Modern research in biology and medicine is experiencing a data explosion in quantity and particularly in complexity. Efficient and accurate processing of these datasets demands state-of-the-art computational methods such as probabilistic graphical models, graph-based image analysis and many inference/optimization algorithms. However, the underlying complexity of biomedical experiments rules out direct out-of-the-box applications of these methods and requires novel formulation and enhancement to make them amendable to specific problems. This thesis explores novel approaches for incorporating prior knowledge into the data analysis workflow that leads to quantitative and meaningful interpretation of the datasets and also allows for sufficient user involvement. As discussed in Chapter 1, depending on the complexity of the prior knowledge, these approaches can be categorized as constrained modeling and learning. The first part of the thesis focuses on constrained modeling where the prior is normally explicitly represented as additional potential terms in the problem formulation. These terms prevent or discourage the downstream optimization of the formulation from yielding solutions that contradict the prior knowledge. In Chapter 2, we present a robust method for estimating and tracking the deuterium incorporation in the time-resolved hydrogen exchange (HX) mass spectrometry (MS) experiments with priors such as sparsity and sequential ordering. In Chapter 3, we introduce how to extend a classic Markov random field (MRF) model with a shape prior for cell nucleus segmentation. The second part of the thesis explores learning which addresses problems where the prior varies between different datasets or is too difficult to express explicitly. In this case, the prior is first abstracted as a parametric model and then its optimum parametrization is estimated from a training set using machine learning techniques. In Chapter 4, we extend the popular Rand Index in a cost-sensitive fashion and the problem-specific costs can be learned from manual scorings. This set of approaches becomes more interesting when the input/output becomes structured such as matrices or graphs. In Chapter 5, we present structured learning for cell tracking, a novel approach that learns optimum parameters automatically from a training set and allows for the use of a richer set of features which in turn affords improved tracking performance. Finally, conclusions and outlook are provided in Chapter 6
