arXiv research

We approximate derivatives of functions on manifolds by embedding them and applying vector-valued operators.

Approximates derivative pricing under fractional stochastic volatility.

Generalizes neural network approximation to infinite-dimensional manifolds and derivatives.

Theory for deep neural network approximation of score function and its derivatives.

Universal approximation theorem for differentiable maps on infinite-dimensional manifolds

Approximates discounted moments for financial products using polynomial expansions.

Novel approach to financial derivatives pricing using rough path theory.

Deep neural networks with piecewise-polynomial activations can approximate smooth functions and their derivatives.

Researchers develop neural networks for approximating functions in Banach spaces.

The paper approximates financial derivatives using neural networks and iterated integrals.

Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood theoretically on their optimality and limitations of their performance. Only recen…

Derives formulas for Monge-Ampère measures and reduces complex conjectures to simpler existence problems.

A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique allows one to obtain remarkably good approximations of the pricing kernels of f…

We derive caplet volatilities for quadratic models, providing an asymptotic approximation.

Estimation of density derivatives is a versatile tool in statistical data analysis. A naive approach is to first estimate the density and then compute its derivative. However, such a two-step approach does not work well because a good density estimator does not necessarily mean a good density-derivative estimator. In t…

New method for CMS derivatives pricing using Watanabe's expansions.

For an embedded submanifold $Σ\subset\mathbb{R}^{N}$, Belkin and Niyogi showed that one can approximate the Laplacian operator using heat kernels. Using a definition of coarse Ricci curvature derived by iterating Laplacians, we approximate the coarse Ricci curvature of submanifolds $Σ$ in the same way. For this purpose…

The paper provides an efficient method to price path-dependent derivatives using multiscale stochastic volatility models.

New neural network with RePU activation approximates smooth functions and their derivatives.

Closed-form relations and approximations for SE(3) derivatives for robust numerical simulations.

Using tools from spectral analysis, singular and regular perturbation theory, we develop a systematic method for analytically computing the approximate price of a derivative-asset. The payoff of the derivative-asset may be path-dependent. Additionally, the process underlying the derivative may exhibit killing (i.e. jum…

Recently, variational approximations such as the mean field approximation have received much interest. We extend the standard mean field method by using an approximating distribution that factorises into cluster potentials. This includes undirected graphs, directed acyclic graphs and junction trees. We derive generaliz…

We develop methods to approximate derivatives for causal inference problems using data.

Modal regression is aimed at estimating the global mode (i.e., global maximum) of the conditional density function of the output variable given input variables, and has led to regression methods robust against heavy-tailed or skewed noises. The conditional mode is often estimated through maximization of the modal regre…

The Black Box Variational Inference (Ranganath et al. (2014)) algorithm provides a universal method for Variational Inference, but taking advantage of special properties of the approximation family or of the target can improve the convergence speed significantly. For example, if the approximation family is a transforma…

JacNet learns Jacobians to enforce structure on derivatives for invertibility and Lipschitz functions.

The paper analyzes risk estimation methods and derives bounds for OCE risk.

Paper studies Gaussian approximation in linear regression with rates derived.

We derive and approximate the conjugate prior of Dirichlet and beta distributions.

Paper introduces efficient methods for estimating cross-partial derivatives and sensitivity indices.

Smoothing splines provide a powerful and flexible means for nonparametric estimation and inference. With a cubic time complexity, fitting smoothing spline models to large data is computationally prohibitive. In this paper, we use the theoretical optimal eigenspace to derive a low rank approximation of the smoothing spl…

Under a Bayesian framework, we formulate the fully sequential sampling and selection decision in statistical ranking and selection as a stochastic control problem, and derive the associated Bellman equation. Using value function approximation, we derive an approximately optimal allocation policy. We show that this poli…

The Laplace approximation calls for the computation of second derivatives at the likelihood maximum. When the maximum is found by the EM-algorithm, there is a convenient way to compute these derivatives. The likelihood gradient can be obtained from the EM-auxiliary, while the Hessian can be obtained from this gradient …

Uniform TD(0) bound derived for function approximation with Markov noise.

Improved matrix approximation using randomized algorithms.

We develop an efficient method to calibrate CDS spreads using asymptotic approximations.

Kristensen and Mele (2011) developed a new approach to obtain closed-form approximations to continuous-time derivatives pricing models. The approach uses a power series expansion of the pricing bias between an intractable model and some known auxiliary model. Since the resulting approximation formula has closed-form it…

We develop a new method to solve complex physics equations more accurately and efficiently.

Method solves complex optimization problems with high probability bounds.

Efficiently approximates higher-order derivatives for generative models.

There has been a growing interest in expressivity of deep neural networks. However, most of the existing work about this topic focuses only on the specific activation function such as ReLU or sigmoid. In this paper, we investigate the approximation ability of deep neural networks with a broad class of activation functi…

New samplers reduce NFEs for diffusion models.

Gaussian and bootstrap methods improve ATE estimator accuracy.

Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite likelihood approach using a general belief updating framework, which leads to a recu…

Study on friction forces for nonholonomic systems using affine connections.

The paper studies the consistency of mean curvature flow via volumetric varifolds.

Study on RNNs' ability to approximate past-dependent Hölder functions and their application to regression.

We propose a modular extension of backpropagation for the computation of block-diagonal approximations to various curvature matrices of the training objective (in particular, the Hessian, generalized Gauss-Newton, and positive-curvature Hessian). The approach reduces the otherwise tedious manual derivation of these mat…