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&#002F;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.

/pdf/autobayes-a-system-for-generating-data-analysis-programs-6mj2scbtim.pdf

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

autofilter is a tool that generates implementations that solve state estimation problems using Kalman filters. From a high-level, mathematics-based description of a state estimation problem, autofilter automatically generates code that computes a statistically optimal estimate using one or more of a number of well-known variants of the Kalman filter algorithm. The problem description may be given in terms of continuous or discrete, linear or nonlinear process and measurement dynamics. From this description, autofilter automates many common solution methods (e.g., linearization, discretization) and generates C or Matlab code fully automatically. autofilter surpasses toolkit-based programming approaches for Kalman filters because it requires no low-level programming skills (e.g., to "glue" together library function calls). autofilter raises the level of discourse to the mathematics of the problem at hand rather than the details of what algorithms, data structures, optimizations and so on are required to implement it. An overview of autofilter is given along with an example of its practical application to deep space attitude estimation.

https://ti.arc.nasa.gov/m/profile/schumann/PDF/WS2004.pdf

Automating the implementation of Kalman filter algorithms

Extracting information from data, often also called data analysis, is an important scientific task. Statistical approaches, 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 knowledge and experience in several areas.

In this paper, we describe AUTOBAYES, a high-level generator system for 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 thus a fully declarative problem description, similar in spirit to a set of differential equations. From this model, AUTOBAYES generates optimized and fully commented C/C++ code which can be linked dynamically into the Matlab and Octave environments. Code is generated by schema-guided deductive synthesis. 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. In this paper, we outline the AUTOBAYES system, its theoretical foundations in Bayesian probability theory, and its application by means of a detailed example.

Generating Data Analysis Programs from Statistical Models

Machine learning has reached a point where many probabilistic methods can be understood as variations, extensions and combinations of a much smaller set of abstract themes, e.g., as different instances of the EM algorithm. This enables the systematic derivation of algorithms customized for different models. Here, we describe the AUTOBAYES system which takes a high-level statistical model specification, uses powerful symbolic techniques based on schema-based program synthesis and computer algebra to derive an efficient specialized algorithm for learning that model, and generates executable code implementing that algorithm. This capability is far beyond that of code collections such as Matlab toolboxes or even tools for model-independent optimization such as BUGS for Gibbs sampling: complex new algorithms can be generated without new programming, algorithms can be highly specialized and tightly crafted for the exact structure of the model and data, and efficient and commented code can be generated for different languages or systems. We present automatically-derived algorithms ranging from closed-form solutions of Bayesian textbook problems to recently-proposed EM algorithms for clustering, regression, and a multinomial form of PCA.

/pdf/automatic-derivation-of-statistical-algorithms-the-em-family-x015imngkc.pdf

Automatic Derivation of Statistical Algorithms: The EM Family and Beyond

Automatic design optimization is highly sensitive to problem formulation. The choice of objective function, constraints and design parameters can dramatically impact on the computational cost of optimization and the quality of the resulting design. The best formulation varies from one application to another. A design engineer will usually not know the best formulation in advance. To address this problem, we have developed a system that supports interactive formulation, testing and reformulation of design optimization strategies. Our system includes an executable, data-flow language for representing optimization strategies. The language allows an engineer to define multiple stages of optimization, each using different approximations of the objective and constraints or different abstractions of the design space. We have also developed a set of transformations that reformulate strategies represented in our language. The transformations can approximate objective and constraint functions, abstract or reparameterize search spaces, or divide an optimization process into multiple stages. The system is applicable in principle to any design problem that can be expressed in terms of constrained optimization; however, we expect the system to be most useful when the design artifact is governed by algebraic and ordinary differential equations. We have tested the system on problems of racing yacht design and jet engine nozzle design. We report experimental results demonstrating that our reformulation techniques can significantly improve the performance of automatic design optimization. Our research demonstrates the viability of a reformulation methodology that combines symbolic program transformation with numerical experimentation. It is an important first step in a research program aimed at automating the entire strategy formulation process.

A transformation system for interactive reformulation of design optimization strategies

Computational science and engineering design can benefit from software tools that facilitate construction of programs for simulating physical systems. Our research adapts the methodology of deductive program synthesis to the problem of synthesizing numerical simulation codes. We have focused on simulators that can be represented as second-order functional programs composed of numerical integration and root-extraction routines. Synthesis of second-order programs appears to present a problem for deductive systems that operate in first order logic. We present a recursive synthesis algorithm that overcomes this difficulty for a class of program synthesis problems. Our system has successfully constructed numerical simulators for computational design of jet-engine nozzles and sailing yachts, among others.

Deductive synthesis of numerical simulation programs from networks of algebraic and ordinary differential equations

Popular Tasks used by Researchers

How can I help with your research?

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

We encountered an error while loading the panel. Please try refreshing the page.

Something went wrong

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

Anyone with the link can view this chat. You can switch it back to private anytime.

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

T. Ellman

Author Tools

Chat about Author

Papers

Deductive synthesis of numerical simulation programs from networks of algebraic and ordinary differential equations