network genetics

Francesco GadaletaUniversity of Liege - Montefiore Institute

Select and Connect the benefits of building networks in geneticsFrancesco Gadaleta PhD - Montefiore Institute ULg

Francesco GadaletaSelect and Connect: the benefits of building networks in genetics

• Genetics and Networks

• Variable selection with penalised regression

• Application to Gene Expression Profiles

• Demo

OUTLINE


Given a set of microarray experiments

HOWselect covariates build networks?


EXPLAIN PREDICTOR

gene interactionbest SNP selection

phenotypesurvival


?ASSOCIATION

CORRELATION

CAUSALITYA B

REGULATION


PENALISED REGRESSION

least squares elastic net ridge regression fused group quadratic programming

hierarchical LASSO nonlinear penalised multivariate linear regression gradient descent


OPTIMISATION PROBLEMS IN MACHINE LEARNING

Def. convex set X

Def. convex function

Optimisation problem


GRADIENT

Where’s the min?

follow the


local minima are also global minima

fast convergence

WHY CONVEXITY?

Introduce gradients, subgradients and epigraphs

…some proofs

here

gradient/coordinate

descent


OPTIMISATION METHODS FOR

GRADIENT DESCENT works fine but can be slow

COORDINATE DESCENT cycle through each predictor in turn compute residuals

convex ANDdifferentiableconvex

PATHWISE COORDINATE DESCENT start with large (sparse model) apply COORDINATE DESCENT decrease (zero coordinates stay zero!)


min

penalty (sparsity)

covariance matrix (association)

gene matrixresponse


MULTICOLLINEARITY

y B C

D

lack of independency

presence of interdependency

least square regression fails

approach singularity

explodes


i

NETWORK CONSTRUCTION


matrix of regression coefficients

symmetric

not symmetric A B

A B

A B


NETWORK VALIDATION

GeneNetWeaver ‣ generates synthetic μA data from regulatory network

‣ several conditions (simulation of μA noise, network

perturbations, time series, generation of samples using

multifactorial equations)

‣ Golden Standard (GS)

Directed unweighted signed network, based on

transcription factor network (TFN) of E.coli [1]


SYNTHETIC DATA GENERATION

‣ Used no noise, multifactorial based GS networks

50 nodes with 3 regulators (TFs)

200 nodes with 10 regulators (TFs)


SELECT AND CONNECT IN ACTION


REAL NETWORK

200 nodes 212 connections


PREDICTED NETWORK

200 nodes 360 connections


DEGREE CORRELATION

86%false positivespredicted hubs correctly detected


BETWEENESS CORRELATION

83%


LASSO is quadratic programming (polynomial)

COMPUTATIONAL COMPLEXITY

Time-complexity of iterative convex optimisation is tricky to analyse (it depends on a convergence criterion)

:-):-(

Coordinate descent requires O(np) operations

:-|


PARALLEL COMPUTATIONS

(permutation tests)


200 genes, 400 permutations, 5 cpus

100 100100 100

as fast as 100 permutations


200 genes, 400 permutations, 40 cpus

100 100100 100 100 100100 100 100 100100 100

1:25 25:50 175:200

as fast as 25 genes and 100 permutations

…


NETWORK INTEGRATION


NETWORK INTEGRATION

how do we connect networks?

how do we deal with diverse datasets?


– Niels Bohr

“Prediction is very difficult, especially about the future.”

genes

www.worldofpiggy.com @worldofpiggy [email protected]


thank you.

www.worldofpiggy.com @worldofpiggy [email protected]

network genetics

Data & Analytics

benefits of building

genetics genetics

francesco gadaletaselect

genetics penalised regression

networks variable selection

genetics optimisation

genetics optimisation

genetics gradient wheres