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Workbench

Just a big TODO list of notes

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AI ML U1

Agents

Goal based agent

Consequentialism

Instead of storing all possible percepts, the best solution is to start from a subset of it and then include others while learning.

Automata

  • Finite-State LTS means that it has finite states and actions, Finite-State Automata means that it has to end at some point.

  • Every non-deterministic automata can be represented as a deterministic automata, even though the states and actions may increase.

  • An FSA is deterministic if the outcome of an action is determined, non-deterministic if the outcome isn't determined (i.e. deterministic if for each state every action leads to one state only, non-deterministic otherwise).

Searching

  • Graph search vs tree-like search

  • Breadth-first search is complete (if there's a solution it will return it, otherwise it won't)

Logic-based Agents

  • Entailment / Models

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AI ML U2

Training

A model can't be verified on the same dataset it has been trained on, because the model is kind of guaranteed to reach the expected output. To verify the correctness of a model, a dataset with different data is required, so that the model will try to guess the output on data it has never seen.

Pearson Correlation Coefficient

The formula calculates the arithmetic means of both x and y, then calculates how much the set of the points change wrt to the mean point. Then, it sums all contributions to calculate the correlation between x and y.

Inductive Bias

Different people (and different AI's) have different experiences, which influences the resulting reasoning.

PCA

  • Reconstruction Error

  • Another PCA interpretation: find an orthogonal projection that minimises the reconstruction error

  • What if the sample cardinality is smaller than the data dimensionality

  • There is a way to retrieve the Principal Components from SVD

Matrix Calculus

  • First derivative of vector to scalar: Gradient (Dx1)

  • Second derivative of vector to scalar: Hessian (DxD, symmetric)

  • First derivative of vector to vector (D->P): Jacobian (DxP)

  • Second derivative of vector to vector (D->P): High-order Tensor (DxPxP)

  • The hessian can be seen as the jacobian of the gradient

  • Quadratic Forms: $x^T A x$ ($A$ symmetric) | If we call $Ax = b$, then $x^T b$ is the dot product between $x$ and itself after $A$ has been applied. Geometrically, it represents the shape of the parabola of the matrix

  • Quadratic form can be applied to asymmetric square matrices too: let $B = \frac{1}{2} A + \frac{1}{2} A^T$, then $B$ is symmetric and the quadratic form can be applied to $B$.

  • Gradient is linear

  • Lagrange multiplier

K-mean

  • Furthest-first Heuristic: first is picked at random, others are picked iteratively based on decreasing distance (updated on each assignment)

Supervised Learning

  • Empirical Risk Minimization
  • Bias error
  • Bias-Variance tradeoff (dartboard)
  • Feature weighting (choosing dominant vs superficial features)

K-NN

  • Advantages and disadvantages

  • Split the data into training (60%), validation (20%), test (20%)

  • The validation data is used to select or fix the hyper-parameter $k$

  • The training loss function can be defined by classifying the training set itself given a parameter $k$

  • Generally, the increasing order of errors should be train, validation, test

  • Remember to estimate scaling / regularizing the data only with the training set, and then apply it to validation / test data too

Decision Trees

  • Supervised w/parameters

  • $p_k = \frac{|S_k|}{|S|}$ probability of picking one label

  • impurity: misclassification in the data during the mode decision (1 - probab of picking the label picked) $1 - \max_{k \in Y}{p_k}$

  • Gini impurity: sort of an entropy of impurities, it's computed as the sum of (prob picking) (prob not picking)

  • Geany Imputiry function: $H(S) = \sum_{k \in Y} p_k (1 - p_k)$

  • Etropy function: $- \sum_{k \in Y} p_k \log_2()$

  • Entropy is derived from impurity: impurity is a general concept, entropy is impurity implemented

  • Impurity of a tree: recursive weighted sum of the entropy of both sides of the current branch of the tree.

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Computer Vision and NLP

  • CV images are stored in standard NumPy arrays

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Statistics

Forchetta: the range of values a variable could assume.

sample vs observation

Data are a random sample of characteristics

Unit profile: connection between an individual and a unit group

Profile of a specific unit: combination of all values for a ?

Box plot

Response Variable Explanatory Variable

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Data Management and Analysis U2

Empty, for now...

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