big challenges with big data in life sciences
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DESCRIPTIONBig Challenges with Big Data in Life Sciences. Shankar Subramaniam UC San Diego. The Digital Human. A Super-Moores Law. Adapted from Lincoln Stein 2012. The Phenotypic Readout. Data to Networks to Biology. NETWORK RECONSTRUCTION. Data-driven network reconstruction of biological systems - PowerPoint PPT Presentation
Big Challenges with Big Data in Life Sciences
Shankar SubramaniamUC San Diego
The Digital Human
A Super-Moores LawAdapted from Lincoln Stein 2012
The Phenotypic Readout
Data to Networks to Biology
NETWORK RECONSTRUCTIONData-driven network reconstruction of biological systemsDerive relationships between input/output dataRepresent the relationships as a networkInverse Problem: Data-driven Network Reconstruction
Network ReconstructionsReverse Engineering of biological networksReverse engineering of biological networks:
Structural identification: to ascertain network structure or topology.
Identification of dynamics to determine interaction details.
Statistical methodsSimulation methodsOptimization methodsRegression techniquesClustering
Network Reconstruction of Dynamic Biological Systems: Doubly Penalized LASSOBehrang Asadi*, Mano R. Maurya*, Daniel Tartakovsky, Shankar SubramaniamDepartment of BioengineeringUniversity of California, San Diego NSF grants (STC-0939370, DBI-0641037 and DBI-0835541) NIH grants 5 R33 HL087375-02* Equal effort
APPLICATIONPhosphoprotein signaling and cytokine measurements in RAW 264.7 macrophage cells.
MOTIVATION FOR THE NOVEL METHODVarious methodsRegression-based approaches (least-squares) with statistical significance testing of coefficientsDimensionality-reduction to handle correlation: PCR and PLSOptimization/Shrinkage (penalty)-based approach: LASSOPartial-correlation and probabilistic model/Bayesian-basedDifferent methods have distinct advantages/disadvantagesCan we benefit by combining the methods?Compensate for the disadvantagesA novel method: Doubly Penalized Linear Absolute Shrinkage and Selection Operator (DPLASSO)Incorporate both statistical significant testing and Shrinkage
LINEAR REGRESSIONGoal: Building a linear-relationship based model
X: input data (m samples by n inputs), zero mean, unit standard deviationy: output data (m samples by 1 output column), zero-meanb: model coefficients: translates into the edges in the networke: normal random noise with zero mean
Ordinary Least Squares solution:
Formulation for dynamic systems:
Most coefficients non-zero, a mathematical artifactPerform statistical significance testingCompute the standard deviation on the coefficients
RatioCoefficient is significant (different from zero) if:
Edges in the network graph represents the coefficients.STATISTICAL SIGNIFICANCE TESTING* Krmer, Nicole, and Masashi Sugiyama. "The degrees of freedom of partial least squares regression."Journal of the American Statistical Association106.494 (2011): 697-705.
Partial least squares finds direction in the X space that explains the maximum variance direction in the Y space
PLS regression is used when the number of observations per variable is low and/or collinearity exists among X valuesRequires iterative algorithm: NIPALS, SIMPLS, etcStatistical significance testing is iterativeCORRELATED INPUTS: PLS* H. WOLD, (1975), Soft modelling by latent variables; the non-linear iterative partial least squares approach, in Perspectives in Probability and Statistics, Papers in Honour of M. S. Bartlett, J. Gani, ed., Academic Press, London.
Derivative of the regression coefcients and degrees of freedom for PLSX: n x py: n x 1S: n x nM: Number of (latent) components
LASSOShrinkage version of the Ordinary Least Squares, subject to L-1 penalty constraint (the sum of the absolute value of the coefficients should be less than a threshold)Where represents the full least square estimates0 < t < 1: causes the shrinkageThe LASSO estimator is then defined as:* Tibshirani, R.: Regression shrinkage and selection via the Lasso, J. Roy. Stat. Soc. B Met., 1996, 58, (1), pp. 267288Cost FunctionL-1 Constraint
Noise and Missing DataMore systematic comparison needed with respect to:Noise: Level, TypeSize (dimension)Level of missing dataCollinearity or dependency among input channelsMissing dataNonlinearity between inputs/outputs and nonlinear dependencyTime-series inputs(/outputs) and dynamic structure
METHODSLinear Matrix Inequalities (LMI)*Converts a nonlinear optimization problem into a linear optimization problem.
Pre-existing knowledge of the system (e.g. ) can be added in the form of LMI constraints:
Threshold the coefficients: * [Cosentino, C., et al., IET Systems Biology, 2007. 1(3): p. 164-173]
METRICSMetrics for comparing the methods
Reconstruction from 80% of datasets and 20% for validation RMSE on the test set, and the number and the identity of the significant predictors as the basic metric to evaluate the performance of each method Fractional error in the estimating the parameters
Sensitivity, specificity, G, accuracy
parameters smaller than 10% of the standard deviation of all parameter values were set to 0 when generating the synthetic data
TP : True PositiveFP : False PositiveTN : True NegativeFN : False Negative
RESULTS: DATA SETSData sets for benchmarking: Two data sets
First set: experimental data measured on macrophage cells (Phosphoprotein (PP) vs Cytokine)*
Second sets consist of synthetic data generated in Matlab. We build the model using 80% of the data-set (called training set) and use the rest of data-set to validate the model (called test set).* [Pradervand, S., M.R. Maurya, and S. Subramaniam, Genome Biology, 2006. 7(2): p. R11].
RESULTS: PP-Cytokine Data SetSchematic representation of Phosphoprotein (PP) vs CytokineSignals were transmitted through 22 recorded signaling proteins and other pathways (unmeasured pathways).
Only measured pathways contributed to the analysis
Schematic graphs from:[Pradervand, S., M.R. Maurya, and S. Subramaniam, Genome Biology, 2006. 7(2): p. R11].
PP-CYTOKINE DATASETCourtesy: AfCS
Measurements of cytokines in response to LPS~ 250 such datasets
RESULTS: COMPARISONComparison on synthetic noisy dataThe methods are applied on synthetic data with 22 inputs and 1 output. The true coefficients for the inputs (about 1/3rd) are made zero to test the methods if they identify them as insignificant.
Effect of noise levelFour outputs with 5, 10, 20 and 40% noise levels, respectively, are generated from the noise-free (true) output.
Effect of noise typeThree outputs with White, t-distributed, and uniform noise types, respectively are generated from the noise-free (true) output
RESULTS: COMPARISONVariability between realizations of data with white noise
PCR, LASSO, and LMIare used to identify significant predictors for 1000 input-output pairs.
Histograms of the coefficients in the three significant predictors common to the three methods:Mean and standard deviation in the histograms of the coefficients computed with PCR, LASSO, and LMI.
MethodPredictor #11011True value-3.405.82-6.95PCRMean-3.814.73-6.06Std.0.330.320.32Frac. Err. in mean0.120.190.13LASSOMean-2.824.48-5.62Std.0.340.320.33Frac. Err. in mean0.170.230.19LMIMean-3.704.74-6.34Std.0.340.320.34Frac. Err. in mean0.090.180.09
RESULTS: COMPARISONComparison of outcome of different methods on the real dataDifferent methods identified unique sets of common and distinct predictors for each output
Graphical illustration of methods PCR, LASSO, and LMI in detection of significant predictors for output IL-6 in PP/cytokine experimental dataset
Only the PCR method detects the true input cAMP
zone I provides validation and it highlights the common output of all the methods
Comparison with respect to different noise types:LASSO is the most robust methods for different noise types.
Missing data RMSE: LASSO less deviation, more robust.
Collinearity: PCR less deviation against noise level, better accuracy and G with increasing noise level.
A COMPARISON (Asadi, et al., 2012)
Methods / CriteriaPCRLASSOLMIIncreasing NoiseRMSEScore= (average RMSE across different noise levels for LS)/(average RMSE across different noise levels for the chosen method) / 0.68degrades gradually with level of noise / 0.56 / 0.94Standard deviation and error in mean of Coefficients. Score = 1 average (fractional error in mean(10,12,20) + (std(10,12,20)/ |true associated coefficients|) ) / 0.53 / 0.47 / 0.55Acc./GScore = average accuracy across different noise levels for chosen method (white noise) / 0.70 / 0.87 / 0.91at high noise all similarFractional Error in estimating the parametersScore = 1- average fractional error in estimating the coefficients across different noise levels for chosen method (white noise)/ 0.81 / .55 / 0.78Types of noiseFractional Error in estimating the parameters Score = 1- average fractional error in estimating the coefficients across different noise levels and different noise types (20% noise level) / 0.80 / 0.56 / 0.79Accuracy and GScore = average accuracy across different noise levels and different noise types / 0.71 / 0.87 / 0.91Dimension ratio / SizeFractional Error in estimating the parametersScore = 1- average fractional error in estimating the coefficients across different noise levels and different ratios (m/n = 100/25, 100/50, 400/100) / 0.77 / 0.53 / 0.75Accuracy and G Score = average accuracy across different white noise levels and different ratios (m/n = 100/25, 100/50, 400/100) / 0.66 / 0.83 / 0.90
DPLASSODoubly Penalized Least Absolute Shrinkage and Selection Operator
OUR APPROACH: DPLASSO
Our approach: DPLASSO includes two parameter select