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Index
L
p
norm, 26
Active constraint, 68
AIS, see annealed importance sampling
Almost everywhere, 52
Ancestral sampling, 171
Annealed importance sampling, 278, 309
Approximate inference, 174
Artificial intelligence, 2
Asymptotically unbiased, 84
Bagging, 144
Bayes’ rule, 51
Bayesian network, see directed graphical model
Bayesian probability, 37
Belief network, see directed graphical model
Bernoulli distribution, 44
Boltzmann distribution, 166
Boltzmann machine, 166
Calculus of variations, 302
CD, see contrastive divergence
Centering trick (DBM), 312
Central limit theorem, 45
Chain rule of probability, 40
Chess, 2
Classical regularization, 128
Classification, 71
Cliffs, 151
Clipping the gradient, 244
Clique potential, see factor (graphical model)
CNN, see convolutional neural network
Collider, see explaining away
Computer vision, 323
Conditional computation, see dynamically struc-
tured nets, 318
Conditional independence, 40
Conditional probability, 39
Constrained optimization, 65
Context-specific independence, 169
Contrast, 324
Contrastive divergence, 284, 309, 310
Convolution, 199, 313
Convolutional neural network, 199
Coordinate descent, 156, 310
Correlation, 41
Cost function, see objective function
Covariance, 41
Covariance matrix, 41
curse of dimensionality, 100
Cyc, 2
D-separation, 169
Dataset augmentation, 324, 329
DBM, see deep Boltzmann machine
Deep belief network, 296, 306, 307, 314
Deep Blue, 2
Deep Boltzmann machine, 296, 306, 308, 310,
314
Deep learning, 2, 5
Denoising score matching, 293
Density estimation, 71
density estimation, 92
Derivative, 58
Detector layer, 204
Dirac delta function, 47
Directed graphical model, 162
Directional derivative, 62
domain adaptation, 193
Dot product, 23
Doubly block circulant matrix, 201
Dream sleep, 284, 304
DropConnect, 149
Dropout, 146, 310
Dynamically structured networks, 318
E-step, 299
Early stopping, 114, 134, 136–138, 150
376
EBM, see energy-based model
Effective number of parameters, 131
Eigendecomposition, 28
Eigenvalue, 29
Eigenvector, 28
ELBO, see evidence lower bound
Element-wise product, see Hadamard product
EM, see expectation maximization
Empirical distribution, 47
Energy function, 166
Energy-based model, 166, 308
Ensemble methods, 144
Equality constraint, 67
Equivariance, 202
Error function, see objective function
Euclidean norm, 26
Euler-Lagrange equation, 302
Evidence lower bound, 296, 298–300, 308
Expectation, 41
Expectation maximization, 298
Expected value, see expectation
Explaining away, 170
Factor (graphical model), 164
Factor graph, 169
Factors of variation, 5
Frequentist probability, 37
Functional derivatives, 302
Gaussian distribution, see Normal distribu-
tion45
Gaussian mixture, 48
GCN, see Global contrast normalization
Gibbs distribution, 165
Gibbs sampling, 173
Global contrast normalization, 325
Global minimum, 13
Gradient, 62
Gradient clipping, 244
Gradient descent, 62
Graphical model, see structured probabilistic
model
Hadamard product, 22
Harmonium, see Restricted Boltzmann ma-
chine177
Harmony theory, 167
Helmholtz free energy, see evidence lower bound
Hessian matrix, 63
Identity matrix, 24
Independence, 40
Inequality constraint, 67
Inference, 159, 174, 296, 298–300, 302, 304
Invariance, 207
Jacobian matrix, 52, 62
Joint probability, 38
Karush-Kuhn-Tucker conditions, 68
Kernel (convolution), 200
KKT conditions, see Karush-Kuhn-Tucker con-
ditions
KL divergence, see Kllback-Leibler divergence42
Kullback-Leibler divergence, 42
Lagrange function, see Lagrangian
Lagrange multipliers, 67, 303
Lagrangian, 67
Learner, 3
Line search, 62
Linear combination, 25
Linear dependence, 26
Local conditional probability distribution, 162
Local minimum, 13
Logistic regression, 3
Logistic sigmoid, 48
Loss function, see objective function
M-step, 299
Machine learning, 3
Manifold hypothesis, 252
manifold hypothesis, 100
Manifold learning, 99, 252
MAP inference, 300
Marginal probability, 39
Markov chain, 171
Markov network, see undirected model164
Markov random field, see undirected model164
Matrix, 21
Matrix inverse, 24
Matrix product, 22
Max pooling, 207
Mean field, 309, 310
Measure theory, 51
Measure zero, 52
Method of steepest descent, see gradient de-
scent
Missing inputs, 71
Mixing (Markov chain), 175
Mixture distribution, 48
377
MNIST, 310
Model averaging, 144
Moore-Penrose pseudoinverse, 139
MP-DBM, see multi-prediction DBM
Multi-modal learning, 197
Multi-prediction DBM, 309, 312
Multinomial distribution, 44
Multinoulli distribution, 44
Naive Bayes, 53
Nat, 42
Negative definite, 63
Negative phase, 283
Netflix Grand Prize, 146
Noise-contrastive estimation, 293
Norm, 26
Normal distribution, 45, 47
Normal equations, 131
Normalized probability distribution, 165
Object detection, 323
Object recognition, 323
Objective function, 12, 58
one-shot learning, 196
Orthogonality, 28
Overfitting, 79
Parameter sharing, 202
Partial derivative, 58
Partition function, 103, 165, 276, 309
PCA, see principal components analysis
PCD, see stochastic maximum likelihood
Persistent contrastive divergence, see stochas-
tic maximum likelihood
Pooling, 199, 313
Positive definite, 63
Positive phase, 283
Precision (of a normal distribution), 45, 47
Predictive sparse decomposition, 183, 265
Preprocessing, 324
Principal components analysis, 31, 296, 326
Principle components analysis, 90
Probabilistic max pooling, 313
Probability density function, 38
Probability distribution, 37
Probability mass function, 37
Product rule of probability, see chain rule of
probability
PSD, see predictive sparse decomposition
Pseudolikelihood, 289
Random variable, 37
Ratio matching, 292
RBM, see restricted Boltzmann machine
Receptive field, 203
Regression, 71
Regularization, 127
Representation learning, 3
Restricted Boltzmann machine, 177, 192, 296,
305, 306, 310, 312, 313
Ridge regression, 129
Scalar, 20
Score matching, 291
Second derivative, 62
Second derivative test, 63
Self-information, 42
Separable convolution, 216
Separation (probabilistic modeling), 167
Shannon entropy, 42, 303
Sigmoid, see logistic sigmoid
Singular value decomposition, 30, 140
SML, see stochastic maximum likelihood
Softmax, 110
Softplus, 48
Spam detection, 3
Sparse coding, 191, 296
spectral radius, 236
Sphering, see Whitening, 326
Square matrix, 26
Standard deviation, 41
Statistic, 83
Steepest descent, see gradient descent
Stochastic gradient descent, 310
Stochastic maximum likelihood, 288, 309, 310
Stochastic pooling, 149
Structure learning, 173
Structured output, 71
Structured probabilistic model, 158
Sum rule of probability, 39
SVD, see singular value decomposition
Symmetric matrix, 28
Tangent plane, 255
Tensor, 21
Test example, 12
Tiled convolution, 212
Toeplitz matrix, 201
Trace operator, 31
Training criterion, 12
Transcription, 71
378
Transfer learning, 193
Transpose, 21
Triangle inequality, 26
Unbiased, 84
Underfitting, 78
Undirected model, 164
Uniform distribution, 38
Unit norm, 28
Unnormalized probability distribution, 164
V-structure, see explaining away
Variance, 41
Variational derivatives, see functional deriva-
tives
Variational free energy, see evidence lower bound
Vector, 20
Weight decay, 129
Whitening, 326
ZCA, see zero-phase components analysis
zero-data learning, 196
Zero-phase components analysis, 326
zero-shot learning, 196
379