MATT DUNLOP

Bayesian neural network priors for edge-preserving inversion

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A gradient-free subspace-adjusting ensemble sampler for infinite-dimensional Bayesian inverse problems

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Stability of Gibbs posteriors from the Wasserstein loss for Bayesian Full Waveform Inversion

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New likelihood functions and level-set prior for Bayesian full-waveform inversion

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Large data and zero noise limits of graph-based semi-supervised learning algorithms

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Hyperparameter estimation in Bayesian MAP estimation: parameterizations and consistency

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Reconciling Bayesian and perimeter regularization for binary inversion

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Multiplicative noise in Bayesian inverse problems: well-posedness and consistency of MAP estimators

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Dimension-robust MCMC in Bayesian inverse problems

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How deep are Deep Gaussian Processes?

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Iterative updating of model error for Bayesian inversion

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Hierarchical Bayesian level set inversion

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The Bayesian formulation of EIT: analysis and algorithms

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MAP estimators for piecewise continuous inversion

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Analysis and Computation for Bayesian Inverse Problems

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CMS/ACM 107 Problem Set Instructions

Exercises are given in the lecture notes at the end of each chapter. The exercise numbers given correspond to those in the lecture notes.

A number of exercises will be assigned each week.

CMS/ACM 107 Week 1 Problem Set

1.3, 1.4, 1.5,
2.1, 2.4, 2.8, 2.9, 2.14, 2.36, 2.37, 2.42.

CMS/ACM 107 Week 2 Problem Set

1.8, 1.9, 1.10, 1.11,
2.2, 2.3, 2.5, 2.7, 2.40(a).

CMS/ACM 107 Week 3 Problem Set

1.7, 1.13,
2.6, 2.17, 2.19, 2.29(a),
3.8, 3.9, 3.10,
4.13, 4.14, 4.15, 4.16, 4.17, 4.18.

CMS/ACM 107 Week 4 Problem Set

1.3,
2.10, 2.11, 2.30, 2.38, 2.39, 2.41,
3.11.

CMS/ACM 107 Week 5 Problem Set

3.11, 3.14, 3.15, 3.16, 3.18, 3.19, 3.20.

CMS/ACM 107 Week 6 Problem Set

1.24, 1.25, 1.26,
3.29, 3.30, 3.31.

CMS/ACM 107 Week 7 Problem Set

Read section 3.8 of the notes up to and including Corollary 3.34.
Exercises 3.13, 3.21.

CMS/ACM 107 Week 8 Problem Set

3.18, 3.19, 3.20.

CMS/ACM 107 Week 9 Problem Set

To be submitted 3.26, 3.30 and 3.31.

CMS/ACM 107 Week 10 Problem Set

To be submitted 3.32 and 3.33.

CMS/ACM 107 Late Submission Policy

Assignments may be handed in late; but each late day will incur a 20% penalty decrease, in order to be fair to other students who hand in on time.

CMS/ACM 107 Problem Set Instructions

Exercises are given in the lecture notes at the end of each chapter. The exercise numbers given correspond to those in the lecture notes.

A number of exercises will be assigned each week, of which one will be marked at random and count for 1% of the course.

CMS/ACM 107 Week 1 Problem Set

To be submitted: 1.3, 1.5, 1.9 and 1.11.
Accessible by end of week: 1.1-1.11.

CMS/ACM 107 Week 2 Problem Set

To be submitted: 1.14, 1.17, 1.22 and 1.25.
To read: Section 1.3 - Eigenvalues and Eigenvectors. Please also read the statements of the Schur Factorization, the Jordan Canonical Form and the SVD; you do not need to read the proofs and, in fact, the proof of the SVD will be covered in lectures anyway.
Accessible by end of week: 1.13-1.14, 1.17-1.18, 1.20, 1.22-1.26.

CMS/ACM 107 Week 3 Problem Set

To be submitted: 1.16.
To read: Exercise 1.15 and its solution at the back of the lecture notes.
Accessible by end of week: All chapter 1 exercises.

CMS/ACM 107 Week 4 Problem Set

To be submitted: 2.1, 2.2, 2.3 and 2.4.

CMS/ACM 107 Week 5 Problem Set

To be submitted: 2.9, 2.37 and 2.39.
Accessible by end of week: 2.11, 2.36.

CMS/ACM 107 Week 6 Problem Set

To be submitted: 2.29(a), 2.29(c), 2.40 and 2.41.
Note: You may use the result of 2.29(b) to prove 2.29(c).

CMS/ACM 107 Week 7 Problem Set

To be submitted: 3.1, 3.3, 3.6 and 3.13.
To read: Exercise 3.2 and its solution at the back of the lecture notes.

CMS/ACM 107 Week 8 Problem Set

To be submitted: 3.7, 3.8, 3.9, 3.10 and 3.17.

CMS/ACM 107 Week 9 Problem Set

To be submitted 3.26, 3.30 and 3.31.

CMS/ACM 107 Week 10 Problem Set

To be submitted 3.32 and 3.33.

CMS/ACM 107 Late Submission Policy

Assignments may be handed in late; but each late day will incur a 20% penalty decrease, in order to be fair to other students who hand in on time. Problem sets will not be graded if handed in late.