Learning Problem Formulations

Machine learning can be broken down into a number of problem formulations. The three major categories comprise supervised, unsupervised and reinforcement 

FIGURE 3.1 A restriction endonuclease Bglll bound to DNA (1DFM) rendered in PyMOL [18]. 

For the purpose of the discussion on machine learning, we will use the following definitions and notation. Let (x,i/) be a labeled example where Xj e x, i = is a vector of numerical attributes Xj and y is an associated label. 

Classification is probably the most common supervised machine learning formalism where an example is assigned a grouping based on some hypothesis learned over a set of training examples x,y). A classification algorithm (or classifier) searches for hypothesis h that minimizes the classification error e = 

Fr h x) y). One common classification problem is binary classification where an example is placed in one of two mutually exclusive groups, y e 1, —1. Note that many binary classifiers produce a real-valued output such that R h0c). A threshold is applied to the real value, signj[ti(x)] e 1,-1 such that if the real value exceeds the threshold t then the output is 1 otherwise the output is —1. 

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The outline of this chapter is as follows. The second section introduces a number of important supervised learning problems and illustrates how a biomolec-ular application can be cast in each problem formulation. Specifically, modeling protein-DNA interactions serves as the example for each of these formulations. The third section summarizes recent applications of machine learning to biomolec-ular modeling. The final section discusses current trends and future directions of machine learning applications to biomolecular modeling. 

As stated at the beginning, all the concepts required in the solved- and proposed-problem sections were learned (or should have been learned) in high school. Assuming that it is necessary to review certain concepts, we will take the opportunity to do an exhaustive review in the solved-problem section. Some of the concepts to be reviewed include, for example, ideal gas mixtures, Dalton s law, and Amagat s law. But we will also keep it simple the focus will be, as in previous chapters, on tackling problem formulation ... 

We now invite you on this important and pleasurable journey to learn, face, formulate, solve, and apply material balance problems in process and bioprocess engineering. 

The proposed reform of pedagogy reform at universities mainly deals with question how to learn in parallel with question what to learn. The proposed approach includes four efforts in engineering teaching increase the scale of hands-on learning, move toward a style emphasizes problem formulation, increase the level of proactive engagement of students and provide functional feedback mechanisms. 

These steps may not proceed in the sequence shown, because a difficult kinetic problem may require cycling of attention among the steps as more is learned about the system, with corrections being made and tests of ideas being applied at each stage. In particular, steps 2 and 3 may be strongly interdependent. Our present concern is with these steps later chapters deal with step 4. Edwards et al., Bunnett, and Pearson have formulated provisional rules for proceeding from the rate equation to the mechanism, which includes step 4. 

We have put this model into mathematical form. Although we have yet no quantitative predictions, a very general model has been formulated and is described in more detail in Appendix A. We have learned and applied here some lessons from Kilkson s work (17) on interfacial polycondensation although our problem is considerably more difficult, since phase separation occurs during the polymerization at some critical value of a sequence distribution parameter, and not at the start of the reaction. Quantitative results will be presented in a forthcoming pub1ication. 

This Section addresses cases with a continuous performance metric, y. We identify the corresponding problem statements and results, which are compared with conventional formulations and solutions. Then Taguchi loss functions are introduced as quality cost models that allow one to express a quality-related y on a continuous basis. Next we present the learning methodology used to solve the alternative problem statements and uncover a set of final solutions. The section ends with an application case study. 

With this book the reader can expect to learn how to formulate and solve parameter estimation problems, compute the statistical properties of the parameters, perform model adequacy tests, and design experiments for parameter estimation or model discrimination. 

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