Skip to content

Commit a67ee26

Browse files
author
Kia Teymourian
committed
update
1 parent 8cab6c8 commit a67ee26

File tree

1 file changed

+106
-36
lines changed

1 file changed

+106
-36
lines changed

‎Code-Example-015.1--Gradient-Descents-Vectorized.ipynb

Lines changed: 106 additions & 36 deletions
Original file line numberDiff line numberDiff line change
@@ -132,52 +132,122 @@
132132
},
133133
{
134134
"cell_type": "code",
135-
"execution_count": 6,
135+
"execution_count": 10,
136136
"metadata": {},
137137
"outputs": [
138138
{
139139
"name": "stdout",
140140
"output_type": "stream",
141141
"text": [
142-
"0 m= 0 Cost= 187.5\n",
143-
"1 m= 0.15 Cost= 165.675\n",
144-
"2 m= 0.29100000000000004 Cost= 146.39043\n",
145-
"3 m= 0.4235400000000001 Cost= 129.350583948\n",
146-
"4 m= 0.5481276000000002 Cost= 114.29417597645278\n",
147-
"5 m= 0.6652399440000002 Cost= 100.99033389279367\n",
148-
"6 m= 0.7753255473600003 Cost= 89.23505902767249\n",
149-
"7 m= 0.8788060145184002 Cost= 78.84809815685139\n",
150-
"8 m= 0.9760776536472963 Cost= 69.67017953139388\n",
151-
"9 m= 1.0675129944284585 Cost= 61.56057063393965\n",
152-
"10 m= 1.153462214762751 Cost= 54.394920212149074\n",
153-
"11 m= 1.2342544818769858 Cost= 48.063351499454924\n",
154-
"12 m= 1.3101992129643667 Cost= 42.46877738491837\n",
155-
"13 m= 1.3815872601865047 Cost= 37.52541169731388\n",
156-
"14 m= 1.4486920245753143 Cost= 33.157453775746546\n",
157-
"15 m= 1.5117705031007955 Cost= 29.29792615624964\n",
158-
"16 m= 1.5710642729147477 Cost= 25.887647551662187\n",
159-
"17 m= 1.6268004165398628 Cost= 22.874325376648713\n",
160-
"18 m= 1.6791923915474711 Cost= 20.211753902806798\n",
161-
"19 m= 1.728440848054623 Cost= 17.859105748520083\n",
162-
"20 m= 1.7747343971713456 Cost= 15.78030583939234\n",
163-
"21 m= 1.818250333341065 Cost= 13.943478239687074\n",
164-
"22 m= 1.859155313340601 Cost= 12.320457372587502\n",
165-
"23 m= 1.8976059945401649 Cost= 10.886356134418314\n",
166-
"24 m= 1.933749634867755 Cost= 9.619184280372027\n",
167-
"25 m= 1.9677246567756896 Cost= 8.499511230136722\n",
168-
"26 m= 1.9996611773691482 Cost= 7.51016812294881\n",
169-
"27 m= 2.029681506726999 Cost= 6.635984553437574\n",
170-
"28 m= 2.057900616323379 Cost= 5.8635559514174425\n",
171-
"29 m= 2.0844265793439765 Cost= 5.1810380386724475\n"
142+
"0 beta = 0 Cost= 187.5\n",
143+
"1 beta = 0.15 Cost= 165.675\n",
144+
"2 beta = 0.29100000000000004 Cost= 146.39043\n",
145+
"3 beta = 0.4235400000000001 Cost= 129.350583948\n",
146+
"4 beta = 0.5481276000000002 Cost= 114.29417597645278\n",
147+
"5 beta = 0.6652399440000002 Cost= 100.99033389279367\n",
148+
"6 beta = 0.7753255473600003 Cost= 89.23505902767249\n",
149+
"7 beta = 0.8788060145184002 Cost= 78.84809815685139\n",
150+
"8 beta = 0.9760776536472963 Cost= 69.67017953139388\n",
151+
"9 beta = 1.0675129944284585 Cost= 61.56057063393965\n",
152+
"10 beta = 1.153462214762751 Cost= 54.394920212149074\n",
153+
"11 beta = 1.2342544818769858 Cost= 48.063351499454924\n",
154+
"12 beta = 1.3101992129643667 Cost= 42.46877738491837\n",
155+
"13 beta = 1.3815872601865047 Cost= 37.52541169731388\n",
156+
"14 beta = 1.4486920245753143 Cost= 33.157453775746546\n",
157+
"15 beta = 1.5117705031007955 Cost= 29.29792615624964\n",
158+
"16 beta = 1.5710642729147477 Cost= 25.887647551662187\n",
159+
"17 beta = 1.6268004165398628 Cost= 22.874325376648713\n",
160+
"18 beta = 1.6791923915474711 Cost= 20.211753902806798\n",
161+
"19 beta = 1.728440848054623 Cost= 17.859105748520083\n",
162+
"20 beta = 1.7747343971713456 Cost= 15.78030583939234\n",
163+
"21 beta = 1.818250333341065 Cost= 13.943478239687074\n",
164+
"22 beta = 1.859155313340601 Cost= 12.320457372587502\n",
165+
"23 beta = 1.8976059945401649 Cost= 10.886356134418314\n",
166+
"24 beta = 1.933749634867755 Cost= 9.619184280372027\n",
167+
"25 beta = 1.9677246567756896 Cost= 8.499511230136722\n",
168+
"26 beta = 1.9996611773691482 Cost= 7.51016812294881\n",
169+
"27 beta = 2.029681506726999 Cost= 6.635984553437574\n",
170+
"28 beta = 2.057900616323379 Cost= 5.8635559514174425\n",
171+
"29 beta = 2.0844265793439765 Cost= 5.1810380386724475\n",
172+
"30 beta = 2.109360984583338 Cost= 4.57796521097097\n",
173+
"31 beta = 2.132799325508338 Cost= 4.045090060413946\n",
174+
"32 beta = 2.1548313659778375 Cost= 3.574241577381767\n",
175+
"33 beta = 2.1755414840191674 Cost= 3.158199857774526\n",
176+
"34 beta = 2.1950089949780174 Cost= 2.7905853943295718\n",
177+
"35 beta = 2.2133084552793365 Cost= 2.465761254429606\n",
178+
"36 beta = 2.2305099479625765 Cost= 2.1787466444139967\n",
179+
"37 beta = 2.246679351084822 Cost= 1.9251405350042066\n",
180+
"38 beta = 2.2618785900197325 Cost= 1.701054176729719\n",
181+
"39 beta = 2.2761658746185485 Cost= 1.5030514705583815\n",
182+
"40 beta = 2.2895959221414355 Cost= 1.3280962793853863\n",
183+
"41 beta = 2.3022201668129494 Cost= 1.173505872464927\n",
184+
"42 beta = 2.3140869568041724 Cost= 1.0369097889100094\n",
185+
"43 beta = 2.325241739395922 Cost= 0.9162134894808864\n",
186+
"44 beta = 2.3357272350321665 Cost= 0.8095662393053119\n",
187+
"45 beta = 2.3455836009302367 Cost= 0.7153327290501723\n",
188+
"46 beta = 2.3548485848744223 Cost= 0.6320679993887337\n",
189+
"47 beta = 2.363557669781957 Cost= 0.5584952842598836\n",
190+
"48 beta = 2.3717442095950396 Cost= 0.49348643317203383\n",
191+
"49 beta = 2.3794395570193374 Cost= 0.4360446123508076\n",
192+
"50 beta = 2.386673183598177 Cost= 0.3852890194731736\n",
193+
"51 beta = 2.3934727925822865 Cost= 0.34044137760649684\n",
194+
"52 beta = 2.3998644250273493 Cost= 0.3008140012531004\n",
195+
"53 beta = 2.4058725595257084 Cost= 0.26579925150723877\n",
196+
"54 beta = 2.411520205954166 Cost= 0.2348602186317958\n",
197+
"55 beta = 2.416828993596916 Cost= 0.20752248918305471\n",
198+
"56 beta = 2.421819253981101 Cost= 0.1833668714421468\n",
199+
"57 beta = 2.426510098742235 Cost= 0.16202296760628054\n",
200+
"58 beta = 2.430919492817701 Cost= 0.1431634941769091\n",
201+
"59 beta = 2.435064323248639 Cost= 0.12649926345471704\n",
202+
"60 beta = 2.4389604638537206 Cost= 0.11177474918858862\n",
203+
"61 beta = 2.4426228360224975 Cost= 0.09876416838303623\n",
204+
"62 beta = 2.446065465861148 Cost= 0.08726801918325036\n",
205+
"63 beta = 2.449301537909479 Cost= 0.07711002175032013\n",
206+
"64 beta = 2.4523434456349102 Cost= 0.06813441521858266\n",
207+
"65 beta = 2.4552028388968155 Cost= 0.06020356928714\n",
208+
"66 beta = 2.4578906685630066 Cost= 0.05319587382211671\n",
209+
"67 beta = 2.4604172284492263 Cost= 0.04700387410922224\n",
210+
"68 beta = 2.462792194742273 Cost= 0.04153262316290836\n",
211+
"69 beta = 2.4650246630577364 Cost= 0.03669822582674612\n",
212+
"70 beta = 2.467123183274272 Cost= 0.032426552340512935\n",
213+
"71 beta = 2.4690957922778156 Cost= 0.02865210164807771\n",
214+
"72 beta = 2.4709500447411465 Cost= 0.025316997016241547\n",
215+
"73 beta = 2.4726930420566777 Cost= 0.02237009856355114\n",
216+
"74 beta = 2.474331459533277 Cost= 0.019766219090753746\n",
217+
"75 beta = 2.4758715719612803 Cost= 0.01746543118859023\n",
218+
"76 beta = 2.4773192776436033 Cost= 0.015432454998238695\n",
219+
"77 beta = 2.478680120984987 Cost= 0.01363611723644358\n",
220+
"78 beta = 2.479959313725888 Cost= 0.012048873190121483\n",
221+
"79 beta = 2.4811617549023346 Cost= 0.010646384350791443\n",
222+
"80 beta = 2.4822920496081946 Cost= 0.009407145212359178\n",
223+
"81 beta = 2.483354526631703 Cost= 0.008312153509640565\n",
224+
"82 beta = 2.484353255033801 Cost= 0.00734461884111842\n",
225+
"83 beta = 2.4852920597317727 Cost= 0.006489705208012267\n",
226+
"84 beta = 2.486174536147866 Cost= 0.005734303521799706\n",
227+
"85 beta = 2.4870040639789943 Cost= 0.005066830591862191\n",
228+
"86 beta = 2.4877838201402547 Cost= 0.004477051510969419\n",
229+
"87 beta = 2.4885167909318393 Cost= 0.00395592271509267\n",
230+
"88 beta = 2.489205783475929 Cost= 0.0034954533110557644\n",
231+
"89 beta = 2.4898534364673734 Cost= 0.0030885825456488103\n",
232+
"90 beta = 2.490462230279331 Cost= 0.0027290715373352223\n",
233+
"91 beta = 2.491034496462571 Cost= 0.002411407610389568\n",
234+
"92 beta = 2.491572426674817 Cost= 0.0021307197645401158\n",
235+
"93 beta = 2.492078081074328 Cost= 0.001882703983947638\n",
236+
"94 beta = 2.492553396209868 Cost= 0.0016635572402162084\n",
237+
"95 beta = 2.4930001924372758 Cost= 0.0014699191774551193\n",
238+
"96 beta = 2.493420180891039 Cost= 0.0012988205851994649\n",
239+
"97 beta = 2.4938149700375765 Cost= 0.001147637869082291\n",
240+
"98 beta = 2.4941860718353217 Cost= 0.001014052821121186\n",
241+
"99 beta = 2.4945349075252023 Cost= 0.0008960170727426972\n"
172242
]
173243
}
174244
],
175245
"source": [
176246
"# Now, we do gradient descent here with a very simple numpy array \n",
177247
"\n",
178248
"learningRate = 0.01\n",
179-
"num_iteration = 30 \n",
180-
"m_current=0\n",
249+
"num_iteration = 100\n",
250+
"beta=0\n",
181251
"\n",
182252
"n = float(size)\n",
183253
"# print(\"Sample size\", n)\n",
@@ -186,7 +256,7 @@
186256
"for i in range(num_iteration):\n",
187257
" \n",
188258
" # Calculate the prediction with current regression coefficients. \n",
189-
" y_prediction = m_current * x1 \n",
259+
" y_prediction = beta * x1 \n",
190260
" \n",
191261
" \n",
192262
" # We compute costs just for monitoring \n",
@@ -196,10 +266,10 @@
196266
" m_gradient = (-1.0/n) * sum (x1 * (y - y_prediction) )\n",
197267
" \n",
198268
" \n",
199-
" print(i , \"m=\", m_current, \" Cost=\", cost)\n",
269+
" print(i , \"beta = \", beta, \" Cost=\", cost)\n",
200270
" \n",
201271
" # update the weights - Regression Coefficients \n",
202-
" m_current = m_current - learningRate * m_gradient "
272+
" beta = beta - learningRate * m_gradient "
203273
]
204274
},
205275
{

0 commit comments

Comments
 (0)