History Matching Using Principal Component Analysis

Imperial Users onl

Predicting Pancreatic Cancer Using Support Vector Machine

This report presents an approach to predict pancreatic cancer using Support Vector Machine Classification algorithm. The research objective of this project it to predict pancreatic cancer on just genomic, just clinical and combination of genomic and clinical data. We have used real genomic data having 22,763 samples and 154 features per sample. We have also created Synthetic Clinical data having 400 samples and 7 features per sample in order to predict accuracy of just clinical data. To validate the hypothesis, we have combined synthetic clinical data with subset of features from real genomic data. In our results, we observed that prediction accuracy, precision, recall with just genomic data is 80.77%, 20%, 4%. Prediction accuracy, precision, recall with just synthetic clinical data is 93.33%, 95%, 30%. While prediction accuracy, precision, recall for combination of real genomic and synthetic clinical data is 90.83%, 10%, 5%. The combination of real genomic and synthetic clinical data decreased the accuracy since the genomic data is weakly correlated. Thus we conclude that the combination of genomic and clinical data does not improve pancreatic cancer prediction accuracy. A dataset with more significant genomic features might help to predict pancreatic cancer more accurately

Minimax Structured Normal Means Inference

We provide a unified treatment of a broad class of noisy structure recovery problems, known as structured normal means problems. In this setting, the goal is to identify, from a finite collection of Gaussian distributions with different means, the distribution that produced some observed data. Recent work has studied several special cases including sparse vectors, biclusters, and graph-based structures. We establish nearly matching upper and lower bounds on the minimax probability of error for any structured normal means problem, and we derive an optimality certificate for the maximum likelihood estimator, which can be applied to many instantiations. We also consider an experimental design setting, where we generalize our minimax bounds and derive an algorithm for computing a design strategy with a certain optimality property. We show that our results give tight minimax bounds for many structure recovery problems and consider some consequences for interactive sampling