Index

A

absolutely consitnuous, [1] absolutely continuous measure, [1]

almost surely, [1], [2], [3] autoencoder, [1]

B

back propagation, [1] base probability measure, [1]

Bayes' rule for events, [1] Borel σ-algebra, [1], [2], [3]

C

concentration parameter, [1] conditional distribution of a RV, [1] conditional expectation by, [1] conditional expectation by a random variable, [1] conditional expectation by an event, [1] conditional expectation given partition, [1] conditional probability density, [1] conditional probability given partition, [1] conditional probability given RV, [1]

conditional probability given σ-algebra, [1] conditional probability measure, [1] contraction loss, [1] contractive autoencoder, [1] correlation matrix, [1] covariance function, [1] covariance matrix, [1], [2], [3] cross-correlation matrix, [1] Cross-covariance matrix, [1]

D

damping factor function, [1] data denoising, [1] data entries, [1] decoder, [1] definition denoising autoencoder, [1]

density, [1] density function, [1] dimension reduction, [1] Dirichlet process, [1] discrete distribution, [1] discrete random variable, [1] distribution, [1]

E

elementary functions, [1] encoder, [1]

event, [1] expectation, [1] experiment, [1]

F

feature vectors, [1] forget gate, [1]

forget gate function, [1] forget rate function, [1]

G

Gaussian kernel, [1]

Gaussian process, [1]

H

hidden layer, [1], [2], [3]

hidden state transition, [1] hidden states, [1]

I

identity function, [1] image measure, [1] index set, [1]

integration, [1] integration exists, [1] integration not defined, [1]

L

law of total probability, [1] law of total probability for events, [1] Lebesgue integration, [1] Lebesgue measure, [1]

long short-term memory, [1] loss function, [1] Lp space, [1] Lp-integrable, [1] LSTM with single forget gate, [1]

M

Mahalanobis distance, [1], [2], [3] marginal density functions, [1] marginal random variable, [1], [2], [3] marginalization, [1] Markov chain, [1] mean function, [1]

measurable function, [1] measurable set, [1] measurable space, [1] measure, [1] measure space, [1] measure theory, [1]

N

neural network, [1]

normalized RV, [1] normalized sample, [1]

O

open sets, [1], [2], [3] orthogonal matrices, [1] orthonormal matrix, [1]

output layer, [1] overcomplete, [1] overcomplete representations, [1]

P

Pearson's correlation, [1] Poisson process, [1] precision matrix, [1] Principal Component Analysis, [1] principal components, [1] probability law, [1]

probability mass, [1] probability measure, [1] probability normalization axiom, [1] probability space, [1] probability theory, [1] product measure, [1]

R

Radon-Nikodym derivative, [1] Radon-Nikodym theorem, [1] random process, [1] random variable, [1] random vector, [1] Randon-Nikodym derivative, [1] real analysis, [1] realization, [1]

reconstruction, [1] recurrent network, [1] recurrent networks, [1] reduced SVD, [1] regressed target values, [1] regular conditional probability, [1] representation, [1] Riemann integration, [1]

S

sample covariance, [1] sample covariance matrix, [1] sample matrix, [1] sample space, [1] sample variances, [1] samples, [1] separable metric space, [1] sequential data, [1], [2], [3]

singular value decomposition, [1] standardize RV vector, [1] standardized RV, [1] standardized sample, [1] standardized sample matrix, [1] state space, [1] stochastic process, [1] support, [1]

T

time-homogenous parameters, [1]

Tonelli's theorem, [1] total variance, [1], [2], [3]

U

uncountable set, [1]

undercomplete, [1] undercomplete representations, [1]

V

variances, [1]

Vitali set, [1]

Σ

σ-algebra generated by a random variable, [1]

σ-algebra generated by event sets, [1] σ-closure, [1]

ℱ

ℱ-measurable function, [1]

𝜎

𝜎-algebra, [1]

𝜎-finite measure, [1]