Related papers: Automatic Backward Differentiation for American Mo…
The compensated quotient-difference (Compqd) algorithm is proposed along with some applications. The main motivation is based on the fact that the standard quotient-difference (qd) algorithm can be numerically unstable. The Compqd algorithm…
Automatic differentiation (AD) has been a topic of interest for researchers in many disciplines, with increased popularity since its application to machine learning and neural networks. Although many researchers appreciate and know how to…
Automatic differentiation (AD) is an important family of algorithms which enables derivative based optimization. We show that AD can be simply implemented with effects and handlers by doing so in the Frank language. By considering how our…
This paper discusses how two classes of approximate computation algorithms can be adapted, in a modular fashion, to achieve exact statistical inference from differentially private data products. Considered are approximate Bayesian…
Automatic differentiation has become an important tool for optimization problems in computational science, and it has been applied to the Hartree-Fock method. Although the reverse-mode automatic differentiation is more efficient than the…
We investigate the automatic differentiation of hybrid models, viz. models that may contain delays, logical tests and discontinuities or loops. We consider differentiation with respect to parameters, initial conditions or the time. We…
Discovering the causal effect of a decision is critical to nearly all forms of decision-making. In particular, it is a key quantity in drug development, in crafting government policy, and when implementing a real-world machine learning…
The pricing of Bermudan options amounts to solving a dynamic programming principle, in which the main difficulty, especially in high dimension, comes from the conditional expectation involved in the computation of the continuation value.…
In this paper we introduce and study the concept of optimal and surely optimal dual martingales in the context of dual valuation of Bermudan options, and outline the development of new algorithms in this context. We provide a…
A stochastic Forward-Backward algorithm with a constant step is studied. At each time step, this algorithm involves an independent copy of a couple of random maximal monotone operators. Defining a mean operator as a selection integral, the…
The spectral deferred correction method is a variant of the deferred correction method for solving ordinary differential equations. A benefit of this method is that is uses low order schemes iteratively to produce a high order…
We establish the convergence of the forward-backward splitting algorithm based on Bregman distances for the sum of two monotone operators in reflexive Banach spaces. Even in Euclidean spaces, the convergence of this algorithm has so far…
In this work, we study the fully automated inference of expected result values of probabilistic programs in the presence of natural programming constructs such as procedures, local variables and recursion. While crucial, capturing these…
This article presents a simple but effective and efficient approach to improve the accuracy and stability of Least-Squares Monte Carlo. The key idea is to construct the ansatz of conditional expected continuation payoff using the…
This paper investigates estimating the variance of a temporal-difference learning agent's update target. Most reinforcement learning methods use an estimate of the value function, which captures how good it is for the agent to be in a…
The exponential increase in the amount of available data makes taking advantage of them without violating users' privacy one of the fundamental problems of computer science. This question has been investigated thoroughly under the framework…
In this document I aim to give an informal treatment of automatic Backward Filtering Forward Guiding, a general algorithm for conditional sampling from a Markov process on a directed acyclic graph. I'll show that the underlying ideas can be…
Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…
Automatic differentiation is everywhere, but there exists only minimal documentation of how it works in complex arithmetic beyond stating "derivatives in $\mathbb{C}^d$" $\cong$ "derivatives in $\mathbb{R}^{2d}$" and, at best, shallow…
Automatic differentiation is a key component in deep learning. This topic is well studied and excellent surveys such as Baydin et al. (2018) have been available to clearly describe the basic concepts. Further, sophisticated implementations…