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- All Subjects: time series
- Creators: Escobedo, Adolfo R.
- Creators: Gardner, Carl
Description
Predicting resistant prostate cancer is critical for lowering medical costs and improving the quality of life of advanced prostate cancer patients. I formulate, compare, and analyze two mathematical models that aim to forecast future levels of prostate-specific antigen (PSA). I accomplish these tasks by employing clinical data of locally advanced prostate cancer patients undergoing androgen deprivation therapy (ADT). I demonstrate that the inverse problem of parameter estimation might be too complicated and simply relying on data fitting can give incorrect conclusions, since there is a large error in parameter values estimated and parameters might be unidentifiable. I provide confidence intervals to give estimate forecasts using data assimilation via an ensemble Kalman Filter. Using the ensemble Kalman Filter, I perform dual estimation of parameters and state variables to test the prediction accuracy of the models. Finally, I present a novel model with time delay and a delay-dependent parameter. I provide a geometric stability result to study the behavior of this model and show that the inclusion of time delay may improve the accuracy of predictions. Also, I demonstrate with clinical data that the inclusion of the delay-dependent parameter facilitates the identification and estimation of parameters.
ContributorsBaez, Javier (Author) / Kuang, Yang (Thesis advisor) / Kostelich, Eric (Committee member) / Crook, Sharon (Committee member) / Gardner, Carl (Committee member) / Nagy, John (Committee member) / Arizona State University (Publisher)
Created2017
Description
The recent technological advances enable the collection of various complex, heterogeneous and high-dimensional data in biomedical domains. The increasing availability of the high-dimensional biomedical data creates the needs of new machine learning models for effective data analysis and knowledge discovery. This dissertation introduces several unsupervised and supervised methods to help understand the data, discover the patterns and improve the decision making. All the proposed methods can generalize to other industrial fields.
The first topic of this dissertation focuses on the data clustering. Data clustering is often the first step for analyzing a dataset without the label information. Clustering high-dimensional data with mixed categorical and numeric attributes remains a challenging, yet important task. A clustering algorithm based on tree ensembles, CRAFTER, is proposed to tackle this task in a scalable manner.
The second part of this dissertation aims to develop data representation methods for genome sequencing data, a special type of high-dimensional data in the biomedical domain. The proposed data representation method, Bag-of-Segments, can summarize the key characteristics of the genome sequence into a small number of features with good interpretability.
The third part of this dissertation introduces an end-to-end deep neural network model, GCRNN, for time series classification with emphasis on both the accuracy and the interpretation. GCRNN contains a convolutional network component to extract high-level features, and a recurrent network component to enhance the modeling of the temporal characteristics. A feed-forward fully connected network with the sparse group lasso regularization is used to generate the final classification and provide good interpretability.
The last topic centers around the dimensionality reduction methods for time series data. A good dimensionality reduction method is important for the storage, decision making and pattern visualization for time series data. The CRNN autoencoder is proposed to not only achieve low reconstruction error, but also generate discriminative features. A variational version of this autoencoder has great potential for applications such as anomaly detection and process control.
The first topic of this dissertation focuses on the data clustering. Data clustering is often the first step for analyzing a dataset without the label information. Clustering high-dimensional data with mixed categorical and numeric attributes remains a challenging, yet important task. A clustering algorithm based on tree ensembles, CRAFTER, is proposed to tackle this task in a scalable manner.
The second part of this dissertation aims to develop data representation methods for genome sequencing data, a special type of high-dimensional data in the biomedical domain. The proposed data representation method, Bag-of-Segments, can summarize the key characteristics of the genome sequence into a small number of features with good interpretability.
The third part of this dissertation introduces an end-to-end deep neural network model, GCRNN, for time series classification with emphasis on both the accuracy and the interpretation. GCRNN contains a convolutional network component to extract high-level features, and a recurrent network component to enhance the modeling of the temporal characteristics. A feed-forward fully connected network with the sparse group lasso regularization is used to generate the final classification and provide good interpretability.
The last topic centers around the dimensionality reduction methods for time series data. A good dimensionality reduction method is important for the storage, decision making and pattern visualization for time series data. The CRNN autoencoder is proposed to not only achieve low reconstruction error, but also generate discriminative features. A variational version of this autoencoder has great potential for applications such as anomaly detection and process control.
ContributorsLin, Sangdi (Author) / Runger, George C. (Thesis advisor) / Kocher, Jean-Pierre A (Committee member) / Pan, Rong (Committee member) / Escobedo, Adolfo R. (Committee member) / Arizona State University (Publisher)
Created2018