arXiv research

Estimates domain truncation error for option pricing PDEs.

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

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…

We accelerate CNF by reducing ODE truncation errors with polynomial regularization.

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

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

Optimal algorithm learns Gaussian under halfspace truncation with minimal samples.

New COS method formula improves option pricing accuracy.

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…

Combines ML and DA to infer unresolved scale parametrisation from noisy 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…

The paper efficiently estimates parameters from truncated Gaussian and linear models.

COS method convergence conditions expanded for heavy-tailed distributions.

SeqRF straightens generative model flows to speed up sampling.

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…

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

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…

In this paper we propose a new kind of high order numerical scheme for backward stochastic differential equations(BSDEs). Unlike the traditional $θ$-scheme, we reduce truncation errors by taking $θ$ carefully for every subinterval according to the characteristics of integrands. We give error estimates of this nonlinear…

New methods stabilize Q-learning with linear approximations.

We show how to compute lower bounds for the supremum Bayes error if the class-conditional distributions must satisfy moment constraints, where the supremum is with respect to the unknown class-conditional distributions. Our approach makes use of Curto and Fialkow's solutions for the truncated moment problem. The lower …

The pricing of options in exponential Levy models amounts to the computation of expectations of functionals of Levy processes. In many situations, Monte-Carlo methods are used. However, the simulation of a Levy process with infinite Levy measure generally requires either to truncate small jumps or to replace them by a …

Completely random measures (CRM) represent the key building block of a wide variety of popular stochastic models and play a pivotal role in modern Bayesian Nonparametrics. A popular representation of CRMs as a random series with decreasing jumps is due to Ferguson and Klass (1972). This can immediately be turned into a…

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

Reference metrics are used to define the differential structure on multicube representations of manifolds, i.e., they provide a simple and practical way to define what it means globally for tensor fields and their derivatives to be continuous. This paper introduces a general procedure for constructing reference metrics…

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…

We consider the problem of numerical approximation for forward-backward stochastic differential equations with drivers of quadratic growth (qgFBSDE). To illustrate the significance of qgFBSDE, we discuss a problem of cross hedging of an insurance related financial derivative using correlated assets. For the convergence…

We propose a communicationally and computationally efficient algorithm for high-dimensional distributed sparse learning. At each iteration, local machines compute the gradient on local data and the master machine solves one shifted $l_1$ regularized minimization problem. The communication cost is reduced from constant …

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…

Recently, Transformer has gained success in automatic speech recognition (ASR) field. However, it is challenging to deploy a Transformer-based end-to-end (E2E) model for online speech recognition. In this paper, we propose the Transformer-based online CTC/attention E2E ASR architecture, which contains the chunk self-at…

New method for constructing truncated vine copulas.

A new FFT method for Heston model option pricing with explicit error bounds.

Inference and learning for probabilistic generative networks is often very challenging and typically prevents scalability to as large networks as used for deep discriminative approaches. To obtain efficiently trainable, large-scale and well performing generative networks for semi-supervised learning, we here combine tw…

Efficiently estimates covariance for sub-Weibull vectors with sub-Gaussian rate.

Paper proposes approximate Stein classes for efficient truncated density estimation.

Paper defines new risk measures for elliptical distributions.

The paper estimates common mean of entangled Gaussians with bounded variances.

New DP framework using data truncation for efficient estimation.

Ensemble of GANs improves performance on disconnected data.

Estimates manifold distances using graph Laplacian, proving consistency.

Unified framework for mean testing under truncation bias.

Paper develops approximation and statistical theory for signature-based path regression.

We develop a unified approach for classification and regression support vector machines for data subject to right censoring. We provide finite sample bounds on the generalization error of the algorithm, prove risk consistency for a wide class of probability measures, and study the associated learning rates. We apply th…

Maximal concentration bounds for stochastic approximation with heavy-tailed noise.

Improves FI-PINNs by combining re-sampling and subset simulation for better failure probability estimation.

An important problem in fiber-optic communications is to invert the nonlinear Schrödinger equation in real time to reverse the deterministic effects of the channel. Interestingly, the popular split-step Fourier method (SSFM) leads to a computation graph that is reminiscent of a deep neural network. This observation all…

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.