Related papers: Fast and General Automatic Differentiation for Fin…
Generalized additive index models (GAIMs) offer a flexible semiparametric framework for capturing complex data relationships, balancing the interpretability of parametric models with the flexibility of nonparametric approaches. However,…
Differentiation along algorithms, i.e., piggyback propagation of derivatives, is now routinely used to differentiate iterative solvers in differentiable programming. Asymptotics is well understood for many smooth problems but the…
In Formal Languages and Automata Theory courses, students find understanding nondeterministic finite-state and pushdown automata difficult. In many cases, this means that it is challenging for them to comprehend the operational semantics of…
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 aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…
Automatic differentiation (AD), a technique for constructing new programs which compute the derivative of an original program, has become ubiquitous throughout scientific computing and deep learning due to the improved performance afforded…
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…
We present a disambiguation algorithm for weighted automata. The algorithm admits two main stages: a pre-disambiguation stage followed by a transition removal stage. We give a detailed description of the algorithm and the proof of its…
In this paper we focus on the subdiffusive Black Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in the considered model. We derive the governing fractional…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
Automatic differentiation, also known as backpropagation, AD, autodiff, or algorithmic differentiation, is a popular technique for computing derivatives of computer programs accurately and efficiently. Sometimes, however, the derivatives…
We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT…
Solving semiparametric models can be computationally challenging because the dimension of parameter space may grow large with increasing sample size. Classical Newton's method becomes quite slow and unstable with intensive calculation of…
In this paper we demonstrate a new technique for deriving discrete adjoint and tangent linear models of finite element models. The technique is significantly more efficient and automatic than standard algorithmic differentiation techniques.…
Thermodynamic and flash equilibrium calculations are the cornerstones of simulation process calculations. The iterative approach, a widely used nonlinear problem-solving technique, relies on derivative calculations throughout the procedure…
Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent…
Let $z_{1},z_{2},...,z_{N}$ be a sequence of distinct grid points. A finite difference formula approximates the $m$-th derivative $f^{(m)}(0)$ as $\sum w_{k}f(z_{k})$, with $w_{k}$ being the weights. We derive an algorithm for finding the…
We propose two novel numerical schemes for approximate implementation of the dynamic programming~(DP) operation concerned with finite-horizon, optimal control of discrete-time systems with input-affine dynamics. The proposed algorithms…
Automatic differentiation (AD) in reverse mode (RAD) is a central component of deep learning and other uses of large-scale optimization. Commonly used RAD algorithms such as backpropagation, however, are complex and stateful, hindering deep…
A recent line of work has shown that end-to-end optimization of Bayesian filters can be used to learn state estimators for systems whose underlying models are difficult to hand-design or tune, while retaining the core advantages of…