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Home arrow Computer Science arrow Statistical modeling and machine learning for molecular biology

Statistical modeling and machine learning for molecular biology


Section I OverviewAcross Statistical Modeling and Machine Learning on a ShoestringABOUT THIS BOOKWHAT WILL THIS BOOK COVER?ClusteringRegressionClassificationORGANIZATION OF THIS BOOKWHY ARE THERE MATHEMATICAL CALCULATIONS IN THE BOOK?WHAT WON'T THIS BOOK COVER?WHY IS THIS A BOOK?REFERENCES AND FURTHER READINGStatistical ModelingWHAT IS STATISTICAL MODELING?PROBABILITY DISTRIBUTIONS ARE THE MODELSDEEP THOUGHTS ABOUT THE GAUSSIAN DISTRIBUTIONHOW DO I KNOW IF MY DATA FITS A PROBABILITY MODEL?AXIOMS OF PROBABILITY AND THEIR CONSEQUENCES: "RULES OF PROBABILITY"RULES OF PROBABILITYNOTATION AND ABUSE OF NOTATIONHYPOTHESIS TESTING: WHAT YOU PROBABLY ALREADY KNOW ABOUT STATISTICSTESTS WITH FEWER ASSUMPTIONSWilcoxon Rank-Sum Test, Also Known As the Mann- Whitney U Test (or Simply the WMW Test)Kolmogorov-Smirnov Test (KS-Test)CENTRAL LIMIT THEOREMEXACT TESTS AND GENE SET ENRICHMENT ANALYSISPERMUTATION TESTSKEY STATISTICAL TESTS FOR COMPARING TWO LISTS OF NUMBERSSOME POPULAR DISTRIBUTIONSThe Uniform DistributionThe 7"-DistributionThe Exponential DistributionThe Chi-Squared DistributionThe Poisson DistributionThe Bernoulli DistributionThe Binomial DistributionEXERCISESREFERENCES AND FURTHER READINGMultiple TestingTHE BONFERRONI CORRECTION AND GENE SET ENRICHMENT ANALYSISMULTIPLE TESTING IN DIFFERENTIAL EXPRESSION ANALYSISFALSE DISCOVERY RATEeQTLs: A VERY DIFFICULT MULTIPLE-TESTING PROBLEMEXERCISESREFERENCES AND FURTHER READINGParameter Estimation and Multivariate StatisticsFITTING A MODEL TO DATA: OBJECTIVE FUNCTIONS AND PARAMETER ESTIMATIONMAXIMUM LIKELIHOOD ESTIMATIONLIKELIHOOD FOR GAUSSIAN DATAHOW TO MAXIMIZE THE LIKELIHOOD ANALYTICALLYTHE DISTRIBUTION OF PARAMETER ESTIMATES FOR MLEsOTHER OBJECTIVE FUNCTIONSBIAS, CONSISTENCY, AND EFFICIENCY OF ESTIMATORSBAYESIAN ESTIMATION AND PRIOR DISTRIBUTIONSMULTIVARIATE STATISTICSA QUICK REVIEW OF VECTORS, MATRICES, AND LINEAR ALGEBRAMLEs FOR MULTIVARIATE DISTRIBUTIONSTHE MULTINOMIAL DISTRIBUTION AND THE CATEGORICAL DISTRIBUTIONHYPOTHESIS TESTING REVISITED: THE PROBLEMS WITH HIGH DIMENSIONSEXAMPLE OF LRT FOR THE MULTINOMIAL: GC CONTENT IN GENOMESEXERCISESREFERENCES AND FURTHER READINGSection II ClusteringDistance-Based ClusteringMULTIVARIATE DISTANCES FOR CLUSTERINGAGGLOMERATIVE CLUSTERINGCLUSTERING DNA AND PROTEIN SEQUENCESIS THE CLUSTERING RIGHT?TECHNIQUES TO EVALUATE CLUSTERING RESULTSK-MEANS CLUSTERING"LEARNING SIGNAL" IN THE K-MEANS ALGORITHMSO WHAT IS LEARNING ANYWAY?CHOOSING THE NUMBER OF CLUSTERS FOR K-MEANSK-MEDOIDS AND EXEMPLAR-BASED CLUSTERINGGRAPH-BASED CLUSTERING: "DISTANCES" VERSUS "INTERACTIONS" OR "CONNECTIONS"CLUSTERING AS DIMENSIONALITY REDUCTIONEXERCISESREFERENCES AND FURTHER READINGMixture Models and Hidden Variables for Clustering and BeyondTHE GAUSSIAN MIXTURE MODELBAYESIAN NETWORKS AND GRAPHICAL MODELSE-M UPDATES FOR THE MIXTURE OF GAUSSIANSDERIVING THE E-M ALGORITHM FOR THE MIXTURE OF GAUSSIANSGAUSSIAN MIXTURES IN PRACTICE AND THE CURSE OF DIMENSIONALITYCHOOSING THE NUMBER OF CLUSTERS USING THE AICAPPLICATIONS OF MIXTURE MODELS IN BIOINFORMATICSINTEGRATING DATA SOURCES WITH SEQUENCE AND EXPRESSION CLUSTERSEXERCISESREFERENCES AND FURTHER READINGSection III RegressionUnivariate RegressionSIMPLE LINEAR REGRESSION AS A PROBABILISTIC MODELDERIVING THE MLEs FOR LINEAR REGRESSIONHYPOTHESIS TESTING IN LINEAR REGRESSIONDERIVING THE DISTRIBUTION OF THE MLE FOR bLEAST SQUARES INTERPRETATION OF LINEAR REGRESSIONAPPLICATION OF LINEAR REGRESSION TO eQTLsFROM HYPOTHESIS TESTING TO STATISTICAL MODELING: PREDICTING PROTEIN LEVEL BASED ON mRNA LEVELFIVE GREAT THINGS ABOUT SIMPLE LINEAR REGRESSIONREGRESSION IS NOT JUST "LINEAR"— POLYNOMIAL AND LOCAL REGRESSIONSGENERALIZED LINEAR MODELSEXERCISESREFERENCES AND FURTHER READINGMultiple RegressionPREDICTING Y USING MULTIPLE XsHYPOTHESIS TESTING IN MULTIPLE DIMENSIONS: PARTIAL CORRELATIONSEXAMPLE OF A HIGH-DIMENSIONAL MULTIPLE REGRESSION: REGRESSING GENE EXPRESSION LEVELS ON TRANSCRIPTION FACTOR BINDING SITESIDENTIFYING TRANSCRIPTION FACTOR BINDING MOTIFS USING THE REDUCE ALGORITHMAIC AND FEATURE SELECTION AND OVERFITTING IN MULTIPLE REGRESSIONMULTIPLE REGRESSION SO FAREXERCISESREFERENCES AND FURTHER READINGRegularization in Multiple Regression and BeyondREGULARIZATION AND PENALIZED LIKELIHOOD DIFFERENCES BETWEEN THE EFFECTS OF L1 AND L2 PENALTIES ON CORRELATED FEATURESREGULARIZATION BEYOND SPARSITY: ENCOURAGING YOUR OWN MODEL STRUCTUREPENALIZED LIKELIHOOD AS MAXIMUM A POSTERIORI (MAP) ESTIMATIONCHOOSING PRIOR DISTRIBUTIONS FOR PARAMETERS: HEAVY-TAILS IF YOU CANPRIOR DISTRIBUTIONS FOR CLUSTERING AND INFINITE MIXTURE MODELSEXERCISESREFERENCES AND FURTHER READINGSection IV ClassificationLinear ClassificationCLASSIFICATION BOUNDARIES AND LINEAR CLASSIFICATIONPROBABILISTIC CLASSIFICATION MODELSSOME POPULAR CLASSIFICATION RULESLOGISTIC REGRESSIONGENE EXPRESSION SIGNATURES AND MOLECULAR DIAGNOSTICSLINEAR DISCRIMINANT ANALYSIS (LDA) AND THE LOG LIKELIHOOD RATIODERIVING THE LDA DECISION BOUNDARYGENERATIVE AND DISCRIMINATIVE MODELS FOR CLASSIFICATIONNAIVE BAYES: GENERATIVE MAP CLASSIFICATIONIDENTIFYING MOTIF MATCHES IN DNA SEQUENCESTRAINING NAIVE BAYES CLASSIFIERSNAIVE BAYES AND DATA INTEGRATIONEXERCISESREFERNCES AND FURTHER READINGChapterv 11 Nonlinear ClassificationTWO APPROACHES TO CHOOSE NONLINEAR BOUNDARIES: DATA-GUIDED AND MULTIPLE SIMPLE UNITSNEURAL NETWORKS: HOW DO WE (AND OTHER ANIMALS) DO CLASSIFICATION?DISTANCE-BASED CLASSIFICATION WITH ^-NEAREST NEIGHBORSSVMs FOR NONLINEAR CLASSIFICATIONDECISION TREESRANDOM FORESTS AND ENSEMBLE CLASSIFIERS: THE WISDOM OF THE CROWDMULTICLASS CLASSIFICATIONEXERCISESREFERENCES AND FURTHER READINGEvaluating ClassifiersCLASSIFICATION PERFORMANCE STATISTICS IN THE IDEAL CLASSIFICATION SETUPMEASURES OF CLASSIFICATION PERFORMANCESOME COMMON MEASURES FOR THE EVALUATION OF CLASSIFIERSROC CURVES AND PRECISION-RECALL PLOTSEVALUATING CLASSIFIERS WHEN YOU DON'T HAVE ENOUGH DATALEAVE-ONE-OUT CROSS-VALIDATIONBETTER CLASSIFICATION METHODS VERSUS BETTER FEATURESEXERCISESREFERENCES AND FURTHER READING
 
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