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**1 - 2**of**2**### Toward Interactive Statistical Modeling

"... When solving machine learning problems, there is currently little automated support for easily experimenting with alternative statistical models or solution strategies. This is because this activity often requires expertise from several different fields (e.g., statistics, optimization, linear algebr ..."

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When solving machine learning problems, there is currently little automated support for easily experimenting with alternative statistical models or solution strategies. This is because this activity often requires expertise from several different fields (e.g., statistics, optimization, linear algebra), and the level of formalism required for automation is much higher than for a human solving problems on paper. We present a system toward addressing these issues, which we achieve by (1) formalizing a type theory for probability and optimization, and (2) providing an interactive rewrite system for applying problem reformulation theorems. Automating solution strategies this way enables not only manual experimentation but also higher-level, automated activities, such as autotuning. Keywords: machine learning, algorithm derivation, interactive modeling, type theory

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"... There has been great interest in creating probabilistic programming languages to simplify the coding of statistical tasks; however, there still does not exist a formal language that simultaneously provides (1) continuous probability distributions, (2) the ability to naturally express custom probabil ..."

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There has been great interest in creating probabilistic programming languages to simplify the coding of statistical tasks; however, there still does not exist a formal language that simultaneously provides (1) continuous probability distributions, (2) the ability to naturally express custom probabilistic models, and (3) probability density functions (PDFs). This collection of features is necessary for mechanizing fundamental statistical techniques. We formalize the first probabilistic language that exhibits these features, and it serves as a foundational framework for extending the ideas to more general languages. Particularly novel are our type system for absolutely continuous (AC) distributions (those which permit PDFs) and our PDF calculation procedure, which calculates PDFs for a large class of AC distributions. Our formalization paves the way toward the rigorous encoding of powerful statistical reformulations.