A new method for pricing options with stochastic volatility and jumps.
problem Pricing options under stochastic volatility and jumps.
method Fourth-order compact finite-difference scheme with implicit-explicit Crank-Nicolson framework.
result The method achieves near-fourth-order spatial accuracy and up to two orders of magnitude lower runtime than quadratic finite elements.
New learning-based methods improve spectral efficiency in mmWave full-duplex systems.
problem Residual self-interference and high pathloss in mmWave full-duplex systems.
method Proposed two learning schemes (ELM-HBF and CNN-HBF) using ADMM and MM algorithms for SI cancellation and joint HBF optimization.
result Learning-based schemes achieve at least 22.1% higher spectral efficiency and faster online prediction and training times.
Improved ridge regression with Frequent Directions for large-scale tasks.
problem Improving performance of ridge regression for large-scale data.
method Combines Frequent Directions with iterative optimization schemes.
result Achieves high accuracy in estimating bias and variance for sketched ridge regression.
In this paper, we study the benefits of using polyharmonic splines and node layouts with smoothly varying density for developing robust and efficient radial basis function generated finite difference (RBF-FD) methods for pricing of financial derivatives. We present a significantly improved RBF-FD scheme and successfull…
Diagonal Frog: High-order positivity-preserving FD schemes for anisotropic Fokker-Planck equations
problem Positivity-preserving discretizations for anisotropic Fokker-Planck equations
method Diagonal Frog discretization
result Second-order accuracy and mass conservation
We show some fundamental results concerning 3-dimensional foliated dynamical systems (FDS3 for short) introduced by Deninger. Firstly, we give a decomposition theorem for an FDS3, which yields a classification of FDS3's. Secondly, for each type of the classification, we construct concrete examples of FDS3…
Debiased learners estimate heterogeneous treatment effects in observational studies.
problem Estimating heterogeneous treatment effects in observational studies with unmeasured confounders.
method Debiased Front-Door (FD) learners, FD-DR-Learner and FD-R-Learner, under specific assumptions.
result Debiased learners satisfy error bounds and stage-error decompositions, delivering reliable HTE estimates.
On-device machine learning (ML) enables the training process to exploit a massive amount of user-generated private data samples. To enjoy this benefit, inter-device communication overhead should be minimized. With this end, we propose federated distillation (FD), a distributed model training algorithm whose communicati…
Linear classification has been widely used in many high-dimensional applications like text classification. To perform linear classification for large-scale tasks, we often need to design distributed learning methods on a cluster of multiple machines. In this paper, we propose a new distributed learning method, called f…
Compressed Federated Distillation reduces communication in federated learning.
problem Communication constraints in Federated Learning.
method Compressed Federated Distillation (CFD) leverages soft labels and quantization techniques.
result Reduces communication by more than 4 orders of magnitude compared to Federated Averaging.
Groups of importance in group theory have flexible stability properties.
problem Stability and flexibility of groups in geometric and combinatorial group theory.
method Establishing Kirchberg's Local Lifting Property and Lubotzky--Shalom's Property FD for specific groups.
result Groups like 3-manifold groups, limit groups, and certain one-relator groups are very flexibly stable. Enhanced DFO using adaptive batch-based FD estimates.
problem Derivative-free optimization with imprecise gradient estimates.
method Adaptive batch-based finite difference estimation and dynamic sampling strategy.
result Algorithm achieves convergence rate similar to KW and SPSA methods.
The article derives some novel independence measures and contrast functions for Blind Source Separation (BSS) application. For the kth order differentiable multivariate functions with equal hyper-volumes (region bounded by hyper-surfaces) and with a constraint of bounded support for k>1, it proves that equality …
FDS tackles long horizon hyperparameter optimization issues.
problem Memory scaling and gradient degradation in long horizon tasks.
method Forward-mode differentiation with sharing (FDS).
result Significantly outperforms greedy gradient-based alternatives.
This paper proposes a numerical method for pricing foreign exchange (FX) options in a model which deals with stochastic interest rates and stochastic volatility of the FX rate. The model considers four stochastic drivers, each represented by an Itô's diffusion with time--dependent drift, and with a full matrix of corre…
Since the debut of Evolution Strategies (ES) as a tool for Reinforcement Learning by Salimans et al. 2017, there has been interest in determining the exact relationship between the Evolution Strategies gradient and the gradient of a similar class of algorithms, Finite Differences (FD).(Zhang et al. 2017, Lehman et al. …
FedAUX improves Federated Learning by better using unlabeled data.
problem Improving Federated Learning performance with unlabeled data.
method FedAUX modifies FD training by unsupervised pre-training and private certainty scoring.
result FedAUX outperforms state-of-the-art Federated Learning methods.
Paper applies subdiffusive dynamics to American and barrier options pricing.
problem Valuation of American and barrier options in subdiffusive financial models.
method Proposes weighted finite difference and Longstaff-Schwartz methods for valuation.
result Numerical valuation of American and barrier options demonstrated.
New method extrapolates spectral densities from smaller models to larger ones.
problem Limited practical computations for large machine learning models.
method Algebraic spectral curve theory for free decompression.
result Framework enables extrapolation of spectral densities with multiple or multi-modal bulks.
Mix2FLD improves FL accuracy with FD, reducing convergence time.
problem Uplink-downlink capacity asymmetry in federated learning.
method Two-way mixup of local samples and model parameters, preserving privacy.
result Achieves up to 16.7% higher test accuracy with reduced convergence time.
The purpose of this note is to attract attention to the following conjecture (metastable r-fold Whitney trick) by clarifying its status as not having a complete proof, in the sense described in the paper. Assume that D=D1⊔…⊔Dr is disjoint union of r disks of dimension s, f:D→Bd a proper …
Efficiently approximates higher-order derivatives for generative models.
problem Expensive computation of higher-order derivatives in generative models.
method Rewrite SM objective in terms of directional derivatives and use finite difference for efficient approximation.
result Comparable results to gradient-based methods but significantly more computationally efficient.
We propose two localized Radial Basis Function (RBF) methods, the Radial Basis Function Partition of Unity method (RBF-PUM) and the Radial Basis Function generated Finite Differences method (RBF-FD), for solving financial derivative pricing problems arising from market models with multiple stochastic factors. We demons…
Study on earthquake metric on Teichmüller space, proving properties and new completions.
problem Understanding the earthquake metric on Teichmüller space.
method Proofs of properties, new completions, and interpretation of the metric.
result Coincidence of various completions for the earthquake metric.
The study of dexterous manipulation has provided important insights in humans sensorimotor control as well as inspiration for manipulation strategies in robotic hands. Previous work focused on experimental environment with restrictions. Here we describe a method using the deformation and color distribution of the finge…
Sketchy reduces memory and compute requirements for adaptive regularization in deep learning.
problem Prohibitive memory and running time for adaptive regularization methods in deep learning.
method Low-rank sketching approach using Frequent Directions (FD) to reduce memory and compute requirements.
result Efficient interpolation between resource requirements and degradation in regret guarantees with rank k. The procedure to remove double intersections called the Whitney trick is one of the main tools in the topology of manifolds. The analogues of Whitney trick for r-tuple intersections were `in the air' since 1960s. However, only recently they were stated, proved and applied to obtain interesting results. Here we prove …
Paper presents a fast and adaptive filter for SI suppression in full-duplex transceivers.
problem Self-interference suppression in full-duplex transceivers with nonlinearity.
method Adaptive projected subgradient method (APSM) in a reproducing kernel Hilbert space (RKHS).
result The proposed method achieves favorable digital SIC performance compared to benchmarks.
QMC and GSA improve option pricing and risk measures efficiency.
problem Efficiently pricing and hedging complex financial instruments.
method Application of QMC and GSA techniques for financial instrument pricing and hedging, comparing MC vs QMC and analyzing greeks computation.
result QMC outperforms MC in most cases, especially in high-dimensional simulations, leading to faster and more stable convergence.
Efficient surrogate modeling for complex PDEs with physical laws.
problem High computational cost of repeated PDE simulations.
method LC-prior Gaussian process with POD and RBF-FD.
result Significantly reduced computational cost and improved accuracy.
VFDS selects dynamic features for efficient HAR tasks, optimizing performance-cost trade-offs.
problem Optimizing feature selection for varying costs and dynamic contexts in machine learning tasks.
method Bayesian learning framework with variational dynamic selection policy.
result VFDS selects different features under changing contexts, saving sensory costs while maintaining HAR accuracy.
In many applications we seek to maximize an expectation with respect to a distribution over discrete variables. Estimating gradients of such objectives with respect to the distribution parameters is a challenging problem. We analyze existing solutions including finite-difference (FD) estimators and continuous relaxatio…
SFG improves on-manifold sampling without labels or additional training.
problem Guiding score-based models on manifolds without labeled data or extra training.
method Developed saddle-free guidance (SFG) that uses curvature of log density estimates.
result SFG achieves state-of-the-art metrics in image generation without labeled data or additional training.
Discovering the underlying physical behavior of complex systems is a crucial, but less well-understood topic in many engineering disciplines. This study proposes a finite-difference inspired convolutional neural network framework to learn hidden partial differential equations from given data and iteratively estimate fu…
A new FFT-based method simplifies causal structure recovery for linear dynamical systems.
problem Efficiently identifying dynamic causal effects from time-series data.
method FFT-based approach to reduce computational complexity to O(Tn3logN). result Significant computational advantage for graph reconstruction.
Asynchronous event sequences are the basis of many applications throughout different industries. In this work, we tackle the task of predicting the next event (given a history), and how this prediction changes with the passage of time. Since at some time points (e.g. predictions far into the future) we might not be abl…
New method learns fair representations by separating out protected attributes.
problem Learning fair representations invariant to protected attributes.
method FD-VAE: disentangles latent space into target, protected, and mutual attributes.
result FD-VAE outperforms previous methods in fairness metrics.
Continuous semi-implicit models enable faster training and better performance in generative modeling.
problem Slow convergence in hierarchical semi-implicit models during training.
method CoSIM, a continuous semi-implicit model that incorporates a continuous transition kernel for efficient training.
result CoSIM achieves superior performance on image generation tasks compared to existing methods.
Finite rank median spaces are a simultaneous generalisation of finite dimensional CAT(0) cube complexes and real trees. If Γ is an irreducible lattice in a product of rank one simple Lie groups, we show that every action of Γ on a complete, finite rank median space has a global fixed point. This is in sharp…
In this paper we modify the model of Itkin, Shcherbakov and Veygman, (2019) (ISV2019), proposed for pricing Quanto Credit Default Swaps (CDS) and risky bonds, in several ways. First, it is known since the Lehman Brothers bankruptcy that the recovery rate could significantly vary right before or at default, therefore, i…
New methods solve complex optimization problems in machine learning.
problem Challenges in stochastic bilevel optimization with constraints and high variables.
method Inexact bilevel stochastic gradient methods for constrained and unconstrained lower-level problems.
result Comprehensive convergence theory for both unconstrained and constrained cases.
Score matching fails to train VAEs robustly, revealing autoencoding loss insights.
problem Catastrophic failure of variational score matching on VAE models.
method Analysis of existing variational score matching objectives and their equivalence to autoencoding losses.
result Score matching methods fail to produce robust VAE models, predicting poor performance.
New probabilistic scheme combines deep learning with Runge-Kutta methods for solving PDEs.
problem Solving high-dimensional semi-linear parabolic PDEs efficiently.
method Probabilistic scheme using deep learning and Runge-Kutta methods.
result Crank-Nicolson schemes are efficient in terms of precision, computational cost, and numerical implementation.
A hybrid ML method improves ship response predictions across different sea conditions.
problem Improving accuracy and generalizability of ML methods for ship response predictions.
method A hybrid machine learning method that corrects forces in a low-fidelity equation of motion.
result The hybrid method offers improved prediction accuracy and generalizability compared to benchmarks.
It was proved in 1998 by Ben-David and Litman that a concept space has a sample compression scheme of size d if and only if every finite subspace has a sample compression scheme of size d. In the compactness theorem, measurability of the hypotheses of the created sample compression scheme is not guaranteed; at the same…
Study SL(2,C) character schemes for finitely generated groups.
problem Characterize SL(2,C) representations of finitely generated groups.
method Define coordinate rings and equations for SL(2,C) character schemes.
result Explicit equations for character schemes of finitely presented groups.
A new method for computing image curvature efficiently and accurately.
problem Low performance, low accuracy, and requirement of second order differentiability in conventional computation schemes.
method Proposes a novel discrete computation scheme for weighted Gaussian curvature.
result More accurate, computationally more efficient, and does not require second order differentiability.
Reduces multiclass and regression compression schemes to binary ones.
problem Developing efficient learning algorithms for multiclass and regression problems.
method Reduces sample compression schemes for binary classes to multiclass and regression settings.
result Establishes new compression schemes for multiclass and regression problems.