.000000,16.500000,75.000000,2.000000
24.000000,4.000000,119.000000,97.000000,2545.000000,17.000000,75.000000,3.000000
18.000000,6.000000,171.000000,97.000000,2984.000000,14.500000,75.000000,1.000000
29.000000,4.000000,90.000000,70.000000,1937.000000,14.000000,75.000000,2.000000
19.000000,6.000000,232.000000,90.000000,3211.000000,17.000000,75.000000,1.000000
23.000000,4.000000,115.000000,95.000000,2694.000000,15.000000,75.000000,2.000000
23.000000,4.000000,120.000000,88.000000,2957.000000,17.000000,75.000000,2.000000
22.000000,4.000000,121.000000,98.000000,2945.000000,14.500000,75.000000,2.000000
25.000000,4.000000,121.000000,115.000000,2671.000000,13.500000,75.000000,2.000000
33.000000,4.000000,91.000000,53.000000,1795.000000,17.500000,75.000000,3.000000
28.000000,4.000000,107.000000,86.000000,2464.000000,15.500000,76.000000,2.000000
25.000000,4.000000,116.000000,81.000000,2220.000000,16.900000,76.000000,2.000000
25.000000,4.000000,140.000000,92.000000,2572.000000,14.900000,76.000000,1.000000
26.000000,4.000000,98.000000,79.000000,2255.000000,17.700000,76.000000,1.000000
27.000000,4.000000,101.000000,83.000000,2202.000000,15.300000,76.000000,2.000000
17.500000,8.000000,305.000000,140.000000,4215.000000,13.000000,76.000000,1.000000
16.000000,8.000000,318.000000,150.000000,4190.000000,13.000000,76.000000,1.000000
15.500000,8.000000,304.000000,120.000000,3962.000000,13.900000,76.000000,1.000000
14.500000,8.000000,351.000000,152.000000,4215.000000,12.800000,76.000000,1.000000
22.000000,6.000000,225.000000,100.000000,3233.000000,15.400000,76.000000,1.000000
22.000000,6.000000,250.000000,105.000000,3353.000000,14.500000,76.000000,1.000000
24.000000,6.000000,200.000000,81.000000,3012.000000,17.600000,76.000000,1.000000
22.500000,6.000000,232.000000,90.000000,3085.000000,17.600000,76.000000,1.000000
29.000000,4.000000,85.000000,52.000000,2035.000000,22.200000,76.000000,1.000000
24.500000,4.000000,98.000000,60.000000,2164.000000,22.100000,76.000000,1.000000
29.000000,4.000000,90.000000,70.000000,1937.000000,14.200000,76.000000,2.000000
33.000000,4.000000,91.000000,53.000000,1795.000000,17.400000,76.000000,3.000000
20.000000,6.000000,225.000000,100.000000,3651.000000,17.700000,76.000000,1.000000
18.000000,6.000000,250.000000,78.000000,3574.000000,21.000000,76.000000,1.000000
18.500000,6.000000,250.000000,110.000000,3645.000000,16.200000,76.000000,1.000000
17.500000,6.000000,258.000000,95.000000,3193.000000,17.800000,76.000000,1.000000
29.500000,4.000000,97.000000,71.000000,1825.000000,12.200000,76.000000,2.000000
32.000000,4.000000,85.000000,70.000000,1990.000000,17.000000,76.000000,3.000000
28.000000,4.000000,97.000000,75.000000,2155.000000,16.400000,76.000000,3.000000
26.500000,4.000000,140.000000,72.000000,2565.000000,13.600000,76.000000,1.000000
20.000000,4.000000,130.000000,102.000000,3150.000000,15.700000,76.000000,2.000000
13.000000,8.000000,318.000000,150.000000,3940.000000,13.200000,76.000000,1.000000
19.000000,4.000000,120.000000,88.000000,3270.000000,21.900000,76.000000,2.000000
19.000000,6.000000,156.000000,108.000000,2930.000000,15.500000,76.000000,3.000000
16.500000,6.000000,168.000000,120.000000,3820.000000,16.700000,76.000000,2.000000
16.500000,8.000000,350.000000,180.000000,4380.000000,12.100000,76.000000,1.000000
13.000000,8.000000,350.000000,145.000000,4055.000000,12.000000,76.000000,1.000000
13.000000,8.000000,302.000000,130.000000,3870.000000,15.000000,76.000000,1.000000
13.000000,8.000000,318.000000,150.000000,3755.000000,14.000000,76.000000,1.000000
31.500000,4.000000,98.000000,68.000000,2045.000000,18.500000,77.000000,3.000000
30.000000,4.000000,111.000000,80.000000,2155.000000,14.800000,77.000000,1.000000
36.000000,4.000000,79.000000,58.000000,1825.000000,18.600000,77.000000,2.000000
25.500000,4.000000,122.000000,96.000000,2300.000000,15.500000,77.000000,1.000000
33.500000,4.000000,85.000000,70.000000,1945.000000,16.800000,77.000000,3.000000
17.500000,8.000000,305.000000,145.000000,3880.000000,12.500000,77.000000,1.000000
17.000000,8.000000,260.000000,110.000000,4060.000000,19.000000,77.000000,1.000000
15.500000,8.000000,318.000000,145.000000,4140.000000,13.700000,77.000000,1.000000
15.000000,8.000000,302.000000,130.000000,4295.000000,14.900000,77.000000,1.000000
17.500000,6.000000,250.000000,110.000000,3520.000000,16.400000,77.000000,1.000000
20.500000,6.000000,231.000000,105.000000,3425.000000,16.900000,77.000000,1.000000
19.000000,6.000000,225.000000,100.000000,3630.000000,17.700000,77.000000,1.000000
18.500000,6.000000,250.000000,98.000000,3525.000000,19.000000,77.000000,1.000000
16.000000,8.000000,400.000000,180.000000,4220.000000,11.100000,77.000000,1.000000
15.500000,8.000000,350.000000,170.000000,4165.000000,11.400000,77.000000,1.000000
15.500000,8.000000,400.000000,190.000000,4325.000000,12.200000,77.000000,1.000000
16.000000,8.000000,351.000000,149.000000,4335.000000,14.500000,77.000000,1.000000
29.000000,4.000000,97.000000,78.000000,1940.000000,14.500000,77.000000,2.000000
24.500000,4.000000,151.000000,88.000000,2740.000000,16.000000,77.000000,1.000000
26.000000,4.000000,97.000000,75.000000,2265.000000,18.200000,77.000000,3.000000
25.500000,4.000000,140.000000,89.000000,2755.000000,15.800000,77.000000,1.000000
30.500000,4.000000,98.000000,63.000000,2051.000000,17.000000,77.000000,1.000000
33.500000,4.000000,98.000000,83.000000,2075.000000,15.900000,77.000000,1.000000
30.000000,4.000000,97.000000,67.000000,1985.000000,16.400000,77.000000,3.000000
30.500000,4.000000,97.000000,78.000000,2190.000000,14.100000,77.000000,2.000000
22.000000,6.000000,146.000000,97.000000,2815.000000,14.500000,77.000000,3.000000
21.500000,4.000000,121.000000,110.000000,2600.000000,12.800000,77.000000,2.000000
21.500000,3.000000,80.000000,110.000000,2720.000000,13.500000,77.000000,3.000000
43.100000,4.000000,90.000000,48.000000,1985.000000,21.500000,78.000000,2.000000
36.100000,4.000000,98.000000,66.000000,1800.000000,14.400000,78.000000,1.000000
32.800000,4.000000,78.000000,52.000000,1985.000000,19.400000,78.000000,3.000000
39.400000,4.000000,85.000000,70.000000,2070.000000,18.600000,78.000000,3.000000
36.100000,4.000000,91.000000,60.000000,1800.000000,16.400000,78.000000,3.000000
19.900000,8.000000,260.000000,110.000000,3365.000000,15.500000,78.000000,1.000000

Für die Regression, die für tiefes Lernen in den meisten Fällen nichtlinear ist, hat die letzte Schicht 1 Neuron mit Identitätsfunktion und Verlustfunktion, die wir optimieren, ist MSE, MAE anstelle der für die Klassifizierung verwendeten binären oder kategorialen Kreuzentropie.