Estimates domain truncation error for option pricing PDEs.
problem Estimating error in option pricing models with domain truncation.
method Derives an estimate of domain truncation error for a multidimensional PDE system.
result Proposes a sharper error estimate for option pricing models.
New high-order scheme reduces BSDE truncation errors.
problem Numerical solution of backward stochastic differential equations (BSDEs).
method Proposes a new θ θ θ -scheme with careful θ θ θ selection for every subinterval. result Error estimates and verification of scheme order.
Study identifies and analyzes three types of errors in learning Fourier operators.
problem Statistical, discretization, and truncation errors in learning Fourier operators.
method Analysis of a Discrete Fourier Transform (DFT) based least squares estimator.
result Established upper and lower bounds on statistical, discretization, and truncation errors.
Truncated CauchyNMF robustly learns subspaces from noisy data.
problem Outliers in non-negative matrix factorization (NMF) cause failure.
method Proposes Truncated CauchyNMF loss to handle outliers.
result Theoretical analysis and experimental validation show Truncated CauchyNMF's robustness.
We accelerate CNF by reducing ODE truncation errors with polynomial regularization.
problem High computation cost of CNF due to large truncation errors in solving ODEs.
method Add polynomial regularization to approximate ODE trajectories with polynomial functions.
result 42.3% to 71.3% reduction of NFE on density estimation, 19.3% to 32.1% on variational auto-encoder.
A new method for multi-objective Bayesian optimization using entropy search and variational lower bound maximization.
problem Efficiently optimizing multiple objectives in continuous domains.
method Approximates the Pareto-frontier using a mixture distribution and optimizes the balance through variational lower bound maximization.
result Demonstrated effectiveness especially with many objective functions.
Score matching method improves density estimation for truncated data on manifolds.
problem Density estimation for truncated data on manifolds with intractable normalising constant.
method Truncated score matching extended to Riemannian manifolds with boundary.
result Score matching estimator approximates true parameter values with low error.
Optimal algorithm learns Gaussian under halfspace truncation with minimal samples.
problem Learning a Gaussian distribution truncated to an unknown halfspace.
method Efficient algorithm using n = i l d e O ( d 2 / ε 2 ) n = ilde{O}(d^2/\varepsilon^2) n = i l d e O ( d 2 / ε 2 ) samples and runtime dominated by empirical covariance matrix computation. result Optimal sample and time complexity bounds for learning a Gaussian under halfspace truncation.
New COS method formula improves option pricing accuracy.
problem Determining the optimal truncation range for COS method.
method Derive new formula using Markov's inequality to ensure convergence.
result New formula leads to more accurate option pricing.
Paper proposes a method to estimate truncated density models using Score Matching.
problem Estimating parameters of truncated probability densities.
method Score Matching with a novel weight function derived from Stein discrepancy.
result The proposed method minimizes a weighted Fisher divergence and corrects outlier-trimming bias.
Paper studies non-convex truncated loss functions for robust learning.
problem Improving generalization with non-convex loss functions.
method Truncating traditional loss functions and using SGD.
result Excess risk bounds and stationary points found by SGD.
Combines ML and DA to infer unresolved scale parametrisation from noisy data.
problem Training ML-based parametrisations from realistic, noisy and sparse observations.
method Two-step process: DA for state estimation, ML for model error prediction.
result Hybrid model produces better forecasts and attractor representation.
Efficient algorithm reduces communication costs in distributed sparse learning.
problem High-dimensional distributed sparse learning with reduced communication costs.
method Two-way Truncation procedure to reduce communication cost, solving l 1 l_1 l 1 regularized minimization problem. result The estimation error decreases exponentially and matches centralized method under mild assumptions.
The paper efficiently estimates parameters from truncated Gaussian and linear models.
problem Estimating parameters from truncated Gaussian and linear models.
method Minimizes finite population negative log-likelihood function with an l1-regularization term.
result Efficient estimation of parameters from truncated samples.
The study compares Fourier-based pricing methods, identifying the most efficient and accurate.
problem Comparing CPU effort and pricing biases of Fourier-based implementations.
method Numerical analysis of seven Fourier-based implementations, focusing on truncation and discretization errors.
result The multi-strike version of the COS method is notably faster, and the strike-optimized Carr Madan's formula is both faster and more accurate.
SeqRF straightens generative model flows to speed up sampling.
problem High global truncation error in ODE-based solvers for generative models.
method SeqRF, a learning technique that straightens the probability flow.
result Significantly improved sampling speed and synthesis quality.
COS method convergence conditions expanded for heavy-tailed distributions.
problem Ensuring convergence of the COS method for various densities.
method Analyzing truncation error and providing conditions for convergence.
result Conditions for COS method convergence extended to include heavy-tailed distributions.
Integration of the form ∫ a ∞ f ( x ) w ( x ) d x \int_a^\infty {f(x)w(x)dx} ∫ a ∞ f ( x ) w ( x ) d x , where w ( x ) w(x) w ( x ) is either sin ( ω x ) \sin (ω{\kern 1pt} x) sin ( ω x ) or cos ( ω x ) \cos (ω{\kern 1pt} x) cos ( ω 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.
problem Handling sparse multiway count data corrupted by false zeros.
method Zero-truncated Poisson regression with tensor completion.
result Accurate estimation of multiway count data from approximately I R 2 log 2 2 ( I ) IR^2\log_2^2(I) I R 2 log 2 2 ( I ) non-zero counts. As in standard linear regression, in truncated linear regression, we are given access to observations ( A i , y i ) i (A_i, y_i)_i ( A i , y i ) i whose dependent variable equals y i = A i T ⋅ x ∗ + η i y_i= A_i^{\rm T} \cdot x^* + η_i y i = A i T ⋅ x ∗ + η i , where x ∗ x^* x ∗ is some fixed unknown vector of interest and η i η_i η i is independent noise; except we are only given an observation if its dep…
New algorithm improves regression error bounds and accelerates performance for low noise.
problem Nonparametric least square regression in RKHS with optimal error bounds.
method Kernel Truncated Randomized Ridge Regression (KTRRR) with optimal generalization error bounds.
result Faster finite-time and asymptotic rates on low noise problems.
New methods stabilize Q-learning with linear approximations.
problem Stabilizing Q Q Q -learning with linear function approximation. method Target network and truncation.
result Provably stable Q Q Q -learning with linear function approximation. 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…
Investigates how reduced precision affects deep neural networks.
problem Predicting sensitivity of DNNs to reduced numerical precision.
method Emulates arbitrary bit-width using truncation method after each batch.
result Shows impact of model parameters on training accuracy.
Paper develops fast low-rank approximation for smoothing splines.
problem Computational infeasibility of fitting cubic smoothing splines to large datasets.
method Low-rank approximation using eigensystem truncation.
result The method provides accurate, fast estimates with error bounds.
PMT uses public data moments to make DP feasible for unbounded data.
problem Applying differential privacy to unbounded data distributions.
method Public-moment-guided Truncation (PMT) using second-moments from public data.
result PMT improves the accuracy and stability of DP models.
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…
Improved semi-supervised learning for large networks using TV-EM and Neural Simpletrons.
problem Challenges in inference and learning for large-scale generative networks.
method Combining Neural Simpletrons with TV-EM for efficient, scalable learning.
result Significant improvements in learning efficiency and performance on semi-supervised tasks.
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…
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.
problem Estimating parameters of Boolean product distributions from truncated samples.
method Introducing fatness of truncation set, using membership queries, and adapting Stochastic Gradient Descent.
result Efficiently learn Boolean product distributions from truncated samples with small sample complexity.
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 + μ t , t ≥ 0 , W_t = B_t + μt, t\geq 0, W t = B t + μ t , t ≥ 0 , where ( B t ) (B_t) ( B t ) is a standard Brownian motion. Truncated variation differs from regular variation by neglect…
A new FFT method for Heston model option pricing with explicit error bounds.
problem Efficiently pricing European options in the Heston model with high accuracy.
method Convolution-FFT method leveraging a continuously differentiable joint characteristic function.
result Explicit error bounds for FFT-based convolution method in Heston model.
New method for constructing truncated vine copulas.
problem High-dimensional parameter space in vine copulas.
method Propose a new score and algorithm for constructing truncated vines.
result New algorithms exploit conditional independences.
Kernel quadrature uses DPPs for sampling with tight error bounds.
problem Efficiently sampling nodes for quadrature rules in RKHS.
method Nodes sampled from a truncated and saturated DPP kernel.
result Tighter quadrature error bounds using DPPs.
Efficiently estimates covariance for sub-Weibull vectors with sub-Gaussian rate.
problem Outliers in high-dimensional covariance estimation.
method Cross-Fitted Norm-Truncated Estimator for Sub-Weibull distributions.
result Achieves optimal sub-Gaussian rate with O ( N d 2 ) O(Nd^2) O ( N d 2 ) operations. The paper estimates common mean of entangled Gaussians with bounded variances.
problem Estimating common mean of entangled Gaussians with bounded variances.
method Iteratively averaging truncated samples.
result Achieves error $O \left(\frac{\sqrt{n\ln n}}{m}
ight)$ with high probability when m = Ω ( n ln n ) m=Ω(\sqrt{n\ln n}) m = Ω ( n ln n ) . Truncated SVD provides a simple yet effective method for approximating high-rank matrices.
problem Estimating high-rank positive semi-definite matrices from partial observations or noisy data.
method Truncated SVD applied to an estimate of the matrix.
result Truncated SVD produces a multiplicative approximation of the original matrix in Frobenius norm.
Paper proposes approximate Stein classes for efficient truncated density estimation.
problem Difficulties in estimating truncated density models due to intractable normalising constants and boundary conditions.
method Adapts score matching to solve the problem, introduces approximate Stein classes and a novel discrepancy measure, TKSD.
result TKSD does not require a fixed weighting function and can be evaluated using only boundary samples, leading to improved accuracy.
Paper defines new risk measures for elliptical distributions.
problem Risk measurement for elliptical distributions.
method DTM, DTS, DTK definitions and formula derivation for specific distributions.
result Explicit formulas for DTE, DTV, DTS, and DTK for various distributions.
Paper proposes an online speech recognition model using Transformer.
problem Challenges in deploying Transformer-based E2E ASR for online speech recognition.
method Chunk self-attention encoder (chunk-SAE) and monotonic truncated attention (MTA) based self-attention decoder (SAD).
result Achieved 23.66% CER with 320 ms latency, significant improvement over offline models.
New algorithm approximates large psd matrices from sketches.
problem Large-scale positive-semidefinite matrices from streaming data.
method Combines Nystrom approximation with rank truncation.
result Achieves prescribed relative error in Schatten 1-norm.
New GaussianSketch approximates kernel distances with almost relative error and small additive term.
problem Approximating kernel distances between point sets efficiently.
method Truncating Gaussian kernel expansions and using RecursiveTensorSketch.
result Approximates kernel distance with almost ( 1 + ε ) (1+\varepsilon) ( 1 + ε ) -relative error and small additive α α α term. Ensemble of GANs improves performance on disconnected data.
problem Disconnected datasets in computer vision cannot be represented by continuous GANs.
method Construct an optimization problem to relate single GAN, ensemble of GANs, conditional GANs, and Gaussian Mixture GANs.
result Ensemble of GANs outperforms single GANs with fewer parameters.
Paper develops approximation and statistical theory for signature-based path regression.
problem Understanding how fast signatures approximate continuous path functionals.
method Develops \(L^2\) approximation rate for smooth functionals of Itô diffusions and establishes consistency of statistical learning procedures.
result Signature-based methods improve prediction over handcrafted features in various real-data applications.
Estimates manifold distances using graph Laplacian, proving consistency.
problem Estimating distances in compact Riemannian manifolds.
method Graph Laplacian estimates of the Laplace-Beltrami operator, bounding errors.
result Proof of consistency for manifold distances.