Machine Learning

Definition

Machine Learning
: A computer program is said to learn from experience $E$ with respect to some class of tasks $T$ and performance measure $P$, if its performance at tasks in $T$, as measured by $P$, improves with experience $E$

• [r] Michell, Machine Learning 1997

• From a scientific and philosophical point of view, machine learning is interesting because developing our understanding of machine learning entails developing our understanding of the principles that underlie intelligence

Task T

ML tasks are usually described in terms of how the ML system should process an example.

An example is a collection of features that have been quantitatively measured from some object or event that we want the ML system to process. We typically represent an example as a vector $x\in {\mathbb{R}}^n$ where each entry $x_i$ of the vector is an feature.

• The features of an image are usually the values of the pixels in the image.

Most common ML tasks:

• Classification
• Classification with missing inputs
  • When some of the inputs may be missing, the learning algorithm must learn a set of functions, each corresponding to classifying x with a different subset of its inputs missing
  • With n input variables, we can now obtain all 2^n^ different classification functions needed for each possible set of missing inputs, but we only need to learn a single function describing the joint probability distribution
• Regression
• Structured output
  • Transcription
  • Machine translation
• Anomaly detection
• Synthesis and sampling
• Imputation of missing values
• Denoising
• Density estimation or probability mass function estimation
  • Probability distribution estimated can be used to solve other tasks, such as the missing value imputation task

Performance Measure P

In order to evaluate the abilities of a machine learning algorithm, we must design a quantitative measure of its performance. Usually this performance measure P is specific to the task T being carried out by the system.

Most common performance measures:

• Accuracy or error rate: classification, structured output
• average log-probability (i.e. Cross-Entropy) the model assigns to some examples: density estimation

Usually we are interested in how well the machine learning algorithm performs on data that it has not seen before. We therefore evaluate these performance measures using a test set of data that is separate from the data used for training the machine learning system.

Experience E

The experience of most ML algorithms is the dataset, a collection of many examples/data points, and an example is a collection of features.

ML algorithms can be broadly categorized as Unsupervised Learning or Supervised Learning by what kind of experience they are allowed to have during the learning process.

• Unsupervised Learning
  • learn useful properties of the structure of this dataset
  • Examples: density estimation, synthesis, denoising, clustering
• Supervised Learning
  • each example is also associated with a label/target
  • Example: classification, regression, structured output
• Semi-Supervised Learning

Describing a Dataset

• Matrix - a different example in each row, a different feature in each column
  • Requires that every example has the same features vectors of the same size
  • With a label vector in SL
• Set - examples as elements

Methods

• Supervised Learning
  • Regression
    • Linear Regression
    • Logistic Regression
    • ridge regression
    • LASSO
  • Classification
    • Linear Classifier
    • Nearest Neighbor
    • Support Vector Machine
  • Deep Learning
  • Decision Tree
    • Random Forest
• Ensemble Learning
• Unsupervised Learning
• Meta-Learning
• Unsupervised Learning
• Semi-Supervised Learning
• Reinforcement Learning

General Concepts & Techniques

• Mercer Kernel & Reproducing Kernel Hilbert Space
• Dimensionality Deduction
• Overfitting and Underfitting
• Hyperparameter
• Cross-Validation
• Estimation
  • Estimation & Bias
  • Maximum Likelihood Estimation
  • Bayesian Statistics

Course Log

2023-01-17

• Supervised Learning
  • Two tasks
    • Regression: Using a set of inputs, predict real-valued output
    • Classification: Using a set of inputs, predict a discrete label (aka class)
  • Tools
    • Deep Learning
• Unsupervised Learning
  • Task: uncover the structure in the data
    • NO correct answer; no supervise
  • Applications
    • predictions
    • recommendations
    • efficient data exploration
      • Learn the dominant topics from a set of news articles.
• A probabilistic model is a set of probability distributions, $p(x|\theta )$

graph TD
B[0. Build Model] --> C[2. Infer hidden variables]
A[1. Data] --Optimization--> C
C --> D[3. Predict & Explore]
A --Supervise--> D

• Differences between Supervised Learning and Unsupervised Learning mainly lie in blocks 1 and 3
• Differences between probabilistic and non-probabilistic approaches mainly lie in blocks 0 and 2

2023-01-19

• Linear Regression

2023-01-24

• Ridge Regression

2023-01-26

• Bias-Variance Trade-Off in Regression
• Cross-Validation

2023-01-31

• Maximum a Posteriori
• Bayesian Linear Regression
• Active Learning

2023-02-02

• Underdetermined Linear System
• LASSO

2023-02-07

• Classification
  • Nearest Neighbor
• Statistical Learning
  • How to find an accurate regression function/ classifier?
  • Key assumption: data (feature and label) are i.i.d. from a distribution, then the past should look like the future
• Generative vs Discriminative Model

2023-02-09

• Linear Classifier
  • Perceptron Algorithm

2023-02-14

• Logistic Regression
• Bayesian Logistic Regression

2023-02-016

• Feature Map, Mercer Kernel, and Mercer's Theorem
• Gaussian Process Regression

2023-02-21/23

• Support Vector Machine

2023-02-28

• Decision Tree
• Ensemble Learning
  • Bootstrap
  • Random Forest

2023-03-2

• Boosting

2023-03-21

• Unsupervised Learning
  • Clustering
    • K-Means

2023-03-23

• Expectation Maximization

2023-03-28

• Clustering
  • K-Means#Soft (Weighted) K-Means
  • Gaussian Mixture Model

2023-03-30

• Matrix Factorization

2023-04-04

• Topic Modeling

2023-04-06

• Principal Components Analysis
  • Probabilistic PCA
  • Kernel PCA

2023-04-11

• Markov Chain

2023-04-13

• Hidden Markov Model

2023-04-18

• Kalman Filter

2023-04-20

• Association Analysis

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