From c394ee2cce5ac08784883cf0ba2d4f0d82f3e7b9 Mon Sep 17 00:00:00 2001 From: Tom Zuidberg Date: Tue, 10 Feb 2026 00:08:46 +0100 Subject: [PATCH] creation of obsidian vault and first notes --- ObsidianNotes/.obsidian/app.json | 1 + ObsidianNotes/.obsidian/appearance.json | 1 + ObsidianNotes/.obsidian/core-plugins.json | 33 ++++ ObsidianNotes/.obsidian/graph.json | 22 +++ ObsidianNotes/.obsidian/workspace.json | 209 ++++++++++++++++++++++ ObsidianNotes/elemlds lecture 8.md | 60 +++++++ ObsidianNotes/elemlds lecture 9.md | 7 + 7 files changed, 333 insertions(+) create mode 100644 ObsidianNotes/.obsidian/app.json create mode 100644 ObsidianNotes/.obsidian/appearance.json create mode 100644 ObsidianNotes/.obsidian/core-plugins.json create mode 100644 ObsidianNotes/.obsidian/graph.json create mode 100644 ObsidianNotes/.obsidian/workspace.json create mode 100644 ObsidianNotes/elemlds lecture 8.md create mode 100644 ObsidianNotes/elemlds lecture 9.md diff --git 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"d74c0c464422592b", + "lastOpenFiles": [ + "elemlds lecture 8.md", + "elemlds lecture 9.md", + "Elements of Machine Learning and Data Science.md", + "Welcome.md" + ] +} \ No newline at end of file diff --git a/ObsidianNotes/elemlds lecture 8.md b/ObsidianNotes/elemlds lecture 8.md new file mode 100644 index 0000000..141b0d0 --- /dev/null +++ b/ObsidianNotes/elemlds lecture 8.md @@ -0,0 +1,60 @@ +# Machine Learning Intro + += Machines that *learn* to perform a task from *experience* + +3 forms of learning based on labels availability: +- Yes -> Supervised learning +- Some -> Semi-supervised learning +- No -> Unsupervised learning + +# Supervised Learning +Training data has labels $\mathcal{D} = \{(x_1, t_1), \dots, (x_N, t_N\}$ +Goal: learn a *predictive* function that yields good performance on *unseen* data + +Data may need to be preprocessed to handle +- Missing/wrong values +- Outliers +- Inconsistencies + +# Features +Feature extraction = process that creates descriptive vectors from samples +- Features should be invariant to irrelevant input variations +- Selecting the *right* features! +- Usually encode some domain knowledge +- Higher-dimensional features are more discriminative + +Curse of dimensionality: complexity increases *exponentially* with number of dimensions + +# Terms, Concepts, Notation +Mostly based on statistics and probability theory +Notation: +- Scalar $x \in \mathbb{R}$ +- Vector-valued $\text{x} \in \mathbb{R}$ +- Datasets $\mathcal{X} \in \mathbb{R}$ +- Labelled datasets $\mathcal{D} = \{(x_1, t_1), \dots, (x_N, t_N\}$ +- Matrices $\text{M} \in \mathbb{R}^{m \times n}$ +- Dot product $\text{w}^\text{T}\text{x} = \sum_{j=1}^D w_j x_j$ + +# Probability Basics +Over random variables: +- Discrete case: $p(X = x_j) = \frac{n_j}{N}$ +- Continuous case: $p(X \in (x_1, x_2)) = \int_{x_1}^{x_2}p(x)\, dx$ where $p(x)$ is the probability desnity function (pdf) of $x$ + +Some formulas: +Let $A \in \{a_i\}, B \in \{b_j\}$ +Consider $N$ trials: +- $n_{ij} = \# \{A = a_i \land B =b_j\}$ +- $c_i = \#\{A=a_i\}$ +- $r_j = \#\{B=b_j\}$ +Then we get: +- Joint probability $p(A=a_i, B=b_j) = \frac{n_{ij}}{N}$ +- Marginal probability $p(A=a_i) = \frac{c_i}{N}$ +- Conditional probability $P(B=b_j | A=a_i)=\frac{n_{ij}}{c_i}$ +- Sum rule $p(A=a_i) = \frac{1}{N}\sum_j n_{ij} = \sum_{b_j}p(A=a_i,B=b_j)$ +- Product rule $P(A=a_i, B =b_j) = \frac{n_{ij}}{c_i}\cdot \frac{c_i}{N} = p(B=b_j |A=a_i)\cdot p(A=a_i)$ + +In short: +- Sum rule: $p(A) = \sum_Bp(A,b)$ +- Product rule: $p(A,B) = p(B|A)p(A)$ +- Bayes' Theorem: $p(A|B)= \frac{p(B|A)p(A)}{\sum_Ap(B|A)p(A)}$ + diff --git a/ObsidianNotes/elemlds lecture 9.md b/ObsidianNotes/elemlds lecture 9.md new file mode 100644 index 0000000..0cccec6 --- /dev/null +++ b/ObsidianNotes/elemlds lecture 9.md @@ -0,0 +1,7 @@ +# Bayes Decision Theory +Goal: predict output class $\mathcal{C}$ from measurements $\text{x}$ by minimizing the probability of misclassification + +>[!tip] Main Equation: +>$$p(X,Y)=\frac{p(X|Y)p(Y)}{p(X)}$$ + +