Automatic differentiation in machine learning: a survey

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD), also called algorithmic differentiation or simply "autodiff", is a family of techniques similar to but more general than backpropagation for efficiently and accurately evaluating derivatives of numeric functions expressed as computer programs. AD is a small but established field with applications in areas including computational fluid dynamics, atmospheric sciences, and engineering design optimization. Until very recently, the fields of machine learning and AD have largely been unaware of each other and, in some cases, have independently discovered each other's results. Despite its relevance, general-purpose AD has been missing from the machine learning toolbox, a situation slowly changing with its ongoing adoption under the names "dynamic computational graphs" and "differentiable programming". We survey the intersection of AD and machine learning, cover applications where AD has direct relevance, and address the main implementation techniques. By precisely defining the main differentiation techniques and their interrelationships, we aim to bring clarity to the usage of the terms "autodiff", "automatic differentiation", and "symbolic differentiation" as these are encountered more and more in machine learning settings.Comment: 43 pages, 5 figure

Automatic Differentiation of Algorithms for Machine Learning

Automatic differentiation---the mechanical transformation of numeric computer programs to calculate derivatives efficiently and accurately---dates to the origin of the computer age. Reverse mode automatic differentiation both antedates and generalizes the method of backwards propagation of errors used in machine learning. Despite this, practitioners in a variety of fields, including machine learning, have been little influenced by automatic differentiation, and make scant use of available tools. Here we review the technique of automatic differentiation, describe its two main modes, and explain how it can benefit machine learning practitioners. To reach the widest possible audience our treatment assumes only elementary differential calculus, and does not assume any knowledge of linear algebra.Comment: 7 pages, 1 figur

Automated Feature Engineering for Deep Neural Networks with Genetic Programming

Feature engineering is a process that augments the feature vector of a machine learning model with calculated values that are designed to enhance the accuracy of a model’s predictions. Research has shown that the accuracy of models such as deep neural networks, support vector machines, and tree/forest-based algorithms sometimes benefit from feature engineering. Expressions that combine one or more of the original features usually create these engineered features. The choice of the exact structure of an engineered feature is dependent on the type of machine learning model in use. Previous research demonstrated that various model families benefit from different types of engineered feature. Random forests, gradient-boosting machines, or other tree-based models might not see the same accuracy gain that an engineered feature allowed neural networks, generalized linear models, or other dot-product based models to achieve on the same data set. This dissertation presents a genetic programming-based algorithm that automatically engineers features that increase the accuracy of deep neural networks for some data sets. For a genetic programming algorithm to be effective, it must prioritize the search space and efficiently evaluate what it finds. This dissertation algorithm faced a potential search space composed of all possible mathematical combinations of the original feature vector. Five experiments were designed to guide the search process to efficiently evolve good engineered features. The result of this dissertation is an automated feature engineering (AFE) algorithm that is computationally efficient, even though a neural network is used to evaluate each candidate feature. This approach gave the algorithm a greater opportunity to specifically target deep neural networks in its search for engineered features that improve accuracy. Finally, a sixth experiment empirically demonstrated the degree to which this algorithm improved the accuracy of neural networks on data sets augmented by the algorithm’s engineered features

Automatic differentiation in machine learning: a survey

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD) is a technique for calculating derivatives of numeric functions expressed as computer programs efficiently and accurately, used in fields such as computational fluid dynamics, nuclear engineering, and atmospheric sciences. Despite its advantages and use in other fields, machine learning practitioners have been little influenced by AD and make scant use of available tools. We survey the intersection of AD and machine learning, cover applications where AD has the potential to make a big impact, and report on some recent developments in the adoption of this technique. We aim to dispel some misconceptions that we contend have impeded the use of AD within the machine learning community

Automatic differentiation in machine learning: a survey

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD) is a technique for calculating derivatives of numeric functions expressed as computer programs efficiently and accurately, used in fields such as computational fluid dynamics, nuclear engineering, and atmospheric sciences. Despite its advantages and use in other fields, machine learning practitioners have been little influenced by AD and make scant use of available tools. We survey the intersection of AD and machine learning, cover applications where AD has the potential to make a big impact, and report on some recent developments in the adoption of this technique. We aim to dispel some misconceptions that we contend have impeded the use of AD within the machine learning community