What will capital letters denote?
What about general measurable spaces? What are the two common measurable spaces we will use?
What will lowercase letters denote?
What notation will we use to surround vectors?
What about the inner product of vectors?
What about the Euclidean norm?
For a random sample of a random variable X, how will we denote an i.i.d. random sample?
How will we denote a multivariate function?
What will we use to denote estimators?
How will we denote a matrix? The identity matrix? and specifically a design matrix?
How will we denote the transpose of a matrix X ∈ Rn x p ? What will its dimension be?
What dimension and matrix type will XTX look like? What about XXT?
How do we denote the inverse of a matrix?
What will be the results of the attached?
What does the column rank of a matrix mean?
When is X said to have full column rank? What is a direct consequence of this?
Why does full column rank prove invertibility?
If A is a m x m symmetric real matrix, when is A said to be:
- positive-definite
- positive semi-definite
- negative definite
- negative semi-definite
- neither positive semi-definite or negative semi-definite
What is the multivariate Gaussian distribution?
What are some defining features of a multi-variate normal?
What is the Gamma distribution?
What is the Beta distribution?
How do we define a vector-value derivative of the F(β) where β is a real p-dim vector, and F is a scalar function?
How do we denote the derivative of a linear mapping for both a column vector and a matrix?
What is the derivative of the quadratic form?
What is the explicit derived solution for β-hatOLS?
What two conditional expectation rules will we use throughout the course?
What basic properties do the Random variables need to have for this?
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ST420 - Basic Notation and Concepts18
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Chapter 1.1: Intro to Statistical Learning - Buzz words and basic concepts11
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Chapter 1.2: Intro to Statistical Learning - First taste of Statistical Machine Learning15
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Chapter 1.3: Intro to Statistical Learning - Statistical learning theory - Loss, Risk and ERM25
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Chapter 1.4: Intro to Statistical Learning - Statistical learning theory - Excess Risk and the Bias-Variance Trade-off24
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Chapter 2.1: Classification (Part I) - Classification concepts, LDA and QDA14
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Chapter 2.2: Classification (Part I) - Logistic Regression13
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Chapter 2.3: Classification (Part I) - Neural Networks20
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Chapter 3.1: Big Data - Issues arising from Big Data15
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Chapter 3.2: Big Data - Multiple testing9
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Chapter 4.1: Regularisation - An overview of regularisation and ridge regression20
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Chapter 4.2: Regularisation - Lasso and constrained forms14
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Chapter 4.3: Regularisation - Concentration inequalities17
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Chapter 4.4: Regularisation- Advanced analysis of Lasso28
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Chapter 4.5: Regularisation- Extension and related other problems8
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Chapter 5.1 - Classification (Part II) - Maximal margin classifier and support vector classifier20
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Chapter 5.2 - Classification (Part II) - Kernel Methods24
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Chapter 6.1 - Cross validation, bootstrap and tree-based methods - Cross validation and bootstrap18
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Chapter 6.2 - Cross validation, bootstrap and tree-based methods - Tree-based methods16
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Chapter 7.1 - Mathematics of statistical machine learning - PAC Bounds11
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Chapter 7.2 - Mathematics of statistical machine learning - Concentration inequalities8
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Chapter 7.3 - Mathematics of statistical machine learning - Finite hypotheses classes6
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Chapter 7.4 - Mathematics of statistical machine learning - From shattering to VC dimension for infinite classes20
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Chapter 7.4 - Mathematics of statistical machine learning - Bounding Estimation error for infinite classes6
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Chapter 7.5 - [NON-EXAMINABLE] Mathematics of statistical machine learning - Rademacher complexity0
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Chapter 7.6 - Mathematics of statistical machine learning - Structural risk minimisation3
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Chapter 6.3: Cross-validation, boosttrap and tree-based methods - Boosting12
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Chapter 8.1 - Topics in big data - Bag of little bootstraps7
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Chapter 8.2 - Topics in big data - Implicit bias of neural networks6
