1 Introduction 1
I Fundamentals 3
2 Probability 5
3 Statistics 63
4 Graphical models 143
5 Information theory 217
6 Optimization 255
II Inference 337
7 Inference algorithms: an overview 339
8 Gaussian filtering and smoothing 353
9 Message passing algorithms 395
10 Variational inference 433
11 Monte Carlo methods 477
12 Markov chain Monte Carlo 493
13 Sequential Monte Carlo 537
III Prediction 567
14 Predictive models: an overview 569
15 Generalized linear models 583
16 Deep neural networks 623
17 Bayesian neural networks 639
18 Gaussian processes 673
19 Beyond the iid assumption 727
IV Generation 763
20 Generative models: an overview 765
21 Variational autoencoders 781
22 Autoregressive models 811
23 Normalizing flows 819
24 Energy-based models 839
25 Diffusion models 857
26 Generative adversarial networks 883
V Discovery 915
27 Discovery methods: an overview 917
28 Latent factor models 919
29 State-space models 969
30 Graph learning 1031
31 Nonparametric Bayesian models 1035
32 Representation learning 1037
33 Interpretability 1061
VI Action 1091
34 Decision making under uncertainty 1093
35 Reinforcement learning 1133
36 Causality 1171