فرادرسگرادیان کاهشی (Gradient Descent) و پیاده سازی آن در پایتون — راهنمای کاربردی
۴۹۷۶ بازدید
آخرین به‌روزرسانی: ۱۷ تیر ۱۴۰۲
زمان مطالعه: ۱۶ دقیقه
«گرادیان کاهشی» (Gradient Descent) یک الگوریتم بهینه‌سازی برای پیدا کردن کمینه یک تابع است. در این الگوریتم کار با یک نقطه تصادفی روی تابع آغاز می‌شود و روی جهت منفی از گرادیان تابع حرکت می‌کند تا به کمینه محلی/سراسری برسد.
فهرست مطالب این نوشته
مثال ملموس
پرسش: کمینه محلی تابع 2(y=(x+5 که از نقطه x=3 آغاز می‌شود برابر چه مقداری است؟
راهکار: پاسخ صرفا با نگاه کردن به نمودار مشخص است. 2(y=(x+5 هنگامی به کمینه خود می‌رسد که x = -5 (یعنی x=-5, y=0). بنابراین، x=-5 کمینه محلی و سراسری تابع است. اکنون، می‌توان دید که چگونه مقدار مشابهی به صورت عددی حاصل می‌شود.
گام اول: مقداردهی اولیه با x=۳ انجام می‌شود. سپس، باید گرادیان تابع (dy/dx = 2*(x+5 را پیدا کرد
گام دوم: حرکت در جهت گرادیان منفی صورت می‌پذیرد. پرسشی که در این وهله مطرح می‌شود آن است که به چه میزان باید حرکت کرد؟ برای محاسبه این میزان نیاز به یک نرخ یادگیری است. فرض می‌کنیم که نرخ یادگیری برابر با ۰/۰۱ است.
گام ۳: اکنون دو تکرار از گرادیان کاهشی انجام می‌شود.
گام ۴: می‌توان مشاهده کرد که مقدار X به آهستگی کاهش پیدا می‌کند و باید به ۵- همگرا شود (کمینه محلی). اما سوال این است که چه تعداد تکرار باید انجام شود؟
در راستای پاسخگویی به این سوال، ابتدا یک متغیر دقت در الگوریتم تنظیم می‌شود که تفاوت بین دو مقدار متوالی x را محاسبه می‌کند. اگر تفاوت بین مقادیر x از دو تکرار متوالی کمتر از دقتی باشد که تعیین شده (توسط کاربر)، باید الگوریتم را متوقف کرد.
گرادیان کاهشی در پایتون
گام اول: مقداردهی اولیه
1cur_x = 3 # The algorithm starts at x=3
2rate = 0.01 # Learning rate
3precision = 0.000001 #This tells us when to stop the algorithm
4previous_step_size = 1 #
5max_iters = 10000 # maximum number of iterations
6iters = 0 #iteration counter
7df = lambda x: 2*(x+5) #Gradient of our functionگام دوم: اجرای یک حلقه به منظور اجرای گرادیان کاهشی
نکته: هنگامی که تفاوت بین مقادیر x از دو تکرار متوالی کمتر از 0.000001 باشد یا هنگامی که تعداد تکرارها از ۱۰۰۰۰ بیشتر شود، باید الگوریتم را متوقف کرد.
1while previous_step_size > precision and iters < max_iters:
2 prev_x = cur_x #Store current x value in prev_x
3 cur_x = cur_x - rate * df(prev_x) #Grad descent
4 previous_step_size = abs(cur_x - prev_x) #Change in x
5 iters = iters+1 #iteration count
6 print("Iteration",iters,"\nX value is",cur_x) #Print iterations
7
8print("The local minimum occurs at", cur_x)خروجی: از خروجی زیر می‌توان مقادیر x را برای اولین ۱۰ تکرار مشاهده کرد که با محاسبات بالا قابل بررسی متقابل است. الگوریتم برای ۵۹۵ تکرار پیش از آنکه متوقف شود اجرا می‌شود. کد و خروجی آن به منظور قابل ارجاع بودن در زیر قرار گرفته‌اند.
In [3]:
1cur_x = 3 # The algorithm starts at x=3
2rate = 0.01 # Learning rate
3precision = 0.000001 #This tells us when to stop the algorithm
4previous_step_size = 1 #
5max_iters = 10000 # maximum number of iterations
6iters = 0 #iteration counter
7df = lambda x: 2*(x+5) #Gradient of our functionIn [4]:
1while previous_step_size > precision and iters < max_iters:
2 prev_x = cur_x #Store current x value in prev_x
3 cur_x = cur_x - rate * df(prev_x) #Grad descent
4 previous_step_size = abs(cur_x - prev_x) #Change in x
5 iters = iters+1 #iteration count
6 print("Iteration",iters,"\nX value is",cur_x) #Print iterations
7
8print("The local minimum occurs at", cur_x)Iteration 1 X value is 2.84 Iteration 2 X value is 2.6832 Iteration 3 X value is 2.529536 Iteration 4 X value is 2.37894528 Iteration 5 X value is 2.2313663744 Iteration 6 X value is 2.0867390469119997 Iteration 7 X value is 1.9450042659737599 Iteration 8 X value is 1.8061041806542846 Iteration 9 X value is 1.669982097041199 Iteration 10 X value is 1.5365824551003748 Iteration 11 X value is 1.4058508059983674 Iteration 12 X value is 1.2777337898784 Iteration 13 X value is 1.152179114080832 Iteration 14 X value is 1.0291355317992152 Iteration 15 X value is 0.9085528211632309 Iteration 16 X value is 0.7903817647399662 Iteration 17 X value is 0.6745741294451669 Iteration 18 X value is 0.5610826468562635 Iteration 19 X value is 0.44986099391913825 Iteration 20 X value is 0.3408637740407555 Iteration 21 X value is 0.23404649855994042 Iteration 22 X value is 0.1293655685887416 Iteration 23 X value is 0.026778257216966764 Iteration 24 X value is -0.07375730792737258 Iteration 25 X value is -0.1722821617688251 Iteration 26 X value is -0.2688365185334486 Iteration 27 X value is -0.36345978816277963 Iteration 28 X value is -0.45619059239952403 Iteration 29 X value is -0.5470667805515336 Iteration 30 X value is -0.6361254449405029 Iteration 31 X value is -0.7234029360416929 Iteration 32 X value is -0.8089348773208591 Iteration 33 X value is -0.8927561797744419 Iteration 34 X value is -0.9749010561789531 Iteration 35 X value is -1.055403035055374 Iteration 36 X value is -1.1342949743542665 Iteration 37 X value is -1.2116090748671813 Iteration 38 X value is -1.2873768933698377 Iteration 39 X value is -1.361629355502441 Iteration 40 X value is -1.4343967683923922 Iteration 41 X value is -1.5057088330245443 Iteration 42 X value is -1.5755946563640535 Iteration 43 X value is -1.6440827632367725 Iteration 44 X value is -1.711201107972037 Iteration 45 X value is -1.7769770858125964 Iteration 46 X value is -1.8414375440963444 Iteration 47 X value is -1.9046087932144176 Iteration 48 X value is -1.9665166173501292 Iteration 49 X value is -2.0271862850031264 Iteration 50 X value is -2.0866425593030637 Iteration 51 X value is -2.1449097081170025 Iteration 52 X value is -2.2020115139546625 Iteration 53 X value is -2.257971283675569 Iteration 54 X value is -2.312811858002058 Iteration 55 X value is -2.3665556208420164 Iteration 56 X value is -2.419224508425176 Iteration 57 X value is -2.4708400182566725 Iteration 58 X value is -2.521423217891539 Iteration 59 X value is -2.570994753533708 Iteration 60 X value is -2.619574858463034 Iteration 61 X value is -2.667183361293773 Iteration 62 X value is -2.713839694067898 Iteration 63 X value is -2.75956290018654 Iteration 64 X value is -2.804371642182809 Iteration 65 X value is -2.8482842093391527 Iteration 66 X value is -2.8913185251523696 Iteration 67 X value is -2.9334921546493224 Iteration 68 X value is -2.974822311556336 Iteration 69 X value is -3.015325865325209 Iteration 70 X value is -3.055019348018705 Iteration 71 X value is -3.093918961058331 Iteration 72 X value is -3.1320405818371646 Iteration 73 X value is -3.1693997702004215 Iteration 74 X value is -3.206011774796413 Iteration 75 X value is -3.2418915393004846 Iteration 76 X value is -3.277053708514475 Iteration 77 X value is -3.3115126343441856 Iteration 78 X value is -3.345282381657302 Iteration 79 X value is -3.378376734024156 Iteration 80 X value is -3.4108091993436727 Iteration 81 X value is -3.4425930153567994 Iteration 82 X value is -3.4737411550496633 Iteration 83 X value is -3.50426633194867 Iteration 84 X value is -3.534181005309697 Iteration 85 X value is -3.563497385203503 Iteration 86 X value is -3.5922274374994325 Iteration 87 X value is -3.620382888749444 Iteration 88 X value is -3.6479752309744553 Iteration 89 X value is -3.675015726354966 Iteration 90 X value is -3.7015154118278666 Iteration 91 X value is -3.7274851035913095 Iteration 92 X value is -3.7529354015194833 Iteration 93 X value is -3.7778766934890937 Iteration 94 X value is -3.8023191596193118 Iteration 95 X value is -3.8262727764269258 Iteration 96 X value is -3.8497473208983872 Iteration 97 X value is -3.8727523744804193 Iteration 98 X value is -3.895297326990811 Iteration 99 X value is -3.917391380450995 Iteration 100 X value is -3.939043552841975 Iteration 101 X value is -3.9602626817851356 Iteration 102 X value is -3.981057428149433 Iteration 103 X value is -4.001436279586445 Iteration 104 X value is -4.021407553994716 Iteration 105 X value is -4.040979402914822 Iteration 106 X value is -4.060159814856525 Iteration 107 X value is -4.078956618559395 Iteration 108 X value is -4.097377486188207 Iteration 109 X value is -4.115429936464443 Iteration 110 X value is -4.133121337735154 Iteration 111 X value is -4.150458910980451 Iteration 112 X value is -4.167449732760842 Iteration 113 X value is -4.1841007381056246 Iteration 114 X value is -4.200418723343512 Iteration 115 X value is -4.216410348876642 Iteration 116 X value is -4.2320821418991095 Iteration 117 X value is -4.247440499061128 Iteration 118 X value is -4.262491689079905 Iteration 119 X value is -4.277241855298307 Iteration 120 X value is -4.291697018192341 Iteration 121 X value is -4.305863077828494 Iteration 122 X value is -4.319745816271924 Iteration 123 X value is -4.333350899946486 Iteration 124 X value is -4.3466838819475555 Iteration 125 X value is -4.359750204308605 Iteration 126 X value is -4.372555200222433 Iteration 127 X value is -4.385104096217984 Iteration 128 X value is -4.3974020142936245 Iteration 129 X value is -4.409453974007752 Iteration 130 X value is -4.421264894527597 Iteration 131 X value is -4.432839596637045 Iteration 132 X value is -4.444182804704305 Iteration 133 X value is -4.4552991486102185 Iteration 134 X value is -4.466193165638014 Iteration 135 X value is -4.4768693023252535 Iteration 136 X value is -4.487331916278748 Iteration 137 X value is -4.497585277953173 Iteration 138 X value is -4.50763357239411 Iteration 139 X value is -4.517480900946228 Iteration 140 X value is -4.527131282927304 Iteration 141 X value is -4.536588657268758 Iteration 142 X value is -4.545856884123382 Iteration 143 X value is -4.5549397464409145 Iteration 144 X value is -4.563840951512097 Iteration 145 X value is -4.572564132481855 Iteration 146 X value is -4.581112849832218 Iteration 147 X value is -4.589490592835574 Iteration 148 X value is -4.597700780978863 Iteration 149 X value is -4.605746765359285 Iteration 150 X value is -4.6136318300521 Iteration 151 X value is -4.621359193451058 Iteration 152 X value is -4.628932009582036 Iteration 153 X value is -4.636353369390395 Iteration 154 X value is -4.643626302002588 Iteration 155 X value is -4.650753775962536 Iteration 156 X value is -4.657738700443285 Iteration 157 X value is -4.664583926434419 Iteration 158 X value is -4.671292247905731 Iteration 159 X value is -4.6778664029476165 Iteration 160 X value is -4.684309074888664 Iteration 161 X value is -4.6906228933908904 Iteration 162 X value is -4.696810435523073 Iteration 163 X value is -4.702874226812612 Iteration 164 X value is -4.708816742276359 Iteration 165 X value is -4.714640407430832 Iteration 166 X value is -4.720347599282215 Iteration 167 X value is -4.725940647296571 Iteration 168 X value is -4.731421834350639 Iteration 169 X value is -4.736793397663627 Iteration 170 X value is -4.742057529710355 Iteration 171 X value is -4.747216379116147 Iteration 172 X value is -4.752272051533824 Iteration 173 X value is -4.757226610503148 Iteration 174 X value is -4.762082078293084 Iteration 175 X value is -4.766840436727223 Iteration 176 X value is -4.771503627992678 Iteration 177 X value is -4.776073555432824 Iteration 178 X value is -4.780552084324168 Iteration 179 X value is -4.784941042637685 Iteration 180 X value is -4.7892422217849315 Iteration 181 X value is -4.793457377349233 Iteration 182 X value is -4.7975882298022485 Iteration 183 X value is -4.801636465206204 Iteration 184 X value is -4.805603735902079 Iteration 185 X value is -4.809491661184038 Iteration 186 X value is -4.813301827960357 Iteration 187 X value is -4.81703579140115 Iteration 188 X value is -4.820695075573127 Iteration 189 X value is -4.824281174061665 Iteration 190 X value is -4.827795550580431 Iteration 191 X value is -4.831239639568823 Iteration 192 X value is -4.834614846777447 Iteration 193 X value is -4.837922549841898 Iteration 194 X value is -4.84116409884506 Iteration 195 X value is -4.844340816868159 Iteration 196 X value is -4.847454000530796 Iteration 197 X value is -4.85050492052018 Iteration 198 X value is -4.853494822109776 Iteration 199 X value is -4.85642492566758 Iteration 200 X value is -4.859296427154229 Iteration 201 X value is -4.862110498611145 Iteration 202 X value is -4.864868288638922 Iteration 203 X value is -4.867570922866143 Iteration 204 X value is -4.87021950440882 Iteration 205 X value is -4.872815114320644 Iteration 206 X value is -4.875358812034231 Iteration 207 X value is -4.877851635793546 Iteration 208 X value is -4.880294603077676 Iteration 209 X value is -4.882688711016122 Iteration 210 X value is -4.8850349367958 Iteration 211 X value is -4.887334238059884 Iteration 212 X value is -4.8895875532986866 Iteration 213 X value is -4.891795802232712 Iteration 214 X value is -4.893959886188058 Iteration 215 X value is -4.896080688464297 Iteration 216 X value is -4.898159074695011 Iteration 217 X value is -4.9001958932011105 Iteration 218 X value is -4.902191975337089 Iteration 219 X value is -4.904148135830347 Iteration 220 X value is -4.90606517311374 Iteration 221 X value is -4.907943869651465 Iteration 222 X value is -4.909784992258436 Iteration 223 X value is -4.911589292413267 Iteration 224 X value is -4.913357506565002 Iteration 225 X value is -4.915090356433702 Iteration 226 X value is -4.9167885493050285 Iteration 227 X value is -4.918452778318928 Iteration 228 X value is -4.920083722752549 Iteration 229 X value is -4.921682048297498 Iteration 230 X value is -4.923248407331548 Iteration 231 X value is -4.9247834391849175 Iteration 232 X value is -4.926287770401219 Iteration 233 X value is -4.927762014993195 Iteration 234 X value is -4.929206774693331 Iteration 235 X value is -4.930622639199464 Iteration 236 X value is -4.932010186415474 Iteration 237 X value is -4.933369982687164 Iteration 238 X value is -4.934702583033421 Iteration 239 X value is -4.936008531372753 Iteration 240 X value is -4.937288360745298 Iteration 241 X value is -4.938542593530392 Iteration 242 X value is -4.939771741659784 Iteration 243 X value is -4.940976306826588 Iteration 244 X value is -4.942156780690056 Iteration 245 X value is -4.943313645076255 Iteration 246 X value is -4.94444737217473 Iteration 247 X value is -4.945558424731236 Iteration 248 X value is -4.946647256236611 Iteration 249 X value is -4.947714311111879 Iteration 250 X value is -4.9487600248896415 Iteration 251 X value is -4.949784824391848 Iteration 252 X value is -4.950789127904011 Iteration 253 X value is -4.951773345345931 Iteration 254 X value is -4.952737878439012 Iteration 255 X value is -4.953683120870232 Iteration 256 X value is -4.954609458452827 Iteration 257 X value is -4.955517269283771 Iteration 258 X value is -4.956406923898095 Iteration 259 X value is -4.957278785420133 Iteration 260 X value is -4.958133209711731 Iteration 261 X value is -4.958970545517496 Iteration 262 X value is -4.959791134607146 Iteration 263 X value is -4.960595311915003 Iteration 264 X value is -4.9613834056767026 Iteration 265 X value is -4.962155737563169 Iteration 266 X value is -4.962912622811905 Iteration 267 X value is -4.963654370355667 Iteration 268 X value is -4.964381282948554 Iteration 269 X value is -4.965093657289583 Iteration 270 X value is -4.965791784143791 Iteration 271 X value is -4.966475948460915 Iteration 272 X value is -4.967146429491697 Iteration 273 X value is -4.967803500901863 Iteration 274 X value is -4.968447430883826 Iteration 275 X value is -4.969078482266149 Iteration 276 X value is -4.969696912620826 Iteration 277 X value is -4.970302974368409 Iteration 278 X value is -4.970896914881041 Iteration 279 X value is -4.97147897658342 Iteration 280 X value is -4.972049397051752 Iteration 281 X value is -4.972608409110717 Iteration 282 X value is -4.973156240928502 Iteration 283 X value is -4.973693116109932 Iteration 284 X value is -4.974219253787734 Iteration 285 X value is -4.974734868711979 Iteration 286 X value is -4.975240171337739 Iteration 287 X value is -4.975735367910985 Iteration 288 X value is -4.976220660552765 Iteration 289 X value is -4.976696247341709 Iteration 290 X value is -4.977162322394875 Iteration 291 X value is -4.977619075946977 Iteration 292 X value is -4.978066694428038 Iteration 293 X value is -4.978505360539477 Iteration 294 X value is -4.978935253328687 Iteration 295 X value is -4.979356548262113 Iteration 296 X value is -4.979769417296871 Iteration 297 X value is -4.980174028950934 Iteration 298 X value is -4.980570548371915 Iteration 299 X value is -4.980959137404477 Iteration 300 X value is -4.981339954656387 Iteration 301 X value is -4.981713155563259 Iteration 302 X value is -4.982078892451994 Iteration 303 X value is -4.9824373146029535 Iteration 304 X value is -4.982788568310895 Iteration 305 X value is -4.983132796944677 Iteration 306 X value is -4.983470141005784 Iteration 307 X value is -4.983800738185668 Iteration 308 X value is -4.984124723421955 Iteration 309 X value is -4.984442228953515 Iteration 310 X value is -4.984753384374445 Iteration 311 X value is -4.985058316686956 Iteration 312 X value is -4.9853571503532175 Iteration 313 X value is -4.985650007346153 Iteration 314 X value is -4.9859370071992295 Iteration 315 X value is -4.986218267055245 Iteration 316 X value is -4.98649390171414 Iteration 317 X value is -4.986764023679857 Iteration 318 X value is -4.98702874320626 Iteration 319 X value is -4.987288168342134 Iteration 320 X value is -4.987542404975292 Iteration 321 X value is -4.987791556875786 Iteration 322 X value is -4.98803572573827 Iteration 323 X value is -4.988275011223505 Iteration 324 X value is -4.988509510999035 Iteration 325 X value is -4.988739320779054 Iteration 326 X value is -4.988964534363473 Iteration 327 X value is -4.989185243676204 Iteration 328 X value is -4.98940153880268 Iteration 329 X value is -4.989613508026626 Iteration 330 X value is -4.989821237866094 Iteration 331 X value is -4.990024813108772 Iteration 332 X value is -4.9902243168465965 Iteration 333 X value is -4.990419830509665 Iteration 334 X value is -4.990611433899471 Iteration 335 X value is -4.990799205221482 Iteration 336 X value is -4.990983221117052 Iteration 337 X value is -4.991163556694711 Iteration 338 X value is -4.991340285560817 Iteration 339 X value is -4.9915134798496 Iteration 340 X value is -4.991683210252608 Iteration 341 X value is -4.991849546047556 Iteration 342 X value is -4.992012555126605 Iteration 343 X value is -4.992172304024073 Iteration 344 X value is -4.992328857943591 Iteration 345 X value is -4.99248228078472 Iteration 346 X value is -4.992632635169025 Iteration 347 X value is -4.9927799824656445 Iteration 348 X value is -4.992924382816332 Iteration 349 X value is -4.993065895160005 Iteration 350 X value is -4.993204577256805 Iteration 351 X value is -4.993340485711669 Iteration 352 X value is -4.993473675997436 Iteration 353 X value is -4.993604202477487 Iteration 354 X value is -4.993732118427937 Iteration 355 X value is -4.993857476059379 Iteration 356 X value is -4.993980326538191 Iteration 357 X value is -4.9941007200074266 Iteration 358 X value is -4.994218705607278 Iteration 359 X value is -4.994334331495133 Iteration 360 X value is -4.994447644865231 Iteration 361 X value is -4.994558691967926 Iteration 362 X value is -4.994667518128567 Iteration 363 X value is -4.994774167765996 Iteration 364 X value is -4.9948786844106765 Iteration 365 X value is -4.994981110722463 Iteration 366 X value is -4.995081488508014 Iteration 367 X value is -4.995179858737854 Iteration 368 X value is -4.995276261563097 Iteration 369 X value is -4.995370736331835 Iteration 370 X value is -4.9954633216051985 Iteration 371 X value is -4.995554055173095 Iteration 372 X value is -4.995642974069633 Iteration 373 X value is -4.99573011458824 Iteration 374 X value is -4.995815512296476 Iteration 375 X value is -4.995899202050547 Iteration 376 X value is -4.995981218009535 Iteration 377 X value is -4.996061593649345 Iteration 378 X value is -4.996140361776358 Iteration 379 X value is -4.996217554540831 Iteration 380 X value is -4.996293203450014 Iteration 381 X value is -4.996367339381013 Iteration 382 X value is -4.996439992593393 Iteration 383 X value is -4.996511192741525 Iteration 384 X value is -4.996580968886694 Iteration 385 X value is -4.99664934950896 Iteration 386 X value is -4.9967163625187805 Iteration 387 X value is 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Iteration 501 X value is -4.9996783719564615 Iteration 502 X value is -4.999684804517332 Iteration 503 X value is -4.999691108426985 Iteration 504 X value is -4.999697286258446 Iteration 505 X value is -4.9997033405332765 Iteration 506 X value is -4.999709273722611 Iteration 507 X value is -4.999715088248159 Iteration 508 X value is -4.999720786483196 Iteration 509 X value is -4.999726370753532 Iteration 510 X value is -4.999731843338461 Iteration 511 X value is -4.999737206471692 Iteration 512 X value is -4.999742462342258 Iteration 513 X value is -4.999747613095413 Iteration 514 X value is -4.999752660833504 Iteration 515 X value is -4.999757607616834 Iteration 516 X value is -4.999762455464498 Iteration 517 X value is -4.999767206355208 Iteration 518 X value is -4.999771862228104 Iteration 519 X value is -4.999776424983542 Iteration 520 X value is -4.9997808964838715 Iteration 521 X value is -4.999785278554194 Iteration 522 X value is -4.9997895729831106 Iteration 523 X value is 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Iteration 569 X value is -4.999918580757781 Iteration 570 X value is -4.999920209142625 Iteration 571 X value is -4.999921804959773 Iteration 572 X value is -4.9999233688605775 Iteration 573 X value is -4.999924901483366 Iteration 574 X value is -4.999926403453699 Iteration 575 X value is -4.999927875384625 Iteration 576 X value is -4.999929317876933 Iteration 577 X value is -4.999930731519394 Iteration 578 X value is -4.999932116889006 Iteration 579 X value is -4.999933474551226 Iteration 580 X value is -4.999934805060202 Iteration 581 X value is -4.999936108958998 Iteration 582 X value is -4.999937386779818 Iteration 583 X value is -4.999938639044221 Iteration 584 X value is -4.999939866263337 Iteration 585 X value is -4.99994106893807 Iteration 586 X value is -4.999942247559309 Iteration 587 X value is -4.999943402608123 Iteration 588 X value is -4.9999445345559606 Iteration 589 X value is -4.999945643864842 Iteration 590 X value is -4.999946730987545 Iteration 591 X value is 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اگر نوشته بالا برای شما مفید بوده، آموزش‌های زیر نیز به شما پیشنهاد می‌شوند:
- مجموعه آموزش‌های هوش محاسباتی
- مجموعه آموزش‌های شبکه‌های عصبی مصنوعی
- مجموعه آموزش‌های آمار، احتمالات و داده‌کاوی
- گنجینه آموزش‌های برنامه نویسی پایتون (Python)
- معرفی منابع جهت آموزش یادگیری عمیق (Deep Learning) — راهنمای کامل
- معرفی منابع آموزش ویدئویی هوش مصنوعی به زبان فارسی و انگلیسی
^^
اگر بازخوردی درباره این مطلب دارید یا پرسشی دارید که بدون پاسخ مانده است، آن را از طریق بخش نظرات مطرح کنید.
منابع:
towardsdatasciencehttps://b.fdrs.ir/15d
«الهام حصارکی»، فارغ‌التحصیل مقطع کارشناسی ارشد مهندسی فناوری اطلاعات، گرایش سیستم‌های اطلاعات مدیریت است. او در زمینه هوش مصنوعی و داده‌کاوی، به ویژه تحلیل شبکه‌های اجتماعی، فعالیت می‌کند.
مطالب مرتبط
سلام. من يه چيزي رو متوجه نشدم. ما كه همون اول فرمول مشتق رو داريم. برا چي همون اول برابر با صفر قرارش نميديم؟!
سلام
اگر بخواهیم برنامه رو جوری بنویسیم که تابع متغیر باشه یعنی هر تابع چند متغیره دلخواهی رو بشه بهش بدیم باید چه کاری انجام بدیم؟
بسیار عالی
بسیار عالی
بابا شیرافکن کارت درسته!!
🙂