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Survival prediction and prognostic factor identification play an important role in machine learning research. This paper employs the machine learning regression algorithms for constructing survival models. The paper suggests a new Bayesian framework for feature selection in high-dimensional Cox regression problems. The proposed approach re- sults in a strong probabilistic statement of the shrinkage criterion for feature selection. The respective regularization technique produces un- biased estimates that possess grouping and oracle properties and whose maximal error risk diverges to a finite value. Experimental results show that the proposed framework outperforms the known algorithms on both simulated data and publicly available real data sets.