Meta
Roadmaps
Bayesian Statistics
Roadmaps
Concepts
- Bayes' rule
- Bayesian estimation of Bayes net parameters
- Bayesian linear regression
- Bayesian logistic regression
- Bayesian model averaging
- Bayesian model comparison
- Bayesian naive Bayes
- Bayesian networks
- Bayesian parameter estimation
- Bayesian parameter estimation in exponential families
- Bayesian parameter estimation: Gaussian distribution
- Bayesian parameter estimation: multinomial distribution
- Bayesian parameter estimation: multivariate Gaussians
- beta process
- Chinese restaurant franchise
- Chinese restaurant process
- collapsed Gibbs sampling
- CRP clustering
- Dirichlet process
- evidence approximation
- Gaussian process regression
- Gaussian processes
- Gibbs sampling as a special case of Metropolis-Hastings
- hierarchical Dirichlet process
- IBP linear-Gaussian model
- importance sampling
- Jeffreys prior
- latent Dirichlet allocation
- learning GP hyperparameters
- MAP parameter estimation
- Markov chain Monte Carlo
- Markov models
- MCMC convergence
- Monte Carlo estimation
- particle filter
- reversible jump MCMC
- sequential Monte Carlo
- uninformative priors
- variational Bayes
- variational inference
- variational inference and exponential families
Data Structures & Algorithms
Course Guides
Concepts
- abstract data types
- analyzing recursive algorithms
- asymptotic complexity
- AVL trees
- b-trees
- Bellman-Ford algorithm
- binary search
- binary search trees
- Bloom filter
- breadth-first search
- depth-first search
- Dijkstra's algorithm
- graph representations
- hash tables
- heap (data structure)
- linked lists
- lower bound on sorting
- merge sort
- minimum spanning trees
- queue
- quicksort
- recursive backtracking
- red-black trees
- representation invariants
- sorting
- stack
- strongly connected components
- topological sort
- tree (data structure)
- trie (data structure)
Differential Geometry
Roadmaps
Concepts
- commuting vector fields
- cotangent bundle
- differentiable manifolds
- differentiable maps between manifolds
- differential forms
- exterior derivative
- Fisher metric
- flows on manifolds
- Hamiltonian flows
- integration on manifolds
- Lie derivatives
- natural gradient
- oriented manifolds
- pullback
- Riemannian metrics
- statistical manifolds
- symplectic manifolds
- tangent bundle
- tensor fields on manifolds
Frequentist Statistics
Concepts
- asymptotics of maximum likelihood
- Bayesian information criterion
- bias-variance decomposition
- bootstrap
- Central Limit Theorem
- Chernoff bounds
- comparing normal populations
- Cramer-Rao bound
- cross validation
- cumulative distribution function
- curse of dimensionality
- exponential families
- Fisher information
- Fisher information matrix
- Fisher's linear discriminant
- generalization
- generalized linear models
- Markov and Chebyshev inequalities
- maximum likelihood
- maximum likelihood in exponential families
- method of moments
- statistical hypothesis testing
- strong law of large numbers
- Student-t distribution
- sufficient statistics
- VC dimension
Linear Algebra
Concepts
- bases
- change of basis
- column space and nullspace
- complex vectors and matrices
- computing matrix inverses
- computing the nullspace
- Cramer's rule
- determinant
- determinant and volume
- diagonalization
- dot product
- eigenvalues and eigenvectors
- four fundamental subspaces
- Gaussian elimination
- inner product
- linear approximation
- linear least squares
- linear regression
- linear regression: closed-form solution
- linear systems as matrices
- linear transformations as matrices
- LU factorization
- matrix inverse
- matrix multiplication
- matrix transpose
- multiplicity of eigenvalues
- orthogonal subspaces
- orthonormal bases
- parameterizing lines and planes
- positive definite matrices
- projection onto a subspace
- QR decomposition
- singular value decomposition
- solution sets of linear systems
- solving difference equations with matrices
- spectral decomposition
- subspaces
- unitary matrices
- vector spaces
- vectors
Logic
Course Guides
Concepts
- Axiom of Choice
- Boolean algebras
- Church-Turing thesis
- compactness of first-order logic
- compactness of propositional logic
- completeness of first-order logic
- DPLL procedure
- first-order logic
- first-order resolution
- first-order unification
- Godel numbering
- Godel's Incompleteness Theorems
- incompleteness of set theory
- Lob's Theorem
- Lowenheim-Skolem theorems
- Peano axioms
- proofs in first-order logic
- propositional logic
- propositional proofs
- propositional resolution
- propositional satisfiability
- reasoning with Horn clauses
- recursive functions
- representability in arithmetic
- Russell's Paradox
- semantics of first-order logic
- structural induction
- Turing machines
- ultraproduct
- undefinability of truth
- Zermelo-Frankl axioms
Machine Learning
Roadmaps
- Bayesian machine learning
- Deep learning from the bottom up
- Differential geometry for machine learning
- Level-Up Your Machine Learning
Course Guides
- Berkeley CS281a: Statistical Learning Theory
- Coursera: Machine Learning
- Stanford CS229: Machine Learning
Concepts
- AdaBoost
- Akaike information criterion
- annealed importance sampling
- backpropagation
- backpropagation for second-order methods
- bagging
- basis function expansions
- Baum-Welch algorithm
- Bayes net parameter learning
- Bayes net structure learning
- Bayes' rule
- Bayesian decision theory
- Bayesian linear regression
- Bayesian logistic regression
- Bayesian model averaging
- Bayesian model comparison
- Bayesian naive Bayes
- Bayesian networks
- Bayesian parameter estimation
- Bayesian parameter estimation in exponential families
- Bayesian parameter estimation: Gaussian distribution
- Bayesian parameter estimation: multinomial distribution
- Bayesian parameter estimation: multivariate Gaussians
- Bayesian PCA
- beta process
- bias-variance decomposition
- binary linear classifiers
- Boltzmann machines
- boosting as optimization
- Chinese restaurant franchise
- Chinese restaurant process
- Chow-Liu trees
- collapsed Gibbs sampling
- comparing Gaussian mixtures and k-means
- computations on multivariate Gaussians
- conditional random fields
- constructing kernels
- convolutional neural nets
- cross validation
- CRP clustering
- curse of dimensionality
- decision trees
- deep belief networks
- early stopping
- EM algorithm for PCA
- Expectation-Maximization algorithm
- F measure
- factor analysis
- feed-forward neural nets
- Fisher's linear discriminant
- fitting logistic regression with iterative reweighted least squares
- forward-backward algorithm
- gamma distribution
- Gaussian discriminant analysis
- Gaussian process classification
- Gaussian process regression
- Gaussian processes
- generalization
- generalized linear models
- Gibbs sampling
- Gibbs sampling as a special case of Metropolis-Hastings
- GP classification with the Laplace approximation
- Hamiltonian Monte Carlo
- hidden Markov models
- hierarchical Dirichlet process
- Hopfield networks
- IBP linear-Gaussian model
- independent component analysis
- Indian buffet process
- information form for multivariate Gaussians
- Jensen's inequality
- K nearest neighbors
- k-means
- k-means++
- kernel SVM
- kernel trick
- Laplace approximation
- LASSO
- latent Dirichlet allocation
- latent semantic analysis
- learning Bayes net parameters with missing data
- learning GP hyperparameters
- learning invariances in neural nets
- learning linear dynamical systems
- linear regression
- linear regression as maximum likelihood
- linear regression: closed-form solution
- linear-Gaussian models
- logistic regression
- MAP parameter estimation
- Markov chain Monte Carlo
- Markov chains
- Markov models
- Markov random fields
- maximum likelihood
- maximum likelihood in exponential families
- MCMC convergence
- mean field approximation
- Metropolis-Hastings algorithm
- mixture of Gaussians models
- MRF parameter learning
- multidimensional scaling
- naive Bayes
- perceptron algorithm
- precision and recall
- principal component analysis
- principal component analysis (proof)
- probabilistic Latent Semantic Analysis
- probabilistic PCA
- probit regression
- random forests
- recurrent neural networks
- restricted Boltzmann machines
- reversible jump MCMC
- ridge regression
- ridge regression as SVD
- sequential Monte Carlo
- slice sampling
- soft margin SVM
- soft weight sharing in neural nets
- softmax regression
- sparse coding
- structured mean field
- support vector machine
- support vector regression
- SVM optimality conditions
- SVM vs. logistic regression
- tangent propagation
- unsupervised pre-training
- variational Bayes
- variational Bayes EM
- variational inference
- variational inference and exponential families
- variational linear regression
- variational logistic regression
- variational mixture of Gaussians
- VC dimension
- Viterbi algorithm
- weight decay in neural networks
Multivariate Calculus
Concepts
- Chain Rule
- conservative vector fields
- cross product
- differential forms
- Divergence Theorem
- dot product
- evaluating multiple integrals: change of variables
- evaluating multiple integrals: polar coordinates
- exterior derivative
- functions of several variables
- gradient
- Green's Theorem
- higher-order partial derivatives
- limits and continuity in R^n
- line integrals
- linear approximation
- multiple integrals
- optimization problems
- parameterizing lines and planes
- partial derivatives
- pullback
- second derivative test
- Stokes' Theorem (three dimensions)
- surface integrals
- vector fields
- vectors
Optimization
Concepts
- automatic differentiation
- BFGS
- conjugate gradient
- convergence of conjugate gradient
- convergence of gradient descent
- convex functions
- convex optimization
- convex sets
- finite-difference approximations to derivatives
- Gauss-Newton algorithm
- gradient
- gradient descent
- KKT conditions
- Lagrange duality
- Lagrange multipliers
- limited memory BFGS
- line search
- natural gradient
- Newton's method (optimization)
- nonlinear conjugate gradient
- optimization problems
- preconditioned conjugate gradient
- second derivative test
- stochastic gradient descent
- truncated Newton
- trust regions
Probabilistic Graphical Models
Roadmaps
Course Guides
Concepts
- adaptive rejection sampling
- annealed importance sampling
- Baum-Welch algorithm
- Bayes Ball
- Bayes net parameter learning
- Bayes net structure learning
- Bayesian estimation of Bayes net parameters
- Bayesian naive Bayes
- Bayesian networks
- Boltzmann machines
- collapsed Gibbs sampling
- computational complexity of graphical model inference
- computations on multivariate Gaussians
- conditional random fields
- converting between graphical models
- d-separation
- deep belief networks
- expectation propagation
- Expectation-Maximization algorithm
- factor graphs
- forward-backward algorithm
- Gaussian BP on trees
- Gaussian MRFs
- Gaussian variable elimination
- Gaussian variable elimination as Gaussian elimination
- Gibbs sampling
- Gibbs sampling as a special case of Metropolis-Hastings
- Hamiltonian Monte Carlo
- hidden Markov models
- HMM inference as belief propagation
- importance sampling
- inference in MRFs
- information form for multivariate Gaussians
- junction trees
- Kalman filter
- Kalman filter derivation
- Kalman smoother
- Kalman smoothing as forward-backward
- latent Dirichlet allocation
- learning Bayes net parameters with missing data
- learning linear dynamical systems
- linear dynamical systems
- linear-Gaussian models
- log-linear MRFs
- loopy belief propagation
- loopy BP as variational inference
- MAP parameter estimation
- Markov chain Monte Carlo
- Markov decision process (MDP)
- Markov random fields
- max-product on trees
- MCMC convergence
- mean field approximation
- Metropolis-Hastings algorithm
- MRF parameter learning
- naive Bayes
- particle filter
- rejection sampling
- restricted Boltzmann machines
- reversible jump MCMC
- sequential Monte Carlo
- structured mean field
- sum-product on trees
- Swedsen-Wang algorithm
- variable elimination
- variational Bayes
- variational inference
- variational inference and exponential families
- variational interpretation of EM
- Viterbi algorithm
Probability Theory
Concepts
- Bayes' rule
- beta distribution
- beta process
- binomial distribution
- Central Limit Theorem
- Chinese restaurant process
- computations on multivariate Gaussians
- computing probabilities by counting
- conditional distributions
- conditional expectation
- conditional independence
- conditional probability
- covariance
- covariance matrices
- cumulative distribution function
- differential entropy
- Dirichlet distribution
- Dirichlet process
- entropy
- expectation and variance
- exponential distribution
- exponential families
- gamma distribution
- Gaussian distribution
- Gaussian processes
- importance sampling
- independent events
- independent random variables
- Indian buffet process
- information form for multivariate Gaussians
- Jensen's inequality
- KL divergence
- Markov and Chebyshev inequalities
- Markov chains
- Markov models
- moment generating functions
- Monte Carlo estimation
- multinomial distribution
- multivariate CDF
- multivariate distributions
- multivariate Gaussian distribution
- mutual information
- PDFs of functions of random variables
- Poisson distribution
- probability
- random variables
- rejection sampling
- sampling from a Gaussian
- strong law of large numbers
- Student-t distribution
- transformation method
- unions of events
- weak law of large numbers
- Wishart distribution
Programming
Roadmaps
Course Guides
Concepts
- abstract data types
- analyzing recursive algorithms
- binary search
- binary search trees
- breadth-first search
- C generics
- C pointers
- C strings
- C struct representation
- call stack
- classes (programming)
- context-free grammars
- depth-first search
- dynamic memory allocation in C
- exceptions (programming)
- floating point representation
- function pointers in C
- generic collections in Java
- graph representations
- hash tables
- heap (data structure)
- inheritance (programming)
- interfaces and abstract classes in Java
- iterators
- linked lists
- machine representations of integers and characters
- merge sort
- multi-dimensional arrays in C
- queue
- quicksort
- recursion (programming)
- recursive backtracking
- regular expressions
- representation invariants
- sorting
- specifications (programming)
- stack
- tree (data structure)
- trie (data structure)
- unit testing
Reinforcement Learning
Concepts
Set Theory
Concepts
- Axiom of Choice
- Boolean algebras
- cardinality
- constructing the integers
- constructing the reals
- countable sets
- defining the cardinals
- equivalence relations
- functions and relations as sets
- incompleteness of set theory
- Lowenheim-Skolem theorems
- natural numbers as sets
- order relations
- ordinal numbers
- Russell's Paradox
- set operations
- structural induction
- ultraproduct
- well orderings
- Zermelo-Frankl axioms
- Zorn's Lemma
Symbolic AI
Concepts
- A* search
- alpha-beta pruning
- arc consistency
- breadth-first search
- constraint satisfaction problems
- depth-first search
- DPLL procedure
- expectimax search
- first-order logic
- first-order unification
- local search
- minimax search
- proofs in first-order logic
- propositional logic
- propositional proofs
- propositional resolution
- propositional satisfiability
- reasoning with Horn clauses
- recursive backtracking
- search problems
- semantics of first-order logic
- simulated annealing
- uninformed search
Theory of Computation
Concepts
- Church-Turing thesis
- computational complexity of graphical model inference
- context-free grammars
- context-free languages
- finite automata
- nondeterministic finite automata
- nondeterministic Turing machines
- NP complexity class
- PAC learning
- propositional satisfiability
- pushdown automata
- register machines
- regular expressions
- regular languages
- Turing machines
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Concepts
- autoregressive generative models
- complex numbers
- constructing the rationals
- dropout
- Euler's formula
- exploding and vanishing gradients
- gamma function
- interpretations between theories
- long short-term memory (LSTM)
- loss function
- multinomial coefficients
- n-gram language models
- neural probabilistic language models
- reversible generative models
- Stirling's approximation
- topology of R^n