Knowledge

Parity learning

Source ๐Ÿ“

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Adam Tauman Kalai, Yishay Mansour, and Elad Verbin, โ€œOn agnostic boosting and parity learning,โ€ in Proceedings of the 40th annual ACM symposium on Theory of computing (Victoria, British Columbia, Canada: ACM, 2008), 629–638,
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Oded Regev, โ€œOn lattices, learning with errors, random linear codes, and cryptography,โ€ in Proceedings of the thirty-seventh annual ACM symposium on Theory of computing (Baltimore, MD, USA: ACM, 2005), 84–93,
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Avrim Blum, Adam Kalai, and Hal Wasserman, โ€œNoise-tolerant learning, the parity problem, and the statistical query model,โ€ J. ACM 50, no. 4 (2003): 506–519.
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Wasserman, Hal; Kalai, Adam; Blum, Avrim (2000-10-15). "Noise-Tolerant Learning, the Parity Problem, and the Statistical Query Model".
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of bits at some fixed locations. The samples are generated using some distribution over the input. The problem is easy to solve using
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provided that a sufficient number of samples (from a distribution which is not too skewed) are provided to the algorithm.
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The noisy version of the parity learning problem is conjectured to be hard and is widely used in cryptography.
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In Learning Parity with Noise (LPN), the samples may contain some error. Instead of samples (
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International Conference on Current Trends in Theory and Practice of Computer Science
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http://portal.acm.org/citation.cfm?id=1060590.1060603
124: 85: 243: 205: 109: 374: 267:"Cryptography from learning parity with noise" 357: 299:http://portal.acm.org/citation.cfm?id=1374466 104: 92: 55:Noisy version ("Learning Parity with Noise") 364: 350: 249: 264: 375: 316: 71:)), the algorithm is provided with ( 13: 14: 399: 320: 258: 237: 183: 177: 148: 142: 1: 230: 336:. You can help Knowledge by 265:Pietrzak, Krzysztof (2012). 110:{\displaystyle b\in \{0,1\}} 79:), where for random boolean 7: 282:10.1007/978-3-642-27660-6_9 218: 10: 404: 315: 39:)) and the assurance that 388:Applied mathematics stubs 332:-related article is a 207: 111: 27:, given some samples ( 208: 112: 225:Learning with errors 122: 83: 49:Gaussian elimination 330:applied mathematics 203: 198: 107: 345: 344: 194: 159: 395: 383:Machine learning 366: 359: 352: 324: 317: 286: 285: 271: 262: 256: 255: 253: 241: 212: 210: 209: 204: 202: 201: 195: 192: 160: 157: 116: 114: 113: 108: 21:machine learning 19:is a problem in 403: 402: 398: 397: 396: 394: 393: 392: 373: 372: 371: 370: 313: 290: 289: 269: 263: 259: 242: 238: 233: 221: 197: 196: 191: 189: 165: 164: 156: 154: 132: 131: 123: 120: 119: 84: 81: 80: 57: 17:Parity learning 12: 11: 5: 401: 391: 390: 385: 369: 368: 361: 354: 346: 343: 342: 325: 311: 310: 302: 294: 288: 287: 257: 235: 234: 232: 229: 228: 227: 220: 217: 200: 190: 188: 185: 182: 179: 176: 173: 170: 167: 166: 163: 155: 153: 150: 147: 144: 141: 138: 137: 135: 130: 127: 106: 103: 100: 97: 94: 91: 88: 56: 53: 9: 6: 4: 3: 2: 400: 389: 386: 384: 381: 380: 378: 367: 362: 360: 355: 353: 348: 347: 341: 339: 335: 331: 326: 323: 319: 318: 314: 308: 303: 300: 295: 292: 291: 283: 279: 275: 268: 261: 252: 247: 240: 236: 226: 223: 222: 216: 213: 186: 180: 174: 171: 168: 161: 151: 145: 139: 133: 128: 125: 117: 101: 98: 95: 89: 86: 78: 74: 70: 66: 62: 52: 50: 46: 43:computes the 42: 38: 34: 30: 26: 22: 18: 338:expanding it 327: 312: 273: 260: 239: 214: 118: 76: 72: 68: 64: 60: 58: 40: 36: 32: 28: 24: 16: 15: 276:: 99--114. 377:Categories 251:cs/0010022 231:References 193:otherwise 172:− 90:∈ 219:See also 158:if  75:,  63:,  31:,  45:parity 328:This 270:(PDF) 246:arXiv 334:stub 278:doi 379:: 272:. 365:e 358:t 351:v 340:. 309:. 301:. 284:. 280:: 254:. 248:: 187:, 184:) 181:x 178:( 175:f 169:1 162:b 152:, 149:) 146:x 143:( 140:f 134:{ 129:= 126:y 105:} 102:1 99:, 96:0 93:{ 87:b 77:y 73:x 69:x 67:( 65:ฦ’ 61:x 41:ฦ’ 37:x 35:( 33:ฦ’ 29:x 25:ฦ’

Index

machine learning
parity
Gaussian elimination
Learning with errors
arXiv
cs/0010022
"Cryptography from learning parity with noise"
doi
10.1007/978-3-642-27660-6_9
http://portal.acm.org/citation.cfm?id=1374466
http://portal.acm.org/citation.cfm?id=1060590.1060603
Stub icon
applied mathematics
stub
expanding it
v
t
e
Categories
Machine learning
Applied mathematics stubs

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