Lemm J.C. — Bayesian field theory :: Электронная библиотека попечительского совета мехмата МГУ

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Lemm J.C. — Bayesian field theory

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Название: Bayesian field theory

Автор: Lemm J.C.

Аннотация:

Lemm, a former teacher of physics and psychology at the University of Munster, Germany, applies Bayesian methods to problems in physics, offering practical examples of Bayesian analysis for physicists working in areas such as neural networks, artificial intelligence, and inverse problems in quantum theory. Nonparametric density estimation problems are also discussed, including, as special cases, nonparametric regression and pattern recognition.

Язык:

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 425

Добавлена в каталог: 04.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\delta$ -loss      62
$\epsilon$ -insensitive error      134 142 165
Absolute loss      61
Adaptive reference function      216
Adaptive template function      197—201 see
Additive models      3 174 179—181
Additive models, generalized      3 179—181
Annealed field      342
Annealing techniques      24 191 216 267 282 331—332 349
Annealing temperature      282
Apparatus function      14 80 127
Approximate fractal      122—123 143 145 159 160 309
Approximate invariance      116—123 143—145 276—283
Approximate periodicity      120—122 126 143 155 156 276 279 280 285
Approximate symmetries      116—123 143—145 276—283
Approximately invariant regression      143—145
Auxiliary fields      221—224 276 277 281 345
Average energy      267 273 279—281 283
Bayesian decision theory      28 59—72
Bayesian field theory      5 7 8 231
Bayesian inverse Hartree — Fock theory (BIHF)      301—306
Bayesian inverse many-body theory      299—306
Bayesian inverse quantum theory (BIQT)      257—306
Bayesian statistics      3 5 8—50
Bayesian time-dependent quantum theory (BITDQ)      288—293
Bayes’ Theorem      28—31 71 73 75
Beliefs      319
Bias-variance decomposition      125 138
Binomial likelihood      14 46 51 65 69
Bit number      21 25 326—328 330
Boltzmann — Gibbs distribution      25 43 331 see
Bootstrap      67 185 189 209 292
Brownian motion      40 147 see
canonical ensemble      328
Canonical ensemble for classical systems      273
Canonical ensemble for many-body quantum systems      299
Canonical ensemble for quantum systems      259 260 279 300
Canonical ensemble, density operator      259 260 279 300
Center of mass      269
Classical limit of inverse quantum statistics      273—275
Classification      3—6 8 14 16 41 42 62 91 161—165 183 185 309 362
Cluster regression      141
Clustering      4 63 141 165
Collapse of the quantum mechanical wave function      258
Computer tomography      127 257
Conditional normalization      363
Conjugate gradient method      348 349 357
Connected correlation function      332 333 339 see
Constructivism      320 321
Controlled prior      44 73
Cross entropy      see "Kullback — Leibler entropy"
Cross-validation      67 106 144 185 189 209—214 292 364
Cumulant expansions      337
Cumulant generating function      25 26 334 335 337
Cumulants      25 26 330—337
Curvature-driven smoothing      185
Data, dependent part      4
Data, finite number of      264
Data, independent      12 13 194
Data, independent part      4
Data, large number of      7
Data, non-training      8
Data, observational      4 9 14 20 27 257 280 281 288 292 293 299 300 see training"
Data, prior      13 15
Data, sampled      279 see training"
Data, sampling      65
Data, test      3 48
Data, training      3 6 8 12 13 15 20 72 see observational"
Decision trees      3 124 182 186 197 215 230 309
Decoherence      258
Density operator      165 258—260 279 300 310
Density operator for canonical ensemble      see "Canonical ensemble density operator"
Density operator for spin systems      258
Design matrix      175 178
Deterministic annealing      24
Dirichlet boundary conditions      352 356 358
Discontinuities      119 120 221 223—225 283 287
Discontinuous template function      221
Discrepancy      66 67 209 242 292
Dissipation-fluctuation theorems      336
Distribution field      115—116
Downhill simplex method      191 349
Dummy variables      173
Effective action      337
Effective template function      220 233
Empirical Bayes approach      194 195
Empirical risk      66
Empirical risk minimization      27 62 64—72 96—99 188 209
Energy      7 20—27 46 49 64 91 96 102 103 106—108 110 115 130—132 170 174 177—179 204 211 235 239 323—325 328—331 334 336 see
Energy functional      see "Energy" "Error
Energy penalty      270 272 275 283—285
Energy, annealed      341
Energy, annealed prior      189
Energy, auxiliary prior      278
Energy, combined      32
Energy, complete      111 128
Energy, component      232
Energy, conditional      341
Energy, conditional prior      189
Energy, joint      341
Energy, joint prior      189 190
Energy, likelihood      26 see
Energy, mixture      341
Energy, mixture prior      232
Energy, prior      see "Specific prior energy"
Energy, quadratic      86
Energy, quenched      341
Energy, quenched prior      189
Energy, specific prior      see "Prior energy"
Energy, symmetry      266
Energy, training      see also "Energy likelihood"
entropy      22 24 25 33 34 43 328 330—331
Error functional      27 64 66 67 70 71 85 86 89 92—94 96 98 99 101 112 124 161 168 185 189 197 198 200 202 209 231 345—348 358 see
Euclidean action      328
Euclidean field theory      5 20 26 216
Euclidean propagator      351
evidence      28 39 193 194 209
Expected risk      59 66 96
Expert knowledge      162 230 321
Expert Systems      3
Exponential family      24 330 332
External field      25 125 330 334 336 342
Factorizing template function      182
Feedforward neural networks      see "Neural networks"
fermions      299—301 306 311
Ferromagnet      242—243
Field      4 5 15 28 85 92 98 99 161 167 188 191 211 217 334—337 339 342 349
Field strength tensor      204
Field theories      5 6 203 204
Field, general      see "General fields"
Filter operator      83 217 221 223
Filtered difference      217—219 222—224 227 248 276 277 281 282
Fisher information      114 115 317
Flexible reference function      126 197—201 see
Free energy      7 23—26 32 326 329 330
Free energy, likelihood      26
Free energy, posterior      26
Free energy, prior      42
Free field      309 see "Wiener
Free field, generalized      309 see
Free scalar field      351
Frequentist statistics      28 40 64—69 71 96 185 188 209 210 314 320
Functional derivative      89 112 134 188 196 198 224 262 263 267 268 275 277 278 290 301—303 331 see
Functional integral      27 41 265 see
Functional integral, Gaussian      27
Functional integral, non-Gaussian      27
Fuzzy methods      230 232 319
Gauge Fields      204
Gauss — Seidel iteration      348 358
Gaussian mixture prior      8 231—257 272 see

Gaussian mixture regression      141
Gaussian prior factor      see "Gaussian process"
Gaussian process      5—8 18 19 42 66 73 85—164 190 198 220 229 265—267 269 272 275 276 300 309 310 316 350
Gaussian process prior      see "Gaussian process"
Gaussian regression      126—137
Gaussian relaxation      354
General fields      112—114
Generalized canonical ensemble      25 43 331 see
Generalized cross-validation      214
Generalized free field      6 309 see
Generalized linear models      172
Generalized method of moments (GMM)      17
Generating function      332—339
Generating function for cumulants      see "Cumulant generating function"
Generating function for moments      see moment "Generating function"
Genetic algorithms      191 216 349
Gibbs distribution      see "Boltzmann — Gibbs distribution"
Gibbs ensemble      see "Boltzmann — Gibbs distribution"
Gibbs random field      20
Gradient      36 45 87 88 90 91 93 95 99 111 119 182 191 261 268 336 348 350 358
Gradient algorithm      36 45 87 91 93 95 101 102 110 225 348 349 351 354 355 358
grand canonical ensemble      328
Grapical models      3 141 324
Grassmann variables      343
Green’s function      351 352
Ground state energy      115 264 270 289
Hamiltonian      115 197 257 259—261 283 288 300 304 310
Hamiltonian, Hartree — Fock      301
Hamiltonian, many-body      299—301
Hamiltonian, nonlocal      288
Hamiltonian, real      289 303
Hamiltonian, two-body      300
Hard constraints      8 192 see "Normalization"
Hartree approximation      182 197
Hartree — Fock approximation      72 182 197 301 302 306 312
Hartree — Fock likelihood      302
Hartree — Fock — Bogoliubov approximation      197
hessian      36 37 39 91—92 95—96 101 102 106 110 111 114 176 191 192 262 268 336 350 351 358 360 361
Hidden states      see "Variables hidden"
High temperature limit      24 240 242 264 332
High temperature solution      242 247 256
Hinge functions      180
hints      185 186
Homotopy methods      191 216 331—332 349
Huber’s loss function      142
Hyperfields      199 202—204 216—223 276 277 282 283 287 310 311 320
Hyperparameter energy      198 207 see
Hyperparameters      7 8 18 19 67 112 121 124 144 167 187—227 229 250 251 254 265 280 289 292 310 317 319
Hyperparameters, discrete      229
Hyperprior energy      204 239 see
Hypothesis testing      64 65 68 69
Image completion      187 249—257 310
Infinitesimal translations      116—120 143 147 266
Influence matrix      132 134 176
Input noise      17 19 75—78 80 81 84 318
Instrument function      14 80 127
Interacting fields      6
Interaction terms      173 174 180 186 203
Invariant group measure      82 83
Inverse Hartree — Fock equation      303
Inverse problems      3
Inverse problems, classical      14 42 44 80 127 211 257
Inverse problems, in quantum theory      4 257—306 see
Inverse quantum theory      8 257—306
Inverse scattering theory      257 264
Inverse spectral theory      257 263 264
Inverse temperature      24—27 184 188 207 232 239 245 246 336
Inverse Wishart distribution      208
Jacobi iteration      348 358
Jacobi matrix      see "Jacobian"
Jacobian      90 112 168 196
Jensen’s Inequality      63
Kerridge inaccuracy      22 40
kinetic energy      261 288 300 351
Kuhn — Tucker conditions      88
Kullback — Leibler distance      see "Kullback — Leibler entropy""
Kullback — Leibler entropy      23 25 43 60 63 110
Lagrange multiplier      24 25 43 45 46 85—95 99 113 131 161 162 168 177 222 232 267 330—332
Lagrange multiplier function      see "Lagrange multiplier"
Lagrange parameter      see "Lagrange multiplier"
Landau — Ginzburg models      230
Laplace’s approximation      see "Maximum A Posteriori Approximation"
Lattice field theories      6
Learning matrix      346 348—357
Legendre transform      334 337
Lie group      82 118 266
Likelihood field      93
Likelihood model of quantum theory      85 258—263 310
Likelihood, normalization      29 89—91 94—95 112 239 246
Linear regression      4 174—179
Linear trial spaces      171—174
Linguistic variables      230 232
Local Gaussian mixture prior      248—249
Local mass      203—204
Local reference function      216—221 248—249
Local template function      216—221 248—249
Log-likelihood      4 21 45 66 85—89 92 97 106 107 114 232 262 292
Log-likelihood field      92
Log-likelihood, non-quadratic      134
Log-likelihood, shifted      162
Log-loss      59—61 63—64 70 71 96 107 141 245
Logistic regression, binary      173
Logistic regression, cumulative      174
Logistic regression, multinomial      174
Logistic regression, ordinal      174
logit      173
loss      15 59—72 142
Loss, $\epsilon$ -insensitive      see " $\epsilon$ -insensitive error"
Loss, absolute      61
Loss, delta      see " $\delta$ -loss"
Loss, general quadratic      61
Loss, Huber’s function      see "Huber’s loss function"
Loss, logarithmic      see "Log-loss"
Loss, quadratic      see "Quadratic error" "Squared-error
Loss, quadratic $\epsilon$ -insensitive      see "Qquadratic $\epsilon$ -insensitive error"
Loss, zero-one      62 161
Low temperature limit      24 40 232 240—242 332
Low temperature solution      242 247 251 255
Magnetic field      125 330 334
Many-body Schroedinger equation      301
MAP      see "Maximum A Posteriori Approximation"
Markov random field      see "Gibbs random field"
Mass      99 106 108 110 235 238 261 273 293—295 305 350—352 354 359 361
Massive relaxation      103 106 110 111 233 350—353 358
Maximum a posteriori approximation      27 36—40 48 50 63—66 68 70 71 90 91 131 132 161 162 167 188 191—197 222 267—269 312
Maximum entropy      24 25 43 331
Maximum entropy prior      43 44
Maximum likelihood approach      64 65 71 261
Maximum Likelihood Approximation      see "Maximum likelihood approach"
Mean field approximation      258
Mean field equation      243
Mean field theory      72 162
Measured prior      44 73—75
Median      61 62
Method of steepest descents      see "Maximum A Posteriori Approximation"
Mixing of templates      215
Mixing template functions      230
Mixture of filtered differences      218 277
Mixture of Gaussian processes      19 229—257 266—268 271 see
MODE      48 49 62
Modified Bessel functions      351 353
Moment expansions      337
Moment generating function      25 26 333
Moments      25 26 330 332 333 335—337
Monotonicity      41 99 113 116
Monte Carlo methods      36 71 161 188 192 209 216 265 292 324 337
Moore — Penrose inverse      135 136 143 169 262 263 290 355
Multimodal energy surface      229
Multiple Reduction Copy Machines (MRCM)      122
Mutual information      33—36 38 60 315

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