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Efficient Automatic Differentiation of Implicit Functions
Charles C. Margossian, Michael Betancourt
Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate the…
The Discrete Adjoint Method: Efficient Derivatives for Functions of Discrete Sequences
Michael Betancourt, Charles C. Margossian, Vianey Leos-Barajas
Gradient-based techniques are becoming increasingly critical in quantitative fields, notably in statistics and computer science. The utility of these techniques, however, ultimatel…
A Geometric Theory of Higher-Order Automatic Differentiation
Michael Betancourt
First-order automatic differentiation is a ubiquitous tool across statistics, machine learning, and computer science. Higher-order implementations of automatic differentiation, how…
On Symplectic Optimization
Michael Betancourt, Michael I. Jordan, Ashia C. Wilson
Accelerated gradient methods have had significant impact in machine learning -- in particular the theoretical side of machine learning -- due to their ability to achieve oracle low…
On the Geometric Ergodicity of Hamiltonian Monte Carlo
Samuel Livingstone, Michael Betancourt, Simon Byrne +1
We establish general conditions under which Markov chains produced by the Hamiltonian Monte Carlo method will and will not be geometrically ergodic. We consider implementations wit…