AutoBayes: a system for generating data analysis programs from statistical models

Abstract

Data analysis is an important scientific task which is required whenever information needs to be extracted from raw data. Statistical approaches to data analysis, which use methods from probability theory and numerical analysis, are well-founded but difficult to implement: the development of a statistical data analysis program for any given application is time-consuming and requires substantial knowledge and experience in several areas.In this paper, we describe AutoBayes, a program synthesis system for the generation of data analysis programs from statistical models. A statistical model specifies the properties for each problem variable (i.e., observation or parameter) and its dependencies in the form of a probability distribution. It is a fully declarative problem description, similar in spirit to a set of differential equations. From such a model, AutoBayes generates optimized and fully commented C/C++ code which can be linked dynamically into the Matlab and Octave environments. Code is produced by a schema-guided deductive synthesis process. A schema consists of a code template and applicability constraints which are checked against the model during synthesis using theorem proving technology. AutoBayes augments schema-guided synthesis by symbolic-algebraic computation and can thus derive closed-form solutions for many problems. It is well-suited for tasks like estimating best-fitting model parameters for the given data. Here, we describe AutoBayes's system architecture, in particular the schema-guided synthesis kernel. Its capabilities are illustrated by a number of advanced textbook examples and benchmarks.

Embedded Probabilistic Programming

“…To start with, the vast majority of standalone probabilistic languages are implemented as interpreters rather than compilers (with the notable exceptions of AutoBayes [13] and HBC [5]). In contrast, an embedded probabilistic language can piggyback on its host language's compilers to remove some interpretive overhead.…”

AutoBayes/CC — Combining Program Synthesis with Automatic Code Certification — System Description —

“…1) is a code certification extension to the AutoBayes synthesis system, which is used in the statistical data analysis domain [2]. Its input specification is a statistical model, i.e., it describes how the statistical variables are distributed and depend on each other and which parameters have to be estimated for the given task.…”

“…The synthesized program uses an iterative EM (expectation maximization) algorithm and consists of roughly 380 lines of code, 90 of which are auto-generated comments to explain the code. For details see http://ase.arc.nasa.gov/schumann/AutoBayesCC and [2]. The code is annotated to prove division-by-zero and array-bounds safety.…”

“…2 shows the runtime distribution for the proof tasks. 2 Most tasks were solved in about two to three seconds, but some tasks took up to 20 seconds. The smaller second peak visible around 15 seconds is due to a non-optimal schedule.…”

Hybrid Decompositional Verification for Discovering Failures in Adaptive Flight Control Systems

“…The range of possible behaviors for the entire system is not currently tractable to explicit techniques. At the system level, we use a combination of unsupervised 19 and supervised 20,21 machine learning techniques in a directed Monte Carlo global sensitivity analysis 22 to model the behavioral structure of the component and to predict the component-level input test vectors. Simulation-based validation depends on heuristics and cannot guarantee that the system is safe; however, validation testing is likely to uncover unsafe behaviors not discovered by using formal methods on simplified systems [23][24][25] .…”