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Important objectives in cancer research are the prediction of a patient's risk based on molecular measurements such as gene expression data and the identification of new prognostic biomarkers (e.g. genes). In clinical practice, this is…
Background: The development of classification methods for personalized medicine is highly dependent on the identification of predictive genetic markers. In survival analysis it is often necessary to discriminate between influential and…
Survival analysis aims to predict the timing of future events across various fields, from medical outcomes to customer churn. However, the integration of clustering into survival analysis, particularly for precision medicine, remains…
A prevalent feature of high-dimensional data is the dependence among covariates, and model selection is known to be challenging when covariates are highly correlated. To perform model selection for the high-dimensional Cox proportional…
Nonnegative matrix factorization (NMF) is a popular method used to reduce dimensionality in data sets whose elements are nonnegative. It does so by decomposing the data set of interest, $\mathbf{X}$, into two lower rank nonnegative matrices…
Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction,…
Non-negative Matrix Factorization (NMF) is an intensively used technique for obtaining parts-based, lower dimensional and non-negative representation. Researchers in biology, medicine, pharmacy and other fields often prefer NMF over other…
For statistical inference on regression models with a diverging number of covariates, the existing literature typically makes sparsity assumptions on the inverse of the Fisher information matrix. Such assumptions, however, are often…
The selection of most informative and discriminative features from high-dimensional data has been noticed as an important topic in machine learning and data engineering. Using matrix factorization-based techniques such as nonnegative matrix…
Variable selection problem for the nonlinear Cox regression model is considered. In survival analysis, one main objective is to identify the covariates that are associated with the risk of experiencing the event of interest. The Cox…
We show how to incorporate information from labeled examples into nonnegative matrix factorization (NMF), a popular unsupervised learning algorithm for dimensionality reduction. In addition to mapping the data into a space of lower…
Survival analysis is an important research topic with applications in healthcare, business, and manufacturing. One essential tool in this area is the Cox proportional hazards (CPH) model, which is widely used for its interpretability,…
To extract the relevant features in a given dataset is a difficult task, recently resolved in the non-negative data case with the Non-negative Matrix factorization (NMF) method. The objective of this research work is to extend this method…
Non-negative matrix factorization (NMF) is an important technique for obtaining low dimensional representations of datasets. However, classical NMF does not take into account data that is collected at different times or in different…
A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming…
Lung cancer has a high rate of recurrence in early-stage patients. Predicting the post-surgical recurrence in lung cancer patients has traditionally been approached using single modality information of genomics or radiology images. We…
This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven model for the factorization where the most salient features in the data are used to…
We analyze connections between two low rank modeling approaches from the last decade for treating dynamical data. The first one is the coherence problem (or coherent set approach), where groups of states are sought that evolve under the…
Survival prediction is an important branch of cancer prognosis analysis. The model that predicts survival risk through TCGA genomics data can discover genes related to cancer and provide diagnosis and treatment recommendations based on…
Prognostic models in survival analysis are aimed at understanding the relationship between patients' covariates and the distribution of survival time. Traditionally, semi-parametric models, such as the Cox model, have been assumed. These…