Machine learning has risen in importance across science, engineering, and business inrecent years. Domain experts have begun to understand how their data analysis problemscan be solved in a principled and efficient manner using methods from machine learning,with its simultaneous focus on statistical and computational concerns. Moreover, the datain many of these application domains has exploded in availability and scale, further underscoring the need for algorithms which find patterns and trends quickly and correctly.However, most people actually analyzing data today operate far from the expert level.Available statistical libraries and even textbooks contain only a finite sample of the possibilities afforded by the underlying mathematical principles. Ideally, practitioners shouldbe able to do what machine learning experts can do--employ the fundamental principles toexperiment with the practically infinite number of possible customized statistical models aswell as alternative algorithms for solving them, including advanced techniques for handlingmassive datasets. This would lead to more accurate models, the ability in some cases toanalyze data that was previously intractable, and, if the experimentation can be greatlyaccelerated, huge gains in human productivity.Fixing this state of affairs involves mechanizing and automating these statistical andalgorithmic principles. This task has received little attention because we lack a suitablesyntactic representation that is capable of specifying machine learning problems and solutions, so there is no way to encode the principles in question, which are themselves amapping between problem and solution. This work focuses on providing the foundationallayer for enabling this vision, with the thesis that such a representation is possible. Wedemonstrate the thesis by defining a syntactic representation of machine learning that isexpressive, promotes correctness, and enables the mechanization of a wide variety of usefulsolution principles.
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