Matrix-vector notation is the predominant idiom in which machine learning formulae are expressed; some models, like Gaussian processes (Rasmussen & Williams, 2006), would be extremely difficult to describe without it. Turning a matrix expression into a computer program is not always easy, however. Although good implementations of primitive matrix operations are available (Golub & Van Loan, 1996) as are packages like MATLAB1, which provide a high-level interface to these primitives, two important tasks must still be carried out manually: (i) computing derivatives of matrix functions and (ii) turning a matrix expression into an efficient computer program. Not having tools to do this can and does harm research: even for the relatively simple example of fitting a linear regression model with gradient methods, the number of types and combinations of basis functions a\u00a0 researcher can experiment with is limited by the need to manually differentiate the objective function and write code for each version. We have addressed these issues by combining a symbolic matrix algebra engine with a\u00a0 superoptimizing compiler: an interesting learning problem in itself. We call our system Coconut.<\/p>\n","protected":false},"excerpt":{"rendered":"
Matrix-vector notation is the predominant idiom in which machine learning formulae are expressed; some models, like Gaussian processes (Rasmussen & Williams, 2006), would be extremely difficult to describe without it. Turning a matrix expression into a computer program is not always easy, however. 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