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Bayesian Machine learning and its application
Alan QiFeb. 23, 2009
Motivation
• massive data from various sources: web pages, facebook, high-throughput biological data, high-throughput chemical data, etc.
• Challenging goal: how to model complex systems and extract knowledge from data.
Bayesian machine learning
Bayesian learning method
Principled way to fuse prior knowledge and new evidence in data
Key issues Model Design
Computation
Wide-range applications
Bayesian learning in practice
Applications:
Recommendation systems (Amazon, NetFlix)
Text Parsing (Finding latent topics in documents)
Systems biology (where computations meets biology)
Computer vision (parsing handwritten diagram automatically)
Wireless communications
Computational finance ....
Learning for biology: understanding gene regulation during organism development
Protein, product of Gene B
DNA
Gene A
Learning functionalities of genes for development
Inferring high-resolution protein-DNA binding locations from low-resolution measurement
Learning regulatory cascades during embryonic stem cell development
6
High
time timetime
genes
High
time timetime
genes
High
time timetime
genes
Wild-type lineageNo C lineage Extra ‘C’ lineages
High
time timetime
genes
Data: gene expression profiles from wide-types & mutants
(Baugh et al, 2005)
Bayesian semisupervised classification for finding tissue-specific genes
BGEN: (Bayesian GENeralization from examples, Qi et al., Bioinformatics 2006)
Labeledexpression
Labeledexpression
Classifier
Graph-based kernels
(F. Chung, 1997, Zhu et al., 2003, Zhou et al. 2004)
Gaussian process classifier that is trained by EP and classifies the whole genome efficiently
Estimating noise and probe quality by approximate leave-one-out error
Gene expression
Biological experiments support our predictions
CNon C
MuscleEpidermis
CNon C
MuscleEpidermis
K01A2.5
R11A5.4 Ge’s lab
Data: genomic sequences
RNA: messager
Consensus SequencesUseful for publication
IUPAC symbols for degenerate sites
Not very amenable to computation
Nature Biotechnology 24, 423 - 425 (2006)
Probabilistic Model
.2
.2
.5
.1
.7.2.2.1.3
.1.2.4.5.4
.1.2.2.2.2
.1.4.1.2.1ACGT
M1 MKM1
Pk(S|M)
Position FrequencyMatrix (PFM)
1 K Count frequenciesAdd pseudocounts
Bayesian learning: Estimating motif models by Gibbs sampling
P(Se
quen
ces|
para
ms1
,par
ams2
)
Parameter1 Parameter2
In theory, Gibbs Sampling less likely to get stuck a local maxima
Bayesian learning: Estimating motif models by expectation maximization
P(Se
quen
ces|
para
ms1
,par
ams2
)
Parameter1 Parameter2
To minimize the effects of local maxima, you should searchmultiple times from different starting points
Scoring A Sequence
11
( | ) ( | )( | )log log log
( | ) ( | ) ( | )
N Ni i i i
ii i i
P S PFM P S PFMP S PFMScore
P S B P S B P S B
To score a sequence, we compare to a null model
A: 0.25
T: 0.25
G: 0.25
C: 0.25
A: 0.25
T: 0.25
G: 0.25
C: 0.25
Background DNA (B)
.2
.2
.5
.1
.7.2.2.1.3
.1.2.4.5.4
.1.2.2.2.2
.1.4.1.2.1ACGT
Log likelihoodratio
-0.3
-0.3
1
-1.3
1.4-0.3-0.3-1.30.3
-1.3-0.30.610.6
-1.3-0.30.3-0.3-0.3
-1.30.6-1.3-0.3-1.3ACGT
Position WeightMatrix (PWM)
PFM
Scoring a Sequence
MacIsaac & Fraenkel (2006) PLoS Comp Bio
Common threshold = 60% of maximum score
Visualizing Motifs – Motif LogosRepresent both base frequency and conservation at each position
Height of letter proportionalto frequency of base at that position
Height of stack proportionalto conservation at that position
Software implemenation: AlignACE
http://atlas.med.harvard.edu/cgi-bin/alignace.pl
• Implements Gibbs sampling for motif discovery– Several enhancements
• ScanAce – look for motifs in a sequence given a model
• CompareAce – calculate “similarity” between two motifs (i.e. for clustering motifs)
Data: biological networks
Network Decomposition
• Infinite Non-negative Matrix Factorization
1. Formulate the discovery of network legos as a non-negative factorization problem
2. Develop a novel Bayesian model which automatically learns the number of the bases.
Network Decomposition
•Synthetic Network Decomposition
Network Decomposition
Data: Movie rating
• User-item Matrix of Ratings
• Recommend: 5 • Not Recommend: 1
X =
Task: how to predict user preference
• “Based on the premise that people looking for information should be able to make use of what others have already found and evaluated.” (Maltz & Ehrlich, 1995)
• E.g., if you like movies A, B, C, D, and E. And I like A, B, C, D but have not seen E yet. What would be my possible rating on E?
Collaborative filtering for recommendation systems
• Matrix factorization as an collaborative filtering approach:
X ≈ Z A where X is N by D, Z is N by K and A is K by D.
xi,j: user i’s rating on movie j
zi,k: user i’s interests in movie category k (e.g., action, thriller, comedy, romance, etc.)
Ak,j: how likely movie j belong to movie category k
Such that xi,j ≈ zi,1 A1,j + zi,2 A22,j + … + zi,K AK,j
Bayesian learning of matrix factorization
• Training: Use probability theory, in particular, Bayeisan inference, to learn the model parameters Z, A given data X, which contains missing elements, i.e., unknown ratings
• Prediction: use estimated Z and A to predict unkown ratings in X
Test resutls
• ‘Jester’ dataset: • Map from [-10,10] to [0,20]• 10 random chosen datasets, each with 1000
users. For each user we randomly hold out 10 ratings for testing
• IMF, INMF and NMF(K=2…9)
Collaborative Filtering
Task
• How to find latent topics and group documents, such as emails, papers, or news into different clusters?
Data: text documents
X =
Computer science papers Biology papers
Assumptions
1. The keywords are shared in different documents of one topic.
2. The more important the keyword is, the more frequent it appears.
Matrix factorization models (again)
X = Z A
xi,j: the frequency word j appears in document zi,k: how much content in document i is related to topic k (e.g., biology, computer science, etc.)
Ak,j: how important word j to topic k
Bayesian Matrix Factorization
• We will use Bayesian methods again to estimate Z and A.
• Once we can identify hidden topics by examining A and cluster documents.
Text Clustering
• ‘20 newsgroup’ dataset• A subset of 815 articles and 477 words.
Discovered hidden topics
Summary
• Bayesian machine learning: A powerful tool enables computers to learn hidden relations from massive data and make sensible predictions.
• Applications in computational biology, e.g., gene expression analysis and motif discovery, and information extraction, e.g., text modeling.