Statistics Department Options

MT 2019

1

Introductions

• Neil Laws

• James Martin

• Geoff Nicholls

• Pier Palamara

• . . . and you?

2

Outline

This session is for both Maths and Maths & Stats students.

Information about:

• Combinations of courses that work well together in Parts Band C

• Part A options useful for our options in future years.

We’ll talk about four different areas:

• Statistics

• Statistical Machine Learning

• Statistical Genetics

• Probability

A few short presentations, plus the opportunity for you to askquestions.

3

Courses in 2019–20 (future years may differ)

Part A:• A8 Probability• A9 Statistics• A12 Simulation and Statistical Programming

Part B:• SB1 Applied and Computational Statistics (double unit)• SB2.1 Foundations of Statistical Inference• SB2.2 Statistical Machine Learning• SB3.1 Applied Probability• SB3.2 Statistical Lifetime Models• SB4.1 Actuarial Science

Part C:• SC1 Stochastic Models in Mathematical Genetics• SC2 Probability and Statistics for Network Analysis• SC4 Advanced Topics in Statistical Machine Learning• SC5 Advanced Simulation Methods• SC6 Graphical Models [NOT running in 2019–20]• SC7 Bayes Methods• SC8 Topics in Computational Biology• SC9 Probability on Graphs and Lattices• SC10 Algorithmic Foundations of Learning

4

Current regulations:

Maths students:

• can take SB3.1 Applied Probability (which counts as a Mathsunit for Maths students)

• plus up to 2 other statistics units.

Maths & Stats students:

• SB1 Applied & Comp Stats (double-unit) is compulsory

• also need to take at least 2 of SB2.1/2.2, SB3.1/3.2.

5

Switching to Maths & Stats is possible

Students who are sufficiently interested in our options can switchto Maths & Stats – with the support of their college.

Some students may wish to consider this:

• the ideal time is during MT of second year(or by/at the start of HT)

• otherwise by the start of 3rd year

• though some students have switched successfully at the startof 4th year.

6

Possible combinations

A8 Probability and A9 Statistics will be assumed everywherebelow. (Not strictly necessary, e.g. don’t need A9 Statistics forSB3.1 Applied Probability.)

∗ denotes a course that we’ll regard as “core knowledge” for aparticular area.

7

Statistics

∗ A12 Simulation and Statistical Programming ∗∗ SB1 Applied and Computational Statistics ∗∗ SB2.1 Foundations of Statistical Inference ∗SB2.2 Statistical Machine LearningSB3.1 Applied Probability

SC4 Advanced Topics in Statistical Machine LearningSC5 Advanced Simulation MethodsSC6 Graphical ModelsSC7 Bayes MethodsSC10 Algorithmic Foundations of Learning

and less central:SC1 Stochastic Models in Mathematical GeneticsSC8 Topics in Computational Biology

8

Statistical Machine Learning

∗ SB2.1 Foundations of Statistical Inference ∗∗ SB2.2 Statistical Machine Learning ∗A12 Simulation and Statistical ProgrammingSB1 Applied and Computational Statistics

SC4 Advanced Topics in Statistical Machine LearningSC5 Advanced Simulation MethodsSC6 Graphical ModelsSC7 Bayes MethodsSC10 Algorithmic Foundations of Learning

9

Statistical Genetics

∗ SB3.1 Applied Probability ∗

SC1 Stochastic Models in Mathematical GeneticsSC2 Probability and Statistics for Network AnalysisSC8 Topics in Computational Biology

10

Probability

∗ A4 Integration ∗Part A Graph TheoryA12 Simulation and Statistical Programming

∗ SB3.1 Applied Probability ∗∗ B8.1 Probability, Measure and Martingales ∗B8.2 Continuous Martingales and Stochastic Calculus

SC9 Probability on Graphs and Lattices

. . .

11

Statistics options in Part A and beyond

“its mainly linear models”

Recent quote from XTX Markets quant

Themes within Statistics

• A good knowledge of probability (ie Part A/SB3a) is key.• [Part A integration is (very) useful for advanced statistics (probability)]

• The principles of statistics are set out in SB2.1 (developed in SC6/7)• [Decision theory from SB2.1 appears in later ML and Stats courses]

• Core statistical models and data analysis SB1.1 (actually doing stuff)• [ubiquitous – appear later in ML and Statistics courses at Part B and C]

• Statistical Computing, Algorithms, R, in Part A SSP/SB1.1&2/SC5• [R & algorithm theory, numerical; many lecturers use R examples in later courses]

• Theory Pre-req or useful, Part A P&S + ….

*SB2.1 Foundations of Statistical Inference

SB3.1 Applied Probability

Part C Graphical Models (possible return) SB1.1, SB2.1

SC10 Algorithmic foundations of Learning SB2.1, SB2.2

• Methods and Data Analysis*SB1.1 Applied StatisticsSB2.2 Statistical Machine LearningSC7 Bayes Methods A12, SB1.1, SB2.1SC4 Adv. Statistical Machine Learning SB2.1, SB2.2

• Computational Statistics (Theory, Methods, Applications)

*A12 Simulation and Statistical Programming

SB1.2 Computational Statistics

SC5 Advanced Simulation A12, SB3.1, PA Integration

• Applications SB4.1 Actuarial StatisticsSC1 Mathematical Genetics SB3.1SC2 Prob. & Stat. for Network Analysis SC8 Topics in Computational Biology

A specimen course… after A12

*SB1.1 Applied Statistics

*SB2.1 Foundations of Statistical Inference

SB3.1 Applied Probability

[options eg SC4, Math papers]

SB1.2 Computational Statistics

SB2.2 Statistical Machine Learning (SB1a/SB2a)

[options]

SC2 Prob. & Stat. for Network Analysis

SC10 Algorithmic foundations of Learning

[options, eg SC1, or perhaps Part C Graphical Models)]

SC4 Adv. Statistical Machine Learning

SC7 Bayes Methods

[options, eg SC5 Adv Sim, SC8]

Pier Palamara 14/11/19

Machine Learning Genomics

Images: Wikimedia

What is Machine Learning?

What is Machine Learning?

What is Machine Learning?

Figure: The Economist

What is Machine Learning?

• “A field of study that gives computers the ability to learn without being explicitly programmed” -- Arthur Samuel, 1959

• Data + Statistics + Computer Science

Machine Learning example: the perceptron

• A very simple neural network

b

b

Rosenblatt, 1957Images: Wikimedia

Machine Learning example: the perceptron

• A very simple neural network

b

b

Rosenblatt, 1957

Domestication

Size

Images: Wikimedia

Machine Learning example: the perceptron

• A very simple neural network

b

Update weightsb

Rosenblatt, 1957Images: Wikimedia

Machine Learning example: the perceptron

• A very simple neural network

b

Update weightsb

Rosenblatt, 1957Images: Wikimedia

Machine Learning example: the perceptron

• Multi-layer perceptron: more complex neural network

Images: Wikimedia

Machine Learning example: the perceptron

• Multi-layer perceptron: more complex neural network

LeCun et al., 1989 Neural Computation

Machine Learning: Deep Learning• Very complex tasks

Machine Learning: Deep Learning• Very complex tasks• Do you know this person?

Machine Learning: Deep Learning• Very complex tasks• Do you know this person?

Machine Learning: Deep Learning• Very complex tasks• Do you know this person?

Machine Learning: Deep Learning• Very complex tasks• Do you know this person?

Karras et al. ArXivThese images were created by a computer!

Machine Learning

• Machine learning involves math!