Class notes
Machine learning
This document containing performing of machine learning
[Show more]
Connected book
Book Title:
Author(s):
- Edition:
- ISBN:
- Edition:
Seller
Follow
Content preview
CS229 Lecture NotesAndrew Ng and Tengyu Ma
June 11, 2023
,Contents
I Supervised learning 5
1 Linear regression 8
1.1 LMS algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2 The normal equations . . . . . . . . . . . . . . . . . . . . . . . 13
1.2.1 Matrix derivatives . . . . . . . . . . . . . . . . . . . . . 13
1.2.2 Least squares revisited . . . . . . . . . . . . . . . . . . 14
1.3 Probabilistic interpretation . . . . . . . . . . . . . . . . . . . . 15
1.4 Locally weighted linear regression (optional reading) . . . . . . 17
2 Classification and logistic regression 20
2.1 Logistic regression . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Digression: the perceptron learning algorithm . . . . . . . . . 23
2.3 Multi-class classification . . . . . . . . . . . . . . . . . . . . . 24
2.4 Another algorithm for maximizing `(θ) . . . . . . . . . . . . . 27
3 Generalized linear models 29
3.1 The exponential family . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Constructing GLMs . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.1 Ordinary least squares . . . . . . . . . . . . . . . . . . 32
3.2.2 Logistic regression . . . . . . . . . . . . . . . . . . . . 33
4 Generative learning algorithms 34
4.1 Gaussian discriminant analysis . . . . . . . . . . . . . . . . . . 35
4.1.1 The multivariate normal distribution . . . . . . . . . . 35
4.1.2 The Gaussian discriminant analysis model . . . . . . . 38
4.1.3 Discussion: GDA and logistic regression . . . . . . . . 40
4.2 Naive bayes (Option Reading) . . . . . . . . . . . . . . . . . . 41
4.2.1 Laplace smoothing . . . . . . . . . . . . . . . . . . . . 44
4.2.2 Event models for text classification . . . . . . . . . . . 46
1
,CS229 Spring 20223 2
5 Kernel methods 48
5.1 Feature maps . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.2 LMS (least mean squares) with features . . . . . . . . . . . . . 49
5.3 LMS with the kernel trick . . . . . . . . . . . . . . . . . . . . 49
5.4 Properties of kernels . . . . . . . . . . . . . . . . . . . . . . . 53
6 Support vector machines 59
6.1 Margins: intuition . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.2 Notation (option reading) . . . . . . . . . . . . . . . . . . . . 61
6.3 Functional and geometric margins (option reading) . . . . . . 61
6.4 The optimal margin classifier (option reading) . . . . . . . . . 63
6.5 Lagrange duality (optional reading) . . . . . . . . . . . . . . . 65
6.6 Optimal margin classifiers: the dual form (option reading) . . 68
6.7 Regularization and the non-separable case (optional reading) . 72
6.8 The SMO algorithm (optional reading) . . . . . . . . . . . . . 73
6.8.1 Coordinate ascent . . . . . . . . . . . . . . . . . . . . . 74
6.8.2 SMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
II Deep learning 79
7 Deep learning 80
7.1 Supervised learning with non-linear models . . . . . . . . . . . 80
7.2 Neural networks . . . . . . . . . . . . . . . . . . . . . . . . . . 84
7.3 Modules in Modern Neural Networks . . . . . . . . . . . . . . 92
7.4 Backpropagation . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.4.1 Preliminaries on partial derivatives . . . . . . . . . . . 99
7.4.2 General strategy of backpropagation . . . . . . . . . . 102
7.4.3 Backward functions for basic modules . . . . . . . . . . 105
7.4.4 Back-propagation for MLPs . . . . . . . . . . . . . . . 107
7.5 Vectorization over training examples . . . . . . . . . . . . . . 109
III Generalization and regularization 112
8 Generalization 113
8.1 Bias-variance tradeoff . . . . . . . . . . . . . . . . . . . . . . . 115
8.1.1 A mathematical decomposition (for regression) . . . . . 120
8.2 The double descent phenomenon . . . . . . . . . . . . . . . . . 121
8.3 Sample complexity bounds (optional readings) . . . . . . . . . 126
, CS229 Spring 20223 3
8.3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . 126
8.3.2 The case of finite H . . . . . . . . . . . . . . . . . . . . 128
8.3.3 The case of infinite H . . . . . . . . . . . . . . . . . . 131
9 Regularization and model selection 135
9.1 Regularization . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
9.2 Implicit regularization effect (optional reading) . . . . . . . . . 137
9.3 Model selection via cross validation . . . . . . . . . . . . . . . 139
9.4 Bayesian statistics and regularization . . . . . . . . . . . . . . 142
IV Unsupervised learning 144
10 Clustering and the k-means algorithm 145
11 EM algorithms 148
11.1 EM for mixture of Gaussians . . . . . . . . . . . . . . . . . . . 148
11.2 Jensen’s inequality . . . . . . . . . . . . . . . . . . . . . . . . 151
11.3 General EM algorithms . . . . . . . . . . . . . . . . . . . . . . 152
11.3.1 Other interpretation of ELBO . . . . . . . . . . . . . . 158
11.4 Mixture of Gaussians revisited . . . . . . . . . . . . . . . . . . 158
11.5 Variational inference and variational auto-encoder (optional
reading) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
12 Principal components analysis 165
13 Independent components analysis 171
13.1 ICA ambiguities . . . . . . . . . . . . . . . . . . . . . . . . . . 172
13.2 Densities and linear transformations . . . . . . . . . . . . . . . 173
13.3 ICA algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
14 Self-supervised learning and foundation models 177
14.1 Pretraining and adaptation . . . . . . . . . . . . . . . . . . . . 177
14.2 Pretraining methods in computer vision . . . . . . . . . . . . . 179
14.3 Pretrained large language models . . . . . . . . . . . . . . . . 181
14.3.1 Open up the blackbox of Transformers . . . . . . . . . 183
14.3.2 Zero-shot learning and in-context learning . . . . . . . 186
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller hariprasadr. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
50843 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now