https://xkcd.com/1056/
Announcements:
¡ñ Guest lecture next Wed
PHYS T + Teams
Copyright By PowCoder代写 加微信 powcoder
ML for cyber security
See you here!
Two graphical model tutorials: week 10 and week 11
Final exam Fri 3 June
5:40 – 8:40 pm Canberra
¡ð On Wattle
¡ð Self-invigilated, video
recording needed
¡ð Instructions will be
Markov random
Conditional independence
Relation to directed graphs
Inference in
graphical models (part 1) –
and factorisation
chains and trees
Bishop 8.3, 8.4.1-8.4.2
Random fields
Definition: Undirected
graph separation
Separation in
undirected vs directed
Conditional
independence in MRFs
Factorisation in
Cliques in graphs
A clique is a subset of nodes in a graph such that there exists an edge between pairs of nodes in the subset. (The nodes in a clique are fully connected.)
maximal clique of a graph
clique. (No other nodes of the graph
destroying the property of full connectedness.)
is a clique which
can be added
a proper subset of another
to a maximal clique without
Factorisation using cliques
Potential function
Normalisation factor / partition function
Major limitation of MRFs, computing this for the entire graph
is usually hard.
Conditional
independence and factorisation
Strictly positive potential functions
Potential function: expressing which configurations of the local variables are
preferred to others.
Global configurations
probability: those with a good balance in satisfying the (possibly conflicting) influences of the clique potentials.
with relatively high
image denoising
corresponding corrupted pixel tend to be the
Neighbouring
pixels tend to be the same.
A pixel is more likely to be background.
Graphical model 2
Conditional independence
Relation to directed graphs
Inference in
graphical models (part 1)
and factorisation
Directed vs
undirected chain graphs
Directed vs undirected chain graphs have the same factors.
Partition function Z
Moralisation
Example taken from https://web.mit.edu/jmn/www/6.034/d-separation.pdf
Bayes Net and MRFs
Graphical model 2
Conditional independence
Relation to directed graphs
Inference in
graphical models (part 1)
and factorisation
Inference in graphical
other nodes.
General ideas:
in graphical
observed values, compute the
¡ñ Exploit graphical structure
models: with some of the nodes in
posterior distributions of one or
– efficiency, transparency
¡ñ Many algorithms expressed in local ¡°message propagation¡± around the graph
¡ñ Focusing on exact inference in this class
(see Chap 10 for approximate inference algorithms)
an essential step
in learning (c.f. EM algorithm)
a graph are clamped to
subsets of
on the simplest graphical model
on a chain graph
to compute p(xn), naive algorithm: O(KN-1)
removing xN
also (8.49)
Recursive evaluation of messages
Other marginals and conditional
¡ñ Computing all marginals
Repeat the above N
times O(N2K2)
Storing all intermediate messages: O(N2K2)
¡ñ Observed nodes
Clamp instead of sum over
¡ñ Computing joint probabilities
distributions
Tree-shaped graphical models
Undirected graph: there is one, and only one, path between any pair
Directed graphs: there is all other nodes have one
Moralisation will
a single node, parent.
not add links ¡ú convert between directed and
Inference can be done similarly ¡ú
called the root, which has
sum-product algorithm, stay tuned
undirected tree.
no parents, and
Markov random
Conditional independence
Relation to directed graphs
Inference in
graphical models (part 1) –
and factorisation
chains and trees
程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com