写在前面
深度学习主要分为回归和分类这两个任务,本文将用一个分类的例子,使用PyTorch来搭建人工智能神经网络,讲解如何搭建用通用模板来搭建一个完整的分类网络模型。【这是深度学习数学原理专题系列的第四篇文章】
问题描述与分析
本文的分类案例,是一个二分类问题,目的是要根据输入的学习时间,来预测能否考试合格,最终输出是考试通过的概率。
题目中给出的数据表明,学习时长为1(小时)的情况下,考试通过情况输出为0,即无法通过;学习时长为2的时候,考试仍然无法通过;学习时长为3的时候,考试可以通过。
那么问题来了,如果学习时长为4(小时)的情况下,能否通过考试呢?那么接下来让我们通过人工智能技术,运用神经网络模型来对此做预测。
Logistic Regression的数学原理
logistic 函数
logistic 函数也可以叫做 sigmoid 函数,logistic函数是最典型的sigmoid函数。
σ
(
w
)
=
1
1
+
e
?
x
\sigma(w) = \dfrac{1}{1+e^{-x}}
σ(w)=1+e?x1? Affine Model 和 Logistic Regression Model 的区别,主要是 Logistic Regression Model 在Affine Model 的后面添加了激活函数(非线性变换)。
Affine Model | Logistic Regression Model |
---|
y
=
x
?
w
+
b
y=x*w+b
y=x?w+b |
y
=
σ
(
x
?
w
+
b
)
y=\sigma(x*w+b)
y=σ(x?w+b) |
PyTorch代码实现
具体的讲解尽在注释中:
import os
os.environ['KMP_DUPLICATE_LIB_OK'] = 'TRUE'
import torch
import matplotlib.pyplot as plt
x_data = torch.Tensor([[1.0], [2.0], [3.0]])
y_data = torch.Tensor([[0], [0], [1]])
class LogisticRegressionModel(torch.nn.Module):
def __init__(self):
super(LogisticRegressionModel, self).__init__()
self.linear = torch.nn.Linear(1, 1)
def forward(self, x):
y_pred = torch.sigmoid(self.linear(x))
return y_pred
model = LogisticRegressionModel()
criterion = torch.nn.BCELoss(size_average=False)
optimizer = torch.optim.SGD(model.parameters(), lr=0.01)
epoch_list = []
loss_list = []
for epoch in range(1000):
y_pred = model(x_data)
loss = criterion(y_pred, y_data)
print('Epoch:{}, Loss:{}, w:{}, b:{}'.format(epoch, loss.item(), model.linear.weight.item(),
model.linear.bias.item()))
optimizer.zero_grad()
loss.backward()
optimizer.step()
epoch_list.append(epoch)
loss_list.append(loss)
print('w = ', model.linear.weight.item())
print('b = ', model.linear.bias.item())
x_test = torch.Tensor([4.0])
y_test = model(x_test)
print('y_pred = ', y_test.data)
plt.plot(epoch_list, loss_list)
plt.ylabel('Loss')
plt.xlabel('Epoch')
plt.show()
x = np.linspace(0, 10, 200)
x_t = torch.Tensor(x).view((200, 1))
y_t = model(x_t)
y = y_t.data.numpy()
plt.plot(x, y)
plt.plot([0, 10], [0.5, 0.5], c='r')
plt.xlabel('Hours')
plt.ylabel('Probability of Pass')
plt.grid()
plt.show()
输出结果为:
Epoch:0, Loss:2.513278007507324, w:0.5654370784759521, b:-0.06634891033172607
Epoch:1, Loss:2.473193883895874, w:0.5492585897445679, b:-0.07836855202913284
Epoch:2, Loss:2.4352242946624756, w:0.5335716605186462, b:-0.09015150368213654
***\torch\nn\_reduction.py:42: UserWarning: size_average and reduce args will be deprecated, please use reduction='sum' instead.
warnings.warn(warning.format(ret))
Epoch:3, Loss:2.399306297302246, w:0.518376350402832, b:-0.10169880092144012
Epoch:4, Loss:2.3653740882873535, w:0.5036717057228088, b:-0.113011933863163
Epoch:5, Loss:2.3333561420440674, w:0.48945561051368713, b:-0.12409284710884094
Epoch:6, Loss:2.303180456161499, w:0.4757249355316162, b:-0.1349439173936844
Epoch:7, Loss:2.2747716903686523, w:0.4624755084514618, b:-0.1455679088830948
Epoch:8, Loss:2.248053550720215, w:0.4497022330760956, b:-0.15596795082092285
Epoch:9, Loss:2.2229487895965576, w:0.43739914894104004, b:-0.16614754498004913
Epoch:10, Loss:2.1993794441223145, w:0.4255594313144684, b:-0.17611046135425568
Epoch:11, Loss:2.1772689819335938, w:0.41417554020881653, b:-0.1858607679605484
Epoch:12, Loss:2.1565403938293457, w:0.40323930978775024, b:-0.19540277123451233
Epoch:13, Loss:2.137118101119995, w:0.39274194836616516, b:-0.2047410011291504
Epoch:14, Loss:2.118929386138916, w:0.3826741576194763, b:-0.21388013660907745
Epoch:15, Loss:2.1019017696380615, w:0.37302619218826294, b:-0.2228250354528427
Epoch:16, Loss:2.085965871810913, w:0.363787978887558, b:-0.23158064484596252
Epoch:17, Loss:2.071054458618164, w:0.35494911670684814, b:-0.2401520162820816
Epoch:18, Loss:2.0571036338806152, w:0.3464989960193634, b:-0.24854424595832825
Epoch:19, Loss:2.044050931930542, w:0.3384268283843994, b:-0.2567625045776367
Epoch:20, Loss:2.0318374633789062, w:0.33072173595428467, b:-0.2648119330406189
Epoch:21, Loss:2.020407199859619, w:0.3233727216720581, b:-0.27269765734672546
Epoch:22, Loss:2.00970721244812, w:0.31636884808540344, b:-0.2804248332977295
Epoch:23, Loss:1.9996867179870605, w:0.3096992075443268, b:-0.2879985570907593
Epoch:24, Loss:1.990297794342041, w:0.30335289239883423, b:-0.29542383551597595
Epoch:25, Loss:1.9814962148666382, w:0.2973191738128662, b:-0.3027056157588959
Epoch:26, Loss:1.9732396602630615, w:0.2915874421596527, b:-0.3098487854003906
Epoch:27, Loss:1.9654889106750488, w:0.28614723682403564, b:-0.31685811281204224
Epoch:28, Loss:1.9582064151763916, w:0.28098830580711365, b:-0.3237382769584656
Epoch:29, Loss:1.9513580799102783, w:0.2761005759239197, b:-0.33049386739730835
Epoch:30, Loss:1.944911241531372, w:0.2714741826057434, b:-0.3371293544769287
Epoch:31, Loss:1.9388360977172852, w:0.267099529504776, b:-0.34364908933639526
Epoch:32, Loss:1.9331045150756836, w:0.26296722888946533, b:-0.35005730390548706
Epoch:33, Loss:1.9276905059814453, w:0.25906819105148315, b:-0.3563581109046936
Epoch:34, Loss:1.922569990158081, w:0.25539350509643555, b:-0.36255550384521484
Epoch:35, Loss:1.9177205562591553, w:0.25193458795547485, b:-0.3686533272266388
Epoch:36, Loss:1.9131208658218384, w:0.2486831098794937, b:-0.3746553659439087
Epoch:37, Loss:1.9087519645690918, w:0.24563096463680267, b:-0.38056519627571106
Epoch:38, Loss:1.904596209526062, w:0.24277034401893616, b:-0.38638633489608765
Epoch:39, Loss:1.9006370306015015, w:0.2400936633348465, b:-0.39212217926979065
Epoch:40, Loss:1.8968589305877686, w:0.2375936210155487, b:-0.3977759778499603
Epoch:41, Loss:1.8932478427886963, w:0.2352631688117981, b:-0.4033508598804474
Epoch:42, Loss:1.8897910118103027, w:0.23309549689292908, b:-0.40884989500045776
Epoch:43, Loss:1.8864762783050537, w:0.23108403384685516, b:-0.41427597403526306
Epoch:44, Loss:1.8832924365997314, w:0.22922247648239136, b:-0.4196319282054901
Epoch:45, Loss:1.8802297115325928, w:0.22750471532344818, b:-0.4249204695224762
Epoch:46, Loss:1.8772778511047363, w:0.22592487931251526, b:-0.43014419078826904
Epoch:47, Loss:1.8744292259216309, w:0.22447733581066132, b:-0.4353055953979492
Epoch:48, Loss:1.8716747760772705, w:0.2231566607952118, b:-0.4404070973396301
Epoch:49, Loss:1.869008183479309, w:0.22195763885974884, b:-0.445451021194458
Epoch:50, Loss:1.8664214611053467, w:0.22087523341178894, b:-0.45043960213661194
Epoch:51, Loss:1.863909363746643, w:0.21990463137626648, b:-0.45537495613098145
Epoch:52, Loss:1.8614659309387207, w:0.21904119849205017, b:-0.4602591395378113
Epoch:53, Loss:1.8590854406356812, w:0.21828047931194305, b:-0.4650941491127014
Epoch:54, Loss:1.8567633628845215, w:0.2176182121038437, b:-0.4698818624019623
Epoch:55, Loss:1.8544952869415283, w:0.21705028414726257, b:-0.47462406754493713
Epoch:56, Loss:1.8522766828536987, w:0.21657274663448334, b:-0.47932255268096924
Epoch:57, Loss:1.8501043319702148, w:0.21618182957172394, b:-0.4839789569377899
Epoch:58, Loss:1.847974181175232, w:0.21587389707565308, b:-0.4885949194431305
Epoch:59, Loss:1.8458837270736694, w:0.21564547717571259, b:-0.49317196011543274
Epoch:60, Loss:1.8438291549682617, w:0.21549321711063385, b:-0.49771156907081604
Epoch:61, Loss:1.841808557510376, w:0.2154139131307602, b:-0.5022151470184326
Epoch:62, Loss:1.8398185968399048, w:0.21540449559688568, b:-0.5066840648651123
Epoch:63, Loss:1.837857961654663, w:0.21546199917793274, b:-0.5111196041107178
Epoch:64, Loss:1.8359237909317017, w:0.21558360755443573, b:-0.5155230760574341
Epoch:65, Loss:1.8340145349502563, w:0.21576660871505737, b:-0.519895613193512
Epoch:66, Loss:1.8321282863616943, w:0.21600840985774994, b:-0.5242384076118469
Epoch:67, Loss:1.8302632570266724, w:0.21630650758743286, b:-0.5285525321960449
Epoch:68, Loss:1.8284183740615845, w:0.21665850281715393, b:-0.5328390598297119
Epoch:69, Loss:1.8265917301177979, w:0.2170621156692505, b:-0.5370990633964539
Epoch:70, Loss:1.8247822523117065, w:0.21751514077186584, b:-0.5413334369659424
Epoch:71, Loss:1.8229892253875732, w:0.21801547706127167, b:-0.5455431342124939
Epoch:72, Loss:1.8212107419967651, w:0.2185610979795456, b:-0.54972904920578
Epoch:73, Loss:1.819446325302124, w:0.21915006637573242, b:-0.5538920164108276
Epoch:74, Loss:1.817694902420044, w:0.21978051960468292, b:-0.5580328702926636
Epoch:75, Loss:1.8159561157226562, w:0.22045068442821503, b:-0.5621524453163147
Epoch:76, Loss:1.8142282962799072, w:0.22115884721279144, b:-0.5662514567375183
Epoch:77, Loss:1.812511682510376, w:0.22190338373184204, b:-0.5703306198120117
Epoch:78, Loss:1.810805082321167, w:0.22268271446228027, b:-0.5743906497955322
Epoch:79, Loss:1.8091076612472534, w:0.22349534928798676, b:-0.5784322023391724
Epoch:80, Loss:1.807419776916504, w:0.22433984279632568, b:-0.5824558734893799
Epoch:81, Loss:1.8057401180267334, w:0.22521480917930603, b:-0.5864623188972473
Epoch:82, Loss:1.8040685653686523, w:0.22611892223358154, b:-0.5904521346092224
Epoch:83, Loss:1.8024041652679443, w:0.22705093026161194, b:-0.5944258570671082
Epoch:84, Loss:1.8007473945617676, w:0.22800959646701813, b:-0.5983840823173523
Epoch:85, Loss:1.7990975379943848, w:0.22899377346038818, b:-0.6023272275924683
Epoch:86, Loss:1.7974538803100586, w:0.23000234365463257, b:-0.6062558889389038
Epoch:87, Loss:1.795816421508789, w:0.23103421926498413, b:-0.6101704835891724
Epoch:88, Loss:1.794184923171997, w:0.2320883870124817, b:-0.6140714883804321
Epoch:89, Loss:1.792559027671814, w:0.23316386342048645, b:-0.6179593205451965
Epoch:90, Loss:1.7909387350082397, w:0.2342597097158432, b:-0.621834397315979
Epoch:91, Loss:1.7893238067626953, w:0.23537501692771912, b:-0.625697135925293
Epoch:92, Loss:1.7877134084701538, w:0.23650892078876495, b:-0.6295478940010071
Epoch:93, Loss:1.786108136177063, w:0.23766060173511505, b:-0.6333870887756348
Epoch:94, Loss:1.7845075130462646, w:0.23882925510406494, b:-0.6372150182723999
Epoch:95, Loss:1.7829111814498901, w:0.24001412093639374, b:-0.6410320401191711
Epoch:96, Loss:1.78131902217865, w:0.24121445417404175, b:-0.6448385119438171
Epoch:97, Loss:1.779731273651123, w:0.24242956936359406, b:-0.6486347317695618
Epoch:98, Loss:1.7781479358673096, w:0.24365879595279694, b:-0.6524209380149841
Epoch:99, Loss:1.7765681743621826, w:0.24490149319171906, b:-0.6561974883079529
Epoch:100, Loss:1.7749923467636108, w:0.24615703523159027, b:-0.6599646210670471
Epoch:101, Loss:1.7734202146530151, w:0.24742484092712402, b:-0.6637226343154907
Epoch:102, Loss:1.7718517780303955, w:0.24870434403419495, b:-0.6674717664718628
Epoch:103, Loss:1.7702871561050415, w:0.24999499320983887, b:-0.6712122559547424
Epoch:104, Loss:1.768725872039795, w:0.2512962818145752, b:-0.6749443411827087
Epoch:105, Loss:1.7671678066253662, w:0.25260770320892334, b:-0.678668200969696
Epoch:106, Loss:1.765613317489624, w:0.2539287805557251, b:-0.6823841333389282
Epoch:107, Loss:1.7640621662139893, w:0.25525903701782227, b:-0.6860922574996948
Epoch:108, Loss:1.7625141143798828, w:0.2565980553627014, b:-0.689792811870575
Epoch:109, Loss:1.760969638824463, w:0.2579454183578491, b:-0.6934859752655029
Epoch:110, Loss:1.7594280242919922, w:0.25930073857307434, b:-0.6971719861030579
Epoch:111, Loss:1.7578896284103394, w:0.26066359877586365, b:-0.7008509635925293
Epoch:112, Loss:1.7563543319702148, w:0.2620336413383484, b:-0.7045230269432068
Epoch:113, Loss:1.7548218965530396, w:0.2634105086326599, b:-0.7081884145736694
Epoch:114, Loss:1.7532925605773926, w:0.26479387283325195, b:-0.7118472456932068
Epoch:115, Loss:1.7517662048339844, w:0.26618337631225586, b:-0.7154996991157532
Epoch:116, Loss:1.7502427101135254, w:0.26757875084877014, b:-0.7191458940505981
Epoch:117, Loss:1.7487220764160156, w:0.26897966861724854, b:-0.7227859497070312
Epoch:118, Loss:1.7472045421600342, w:0.27038583159446716, b:-0.726419985294342
Epoch:119, Loss:1.7456897497177124, w:0.2717970013618469, b:-0.7300481796264648
Epoch:120, Loss:1.7441776990890503, w:0.27321287989616394, b:-0.7336706519126892
Epoch:121, Loss:1.742668628692627, w:0.2746332585811615, b:-0.7372874617576599
Epoch:122, Loss:1.7411620616912842, w:0.2760578393936157, b:-0.7408987283706665
Epoch:123, Loss:1.7396583557128906, w:0.2774864435195923, b:-0.7445045709609985
Epoch:124, Loss:1.7381576299667358, w:0.2789188027381897, b:-0.7481051087379456
Epoch:125, Loss:1.7366595268249512, w:0.28035473823547363, b:-0.7517004609107971
Epoch:126, Loss:1.7351641654968262, w:0.2817940413951874, b:-0.755290687084198
Epoch:127, Loss:1.7336713075637817, w:0.2832365036010742, b:-0.758875846862793
Epoch:128, Loss:1.732181429862976, w:0.28468194603919983, b:-0.7624560594558716
Epoch:129, Loss:1.7306939363479614, w:0.2861301898956299, b:-0.7660314440727234
Epoch:130, Loss:1.7292091846466064, w:0.28758105635643005, b:-0.7696020007133484
Epoch:131, Loss:1.7277271747589111, w:0.2890343964099884, b:-0.7731678485870361
Epoch:132, Loss:1.7262475490570068, w:0.2904900312423706, b:-0.7767290472984314
Epoch:133, Loss:1.7247707843780518, w:0.2919478416442871, b:-0.7802857160568237
Epoch:134, Loss:1.7232964038848877, w:0.2934076488018036, b:-0.7838378548622131
Epoch:135, Loss:1.7218246459960938, w:0.2948693335056305, b:-0.7873855829238892
Epoch:136, Loss:1.7203559875488281, w:0.2963327467441559, b:-0.7909289598464966
Epoch:137, Loss:1.7188892364501953, w:0.2977977693080902, b:-0.7944679856300354
Epoch:138, Loss:1.7174255847930908, w:0.2992643117904663, b:-0.7980027794837952
Epoch:139, Loss:1.7159638404846191, w:0.30073222517967224, b:-0.8015334010124207
Epoch:140, Loss:1.7145053148269653, w:0.30220139026641846, b:-0.8050598502159119
Epoch:141, Loss:1.7130489349365234, w:0.3036717176437378, b:-0.8085822463035583
Epoch:142, Loss:1.7115952968597412, w:0.3051430881023407, b:-0.8121005892753601
Epoch:143, Loss:1.710144281387329, w:0.30661541223526, b:-0.8156149387359619
Epoch:144, Loss:1.708695411682129, w:0.3080885708332062, b:-0.8191252946853638
Epoch:145, Loss:1.7072491645812988, w:0.3095625042915344, b:-0.8226317763328552
Epoch:146, Loss:1.7058055400848389, w:0.3110371232032776, b:-0.8261343836784363
Epoch:147, Loss:1.704364538192749, w:0.3125123381614685, b:-0.8296331763267517
Epoch:148, Loss:1.7029259204864502, w:0.3139880895614624, b:-0.8331282138824463
Epoch:149, Loss:1.7014896869659424, w:0.3154642581939697, b:-0.83661949634552
Epoch:150, Loss:1.7000558376312256, w:0.3169408142566681, b:-0.8401070237159729
Epoch:151, Loss:1.6986244916915894, w:0.31841766834259033, b:-0.8435909152030945
Epoch:152, Loss:1.6971958875656128, w:0.3198947608470917, b:-0.8470711708068848
Epoch:153, Loss:1.6957697868347168, w:0.32137200236320496, b:-0.8505477905273438
Epoch:154, Loss:1.6943457126617432, w:0.3228493630886078, b:-0.8540208339691162
Epoch:155, Loss:1.6929242610931396, w:0.3243267834186554, b:-0.8574903607368469
Epoch:156, Loss:1.6915051937103271, w:0.3258041739463806, b:-0.8609563708305359
Epoch:157, Loss:1.6900886297225952, w:0.32728150486946106, b:-0.8644188642501831
Epoch:158, Loss:1.6886746883392334, w:0.32875871658325195, b:-0.8678779006004333
Epoch:159, Loss:1.687263011932373, w:0.3302357792854309, b:-0.8713334798812866
Epoch:160, Loss:1.6858537197113037, w:0.33171263337135315, b:-0.8747856616973877
Epoch:161, Loss:1.6844466924667358, w:0.3331892490386963, b:-0.8782344460487366
Epoch:162, Loss:1.683042287826538, w:0.33466556668281555, b:-0.881679892539978
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Epoch:945, Loss:1.04102623462677, w:1.207563877105713, b:-2.916898250579834
Epoch:946, Loss:1.0405561923980713, w:1.208404779434204, b:-2.9188966751098633
Epoch:947, Loss:1.0400868654251099, w:1.209245204925537, b:-2.920894145965576
Epoch:948, Loss:1.039617896080017, w:1.210085153579712, b:-2.9228904247283936
Epoch:949, Loss:1.039149522781372, w:1.210924506187439, b:-2.9248855113983154
Epoch:950, Loss:1.0386816263198853, w:1.2117633819580078, b:-2.926879644393921
Epoch:951, Loss:1.0382142066955566, w:1.2126017808914185, b:-2.928872585296631
Epoch:952, Loss:1.0377473831176758, w:1.213439702987671, b:-2.9308645725250244
Epoch:953, Loss:1.0372810363769531, w:1.2142771482467651, b:-2.9328553676605225
Epoch:954, Loss:1.0368150472640991, w:1.2151141166687012, b:-2.934845209121704
Epoch:955, Loss:1.0363497734069824, w:1.215950608253479, b:-2.9368338584899902
Epoch:956, Loss:1.035884976387024, w:1.2167866230010986, b:-2.93882155418396
Epoch:957, Loss:1.0354206562042236, w:1.21762216091156, b:-2.940808057785034
Epoch:958, Loss:1.034956693649292, w:1.2184572219848633, b:-2.942793607711792
Epoch:959, Loss:1.0344934463500977, w:1.2192918062210083, b:-2.9447779655456543
Epoch:960, Loss:1.0340306758880615, w:1.2201259136199951, b:-2.9467613697052
Epoch:961, Loss:1.0335686206817627, w:1.2209595441818237, b:-2.9487435817718506
Epoch:962, Loss:1.0331064462661743, w:1.2217926979064941, b:-2.9507248401641846
Epoch:963, Loss:1.032645344734192, w:1.2226252555847168, b:-2.952704906463623
Epoch:964, Loss:1.032184362411499, w:1.2234573364257812, b:-2.954684019088745
Epoch:965, Loss:1.0317240953445435, w:1.2242889404296875, b:-2.956662178039551
Epoch:966, Loss:1.031264305114746, w:1.2251200675964355, b:-2.958639144897461
Epoch:967, Loss:1.030804991722107, w:1.2259507179260254, b:-2.9606151580810547
Epoch:968, Loss:1.0303462743759155, w:1.226780891418457, b:-2.962589979171753
Epoch:969, Loss:1.0298877954483032, w:1.2276105880737305, b:-2.9645638465881348
Epoch:970, Loss:1.0294300317764282, w:1.2284398078918457, b:-2.966536521911621
Epoch:971, Loss:1.0289727449417114, w:1.2292686700820923, b:-2.968508243560791
Epoch:972, Loss:1.0285160541534424, w:1.2300970554351807, b:-2.9704787731170654
Epoch:973, Loss:1.028059482574463, w:1.2309248447418213, b:-2.9724483489990234
Epoch:974, Loss:1.0276036262512207, w:1.2317522764205933, b:-2.974416971206665
Epoch:975, Loss:1.0271483659744263, w:1.232579231262207, b:-2.976384401321411
Epoch:976, Loss:1.02669358253479, w:1.2334057092666626, b:-2.978350877761841
Epoch:977, Loss:1.026239275932312, w:1.23423171043396, b:-2.980316162109375
Epoch:978, Loss:1.025785207748413, w:1.2350572347640991, b:-2.9822804927825928
Epoch:979, Loss:1.025331974029541, w:1.23588228225708, b:-2.984243869781494
Epoch:980, Loss:1.024878978729248, w:1.2367068529129028, b:-2.9862060546875
Epoch:981, Loss:1.0244266986846924, w:1.2375309467315674, b:-2.9881672859191895
Epoch:982, Loss:1.0239746570587158, w:1.2383545637130737, b:-2.9901273250579834
Epoch:983, Loss:1.0235233306884766, w:1.2391777038574219, b:-2.992086410522461
Epoch:984, Loss:1.0230722427368164, w:1.2400003671646118, b:-2.994044542312622
Epoch:985, Loss:1.022621750831604, w:1.2408225536346436, b:-2.9960014820098877
Epoch:986, Loss:1.0221718549728394, w:1.241644263267517, b:-2.997957468032837
Epoch:987, Loss:1.0217223167419434, w:1.2424654960632324, b:-2.9999125003814697
Epoch:988, Loss:1.0212732553482056, w:1.2432862520217896, b:-3.001866340637207
Epoch:989, Loss:1.0208247900009155, w:1.2441065311431885, b:-3.003819227218628
Epoch:990, Loss:1.0203766822814941, w:1.2449263334274292, b:-3.0057711601257324
Epoch:991, Loss:1.019929051399231, w:1.2457457780838013, b:-3.0077219009399414
Epoch:992, Loss:1.019482135772705, w:1.2465647459030151, b:-3.009671688079834
Epoch:993, Loss:1.0190353393554688, w:1.2473832368850708, b:-3.01162052154541
Epoch:994, Loss:1.0185893774032593, w:1.2482012510299683, b:-3.013568162918091
Epoch:995, Loss:1.0181435346603394, w:1.2490187883377075, b:-3.015514850616455
Epoch:996, Loss:1.0176984071731567, w:1.2498358488082886, b:-3.017460584640503
Epoch:997, Loss:1.0172535181045532, w:1.2506524324417114, b:-3.0194051265716553
Epoch:998, Loss:1.0168094635009766, w:1.251468539237976, b:-3.021348714828491
Epoch:999, Loss:1.0163655281066895, w:1.2522841691970825, b:-3.0232913494110107
w = 1.2530994415283203
b = -3.0252327919006348
y_pred = tensor([0.8794])
根据输出结果可以看出,输入值为 4 的时候,即学习时长为 4(小时)的情况下,有 87.94% 的概率是可以通过考试的。说明本次训练时成功的,基本能做出正确的预测。从下图也可以看出,蓝线和红线的交点所对应的时间坐标正是 2.5(小时),即这个模型预测得到,一般学习时间超过 2.5 小时的情况下,考试便可以顺利通过。
写到这里,差不多本文也就要结束了,如有错误,敬请指正。如果我的这篇文章帮助到了你,那我也会感到很高兴,一个人能走多远,在于与谁同行。
参考文章
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