arXiv research

Estimates domain truncation error for option pricing PDEs.

Truncated densities are probability density functions defined on truncated domains. They share the same parametric form with their non-truncated counterparts up to a normalizing constant. Since the computation of their normalizing constants is usually infeasible, Maximum Likelihood Estimation cannot be easily applied t…

Generalized score matching for densities on general domains.

New kernels capture both local and non-local interactions efficiently.

Study identifies and analyzes three types of errors in learning Fourier operators.

Eigenvalues of manifolds with cylindrical boundaries approximated by graph Laplacians.

A new method for multi-objective Bayesian optimization using entropy search and variational lower bound maximization.

We study inference and learning based on a sparse coding model with `spike-and-slab' prior. As in standard sparse coding, the model used assumes independent latent sources that linearly combine to generate data points. However, instead of using a standard sparse prior such as a Laplace distribution, we study the applic…

In this paper, we study a flag complex which is naturally associated to the Thurston theory of surface diffeomorphisms for compact connected orientable surfaces with boundary. The various pieces of the Thurston decomposition of a surface diffeomorphism, thick domains and annular or thin domains, fit into this flag comp…

Boundary effects inflate variance in Gaussian processes, leading to acquisition bias.

Paper proves isoperimetric inequality for Minkowski spacetime.

Graph-structured data arise ubiquitously in many application domains. A fundamental problem is to quantify their similarities. Graph kernels are often used for this purpose, which decompose graphs into substructures and compare these substructures. However, most of the existing graph kernels do not have the property of…

PMT uses public data moments to make DP feasible for unbounded data.

The problem of an arbitrary truncated Levy flight description using the method of cumulant approach has been solved. The set of cumulants of the truncated Levy distribution given the assumption of arbitrary truncation has been found. The influence of truncation shape on the truncated Levy flight properties in the Gauss…

Efficiently estimate Boolean product distribution parameters from truncated samples.

In the paper "On Truncated Variation of Brownian Motion with Drift" (Bull. Pol. Acad. Sci. Math. 56 (2008), no.4, 267 - 281) we defined truncated variation of Brownian motion with drift, $W_t = B_t + μt, t\geq 0,$ where $(B_t)$ is a standard Brownian motion. Truncated variation differs from regular variation by neglect…

Optimal algorithm learns Gaussian under halfspace truncation with minimal samples.

New method for constructing truncated vine copulas.

Non-negative matrix factorization (NMF) minimizes the Euclidean distance between the data matrix and its low rank approximation, and it fails when applied to corrupted data because the loss function is sensitive to outliers. In this paper, we propose a Truncated CauchyNMF loss that handle outliers by truncating large e…

Paper proposes approximate Stein classes for efficient truncated density estimation.

Paper defines new risk measures for elliptical distributions.

Integration of the form $\int_a^\infty {f(x)w(x)dx}$, where $w(x)$ is either $\sin (ω{\kern 1pt} x)$ or $\cos (ω{\kern 1pt} x)$, is widely encountered in many engineering and scientific applications, such as those involving Fourier or Laplace transforms. Often such integrals are approximated by a numerical integration…

New DP framework using data truncation for efficient estimation.

Unified framework for mean testing under truncation bias.

Score matching method improves density estimation for truncated data on manifolds.

In this paper, we revisit the recurrent back-propagation (RBP) algorithm, discuss the conditions under which it applies as well as how to satisfy them in deep neural networks. We show that RBP can be unstable and propose two variants based on conjugate gradient on the normal equations (CG-RBP) and Neumann series (Neuma…

State construction is important for learning in partially observable environments. A general purpose strategy for state construction is to learn the state update using a Recurrent Neural Network (RNN), which updates the internal state using the current internal state and the most recent observation. This internal state…

Truncated backpropagation through time (TBPTT) is a popular method for learning in recurrent neural networks (RNNs) that saves computation and memory at the cost of bias by truncating backpropagation after a fixed number of lags. In practice, choosing the optimal truncation length is difficult: TBPTT will not converge …

The method approximates stationary distributions of Markov models by truncating irrelevant states.

This paper considers the valuation of a European call option under the Heston stochastic volatility model. We present the asymptotic solution to the option pricing problem in powers of the volatility of variance. Then we introduce the artificial boundary method for solving the problem on a truncated domain, and derive …

Paper tackles overestimation bias in continuous control, improving performance by 25%.

We consider an appoximation of a catenoid constructed from "odd" truncated cones that maintains minimality in a certain sense. Thorough this procedure, we obtain a discrete curve approximating a catenary by exploiting the fact that it is the function that generates a catenoid. In this investigation, the theory of the G…

Choppy optimizes ranked list truncation using Transformer architecture.

This paper addresses challenges in flexibly modeling multimodal data that lie on constrained spaces. Such data are commonly found in spatial applications, such as climatology and criminology, where measurements are restricted to a geographical area. Other settings include domains where unsuitable recordings are discard…

New COS method formula improves option pricing accuracy.

The generalized correlation approach, which has been successfully used in statistical radio physics to describe non-Gaussian random processes, is proposed to describe stochastic financial processes. The generalized correlation approach has been used to describe a non-Gaussian random walk with independent, identically d…

Lower bound shows super-polynomial gap for estimating truncated Gaussian means.

As in standard linear regression, in truncated linear regression, we are given access to observations $(A_i, y_i)_i$ whose dependent variable equals $y_i= A_i^{\rm T} \cdot x^* + η_i$, where $x^*$ is some fixed unknown vector of interest and $η_i$ is independent noise; except we are only given an observation if its dep…

The paper analyzes and mitigates biases in scalable Gaussian Process methods.

We show that generalised geometry gives a unified description of maximally supersymmetric consistent truncations of ten- and eleven-dimensional supergravity. In all cases the reduction manifold admits a "generalised parallelisation" with a frame algebra with constant coefficients. The consistent truncation then arises …

Proposes a method to handle sparse multiway count data with false zeros using zero-truncated Poisson regression.

Adaptive Nucleus Truncation Improves Long-Form Reasoning

The paper studies deformation spaces of Coxeter truncation polytopes.

Estimates inverse temperature of Ising models with a single sample.

The paper connects quantum $6j$-symbols to tetrahedra volumes via discrete Fourier transforms.

Typically, operational risk losses are reported above some threshold. This paper studies the impact of ignoring data truncation on the 0.999 quantile of the annual loss distribution for operational risk for a broad range of distribution parameters and truncation levels. Loss frequency and severity are modelled by the P…

Bayesian method estimates LTLL distribution parameters for time-to-event data.

Learning with a {\it convex loss} function has been a dominating paradigm for many years. It remains an interesting question how non-convex loss functions help improve the generalization of learning with broad applicability. In this paper, we study a family of objective functions formed by truncating traditional loss f…