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人工智能/AI Checklist.md

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+# AI2018 Checklist
+created by Toni Chan
+
+
+# A. SEARCH
+
+## 1. Uninformed Search, Heuristic Search
+
+- Search Establishment
+    - Goal
+    - Goal Formulation: current step
+    - Problems Formulation: actions to goal
+    - Search: looking for actions
+    - Execution: take action
+
+- Uninformed: no guidance, informed: yes
+- Types
+    - Deterministic, fully observable
+    - Non-observable
+    - Non-Deterministic/Parcially observable
+    - Unknown state space
+
+- Well-defined search problems:
+    - Initial state
+    - Actions
+    - Transition model
+        - State space, directed networks and paths
+    - Goal test
+    - Path cost
+
+- Formulations: incremental(starting from zero), complete-state(starting from end)
+
+- Tree search; Graph search: add explored set
+
+- node DS: state, parent, action, cost
+
+- Measuring performance: completeness, optimality, time, space
+
+- Uninformed search
+    - BFS(FIFO): reaches all finite states, ^depth time, ^depth space, optimal at cost=1(=Uniform cost) while not general
+    - DFS(LIFO): not complete and fails in infinite state, ^depth time, *depth space, not optimal 
+        - can set limit to depth: DLS
+        - Iterative-deepening: auto set new limits
+
+- Informed: heuristic
+    - Best-first: evaluation function f as cost estimate to to first expand
+        - heuristic functions: calc by current state, f=h then greedy
+        - A* search: f = g(cost) + h(estimate)
+            - to reach optimal: admissibility(never overestimate), consistency(h adheres to triangularity; consistency->admissibility)
+
+
+
+## 2. Adversarial Search: MinMax, Evaluation funcs, Alpha-Beta Search, Stochastic
+
+- Game
+    - Initial state
+    - Players
+    - Actions
+    - Results: transition model of a move
+    - Terminal-tests: when the game ends
+    - Utility: player's final score
+
+- MINMAX
+    - Determined by minimax value; max want to maximize value, min want to minimize value
+    - complete if finite; optimal against optimal opponent; dfs time-space
+    - impractical: limit depth/alpha-beta pruning/no exhaustive search
+
+- Alpha-beta Pruning
+    - a: begin at -inf, highest max-node utility that search has found on the path; if in a min node, successors has utility<=a, then prune
+    - b: begin at +inf, lowest min-node utility that has found; if in a max node, successors has utility>=b, then prune
+    - at time of convergence to no overlap: prune
+    - highly dependent on move ordering: try to examine the potentially best successors
+    - timing ^depth/2 at best-first, ^3depth/4 at random
+
+
+
+# B. STATISTICAL LEARNING
+
+## 3. Probability Theory, Model Selection, Curse of Dimentionality, Decision Theory, Information Theory, Probability Distribution
+
+- Supervised & Unsupervised
+    - Supervised: training data with known input-target vector pairs
+        - Classification
+        - Regression
+    - Unsupervised: training data only with input vectors, no targets
+        - Density estimate
+        - Clustering
+        - Hidden Markov Models
+    - Reinforcement learning: find suitable actions to take in given situations to maximize reword; discover best results by trial-error; tradeoff between exploration & exploitation **??**
+
+- Model comparison/selection
+    - training data
+    - validation set
+    - model select with min error or validation set
+    - use S-fold cross-validation on limited data
+
+- Error functions: Sum-of-Square Error/Root-Mean-Square Error
+
+- Dealing overfitting
+    - more data
+    - regularization: penalty
+    - bayesian: prior
+    - cross-validation
+
+- Curse of Dimensionality: too many variables
+
+- Rules of probability: sume, product, Bayes' Theorem
+    - p(Y|X) * p(X) = p(X,Y) = p(X|Y) * p(Y)
+
+- Expectitaion, multiple variables, conditional expectation, variance, covariance
+
+- Gaussian Distribution 
+    - **See Formulas**
+
+- Maximum Likelihood Estimator for Variance is Biased: underestimate
+
+- Curve fitting: probabilistic perspective 
+    - Express uncertainty over the value of target variable by probability distribution;
+    - More Bayesian approach: maximizing posterior distribution = minimizing regularized sum-of-squares error
+    - Full Bayesian approach: **formulas**
+    - Conjugacy: choose a prior, then posterior distribution has same functional form **??**
+
+- Decision Theory 
+    - misclassification rate: p(mistake)=p(false pos)+p(miss)
+    - minimize expected loss: sum of posterior class probabilities
+    - reject option: introduce threshold theta for probabilities
+    - Inference & Decision: inference stage - decision stage: discriminant function
+    - Three distinct approaches:
+        - first solve inference problem of class-condition densities individually, separately infer prior class probabilities; then use bayes find posterior class probabilities: generative models
+            - Demanding, may need large training set
+            - allows marginal density of data to be determined from, helpful to detect new data of low probability
+        - first solve inference problem of posterior class probabilities, then use decision theory to assign each new x to one of the classes: discriminative models
+            - no waste of computational resources
+        - find a function(discriminant function) mapping each x onto a class label: no probability role.
+            - combining inference and decision into single problem
+
+- Information theory: entropy
+    - h(x) = -log p(x); H(x) = -Sum(x):p(x)logp(x)
+    - lower probability: higher info content
+    - nonuniform distribution has smaller entropy than uniform ones
+    - entropy is a lower bound of number of bits to transmit state of random variable: Shannon
+    - distributions sharply peaked around a few values will have low entropy
+    - max entropy configuration: use Lagrange multiplier enforce normalization constraints: then p(x)=1/M, M total number of states;  H=lnM
+    - relative entropy: calc(dx):p(x)ln(q(x)/p(x))
+    - mutual information: calccalc(dx,dy):p(x,y)ln(p(x)p(y)/p(x,y)) = H(x) - H(x|y) = H(y) - H(y|x)
+
+- Gaussian Distribution - continued 
+    - single & multivariate
+    - mahalanobis/euclidean distance
+    - jacobian factor/matrix **??**
+    - expectation: still μ's matrix
+    - second order moments: covariance: Σ matrix
+    - μ has D paramters, Σ has D(D+1)/2 (D for dimensions)
+    - Σ=diag(σi^2): mutually independent, 2D parameters; Σ=σ^2I: isotropic, D+1 parameters
+    - Partitioned Gaussians **??** : marginal=single gaussian with μa,Σaa
+    - Bayes: **Formulas**
+    - Maximum Likelihood: **Formulas** E(μML)=μ, E(ΣML)=N-1/N*Σ
+        - Bayesian Treatment: Know σ^2 for μ; Know μ for σ^2; for both
+            - Know σ^2 for μ: **Formulas**
+            - Know μ for σ^2: **Formulas** Gamma Distribution
+            - For both: Normal-Gamma/Gaussian-Gamma
+
+- Non-Parametric methods
+    - P = calc(at R,dx):p(x): p(x) = K/NV 
+    - Kernel density estimator: fix V check K 
+        - Parzen Window **??**
+    - K-nearest-neighbor: fix K check V
+        - density estimation: K goven radius of sphere
+
+## 4. Linear Models for Regression: Linear Basis Function Models, Bias-Variance Decomposition
+
+- Linear regression: y(x,w) = sum(i):w_0+w_i*x_i
+    - Linear basis function model: linear combinations of mixed non linear functions of input variables
+        - Polynomial, Gaussian, sigmoid, Fourier
+    - Maximal likelihood; Least Squares: **Formulas** **??**
+        - Bias compensates for difference between averages of target values and weighted sum of averages of basis function values
+        - Geometric interpretation of least-squares: finding orthogonal projection of data vector onto subspace spanned by basis functions
+    - Gradient Descent: if function J(w) is defined and diffrentiable in neighborhood, then J(w) decreases fastest if one goes from w0 in direction of negative gradient of J at w0: -J'(w0)
+        - stochasticL w(t+1) = w(t) - learning rate*delta(Error Function)
+        - LMS: functions
+    - Regularized least squares: **??**
+        - weight decay
+        - Regularizer: lasso = sparse model, q = 1; quadratic, q = 2
+        - regulaization: allows complex models to be trained on limited data without overfitting
+    - Multiple output: **Formulas**
+
+- Bias-Variance Decomposition
+    - Error due to Bias: difference of expected prediction and correct value; underfitting
+    - Error due to Variance: variability of a model prediction for a given data point; overfitting
+    - Err(x) = Bias^2 + Variance + Irreducible error
+    - Trade-off: minimizing Err(x)
+
+## 5. Linear Models for Regression: Basic Concepts
+
+- Concepts
+    - Decision regions: input space divided
+    - Decision boundaries: linear-linear function of input sector x; (D-1)-dim hyperplane within D-dim input space
+    - Datasets whose classes can be separated exactly by linear decision surfaces
+
+- Representation of Class Labels
+    - 1-hot vectors
+    - y(x) = f(w^T*x+w0): f as activation function, f^-1 as link function
+
+- Approaches of classification
+    - Discriminant function: no compute possibilities
+        - Least-squares: model predictions as close as possible to a set of targets
+        - Fisher's linear discriminant: maximum class separation in output space
+        - Perceptroon algo of Rosenblatt: generalized linear model
+    - Generative approach
+        - model class-conditional densities and class priors
+        - compute posterior probabilities thru bayes
+    - Discriminative approach
+        - model posteriors directly, and optimaize parameters using training set(logistic regression, etc)
+
+
+## 6. K-means Clustering, GMM, EM, Boosting
+
+- K-means Clustering
+    - Goal: finding assignment of point clusters according to some objective function
+    - Algorithm: P
+        - Pick random k; 
+        - Random scatter cluster centers; 
+        - Repeat
+            - Assign each data point to closest cluster center
+            - Move each center to the mean of points assigned
+    - Distance: J = sum(n):sum(k):rnk||xn-μk||^2
+    - Online: μk = sum(n):rnk*xn / sum(n): rnk; μknew = μkold + yn(xn-μkold) - nearest prototype to xn
+    - K-medoids: work with other distance matrix other than Euclid
+    - Limitations: only converge to local minimuml not considering data density and probabilistic distribution
+
+- Mixtures of Gaussians
+    - **Formulas**
+    - Difficulty of GMM by ML: singularities; identifiability; no closed form solution
+
+- Expectiation-Maximization algorithm
+    - For GMM: use responsibility
+        - Initialize means μ, covariances Σ, mixing coefficients π, and evaluate initial value of log likelihood
+        - E-step: evaluate responsibilities using current parameter values;
+        - M-step: re-estimate parameters using current possibilities;
+        - Evaluate log likelihood and check for convergence of either parameters or log likelihood; criterion not satisfied return to 2
+    - Alternative view of EM
+        - Goal: find maximum likelihood solution for models having high latent variables
+    - General: distribution p(X,Z|θ) over observed vars X and latent Z, parameter θ, to maximize p(X|θ) for θ.
+        - Choose initial setting of parameters θold;
+        - E-step: evaluate p(Z|X, θold);
+        - M-step: evaluate θnew by argmax Q(θ,θold) = sum(Z):p(Z|X, θold)ln(p(X,Z|θ));
+        - Check convergence of log likelihood/parameter values; convergence criterion not satisfied then replace and return to 2
+    - **Formulas**
+    - Relation to K-means **???**
+
+
+# C. NEURAL NETWORKS
+
+## 7. Stochastic Gradient Descent, BackPropagation, FeedForward Neural Networks
+
+- Neural Networks
+    - A neuron: input links; input function; activation function; output; output links
+    - Activation functions: sigmoid/logistic, tanh, ReLU
+    - Building: select structures(Feed-forward, recurrent); select weights(by training and learning)
+        - collection fo acyclic graph: layerwise
+        - common: fully-connected layers
+    - Perceptron networks: 1 layer FFNN, no hidden
+        - Multilayer perceptrons
+        - Hebbian theory
+    - Representation power: NN with Fully connected layers are universal approximators, approx any continuous func
+        - mathly sound, but weak
+        - layers increase, capacity increase
+
+- Optimization & Gradient Descent
+    - Random search: slow, not accurate
+    - Gradient: vectors along each dimension
+        - numerical: approximate, slow; analytic: exact, fast. always use analytic, but use numeric to check correctness
+        - stochastic: using minibatch
+
+- BackProp: computing gradients of expressions thru recursive application of chain rule
+    - computational graph
+        - allow simple functions form complex models
+        - auto differentiation
+    - Forward pass: traverse in topological order, fill values; Backward pass: traverse reversed, calculate deriatives at each node, and add by learning rate
+    -  **Examples**
+
+## 8. Convolutional NN
+
+- Architecture
+    - Convolutional layer: filter as weighted sum
+        - strides: do once every n move. output size: (N-F)/Stride + 1
+        - practice: zero pad borders
+        - number of weights: filter size * dimentions * filter number; number of bias: filter number
+    - Pooling layer: downsample and reduce parameters and control overfitting
+        - usually choose MAX function
+    - Normalization layer: implementing inhibition schemes. obsolete
+    - Fully connected layer: regular fully connected activations, compute with matrix multiplication, follow by bias offset
+
+- Reducing overfitting
+    - Data augmentation: image translations, alter RGB intensities, PCA, multiples of principal components
+    - Dropout: reduce complex co-adaptations; zero output neuron output at 50%
+    - Transfer learning
+        - Train on whole
+        - Small dataset: feature extractor
+        - Medium dataset: fine tuning
+
+- Application
+    - Classification
+    - CV Tasks
+        - Semantic segmentation: no objects
+        - Classification + localization: single object
+            - Aside: Human pose estimation
+        - Object detection, instance segmentation: multiple objects
+
+## 9. Recurrent NN: Vanilla, LSTM, GRU
+
+- RNN: a family of neural networks for processing sequential data
+    - recurrence formula: ht = fW(ht-1,xt)
+    - Vanilla RNN: ht = tanh(Whh * ht-1 + Wxh * xt), yt = Why * yt, softmax output
+        - exploding/vanishing gradients: gradient clipping
+    - Reuse same weight matrix at every time-step
+    - Compute loss: backpropagation thru time; Forward thru entire sequence to compute loss, then backward thru entire sequence to compute gradient
+        - Truncated BP: do forward and backward pass part by part
+    - How to train: Backprop
+        - take derivative of loss with respect to each parameter
+        - shift parameters in opposite direction 
+        - Hard to train: vanishing gradient
+        - gradient flow: not trained to capture long-term dependencies, depend on few words
+
+- Usages
+    - Seq2Seq: machine translation: *I-*O, not same time
+    - Visual Q-A
+    - Image captioning: 1I-*O, CNN+RNN
+        - Attention: weighed combination of features; distribution over L locations
+    - Video action classification
+    - Image Classification: 1I-1O
+    - Sentiment Analysis: *I-1O
+    - Videl Storyline: *I-*O, same time
+    - Character generation: feed back to model
+
+- Multilayer RNNs
+- Bidirectional RNNs
+- LSTM
+    - **i**mput, **f**orget, **o**output, **g**ate
+    - **Graph**
+        (i,f,o,g)^T = (σ,σ,σ,tanh)^T * W * (ht-1,xt)^T
+        ct = f · ct-1 + i * g
+        ht = o · tanh(ct)    
+    - additive update function for cell state has better behaved derivative
+    - gating functions allow network to decide how much vanishes, and take different values at each time step; values are learnt functions of current input and hidden state
+- GRU
+    - single gating unit simultaneously control forgetting factor and decision to update state unit
+    - reset and update gates individually "ignore" parts of state vector; update gate either copy or ignore with new targeet state value; reset gate control which part of state get used to compute the next target state