A new retraction on Stiefel manifold with a closed-form inverse.
problem Efficiency in Riemannian computing applications.
method Introduces a new retraction on the compact Stiefel manifold with a closed-form inverse.
result The retraction is second-order accurate and features a closed-form inverse.
New retraction on symplectic Stiefel manifold with closed-form inverse.
problem Efficient mapping of manifold data to Euclidean domain.
method Introduces a new retraction map with a closed-form inverse.
result The new retraction has a closed-form inverse, unlike previous methods.
This paper proposes a method to approximate non-Gaussian likelihoods in Gaussian Processes.
problem Approximating non-Gaussian likelihoods in Gaussian Processes.
method Proposes a piece-wise constant approximation for the inverse-link function.
result Yields a closed form solution for the SVGP lower bound.
This paper introduces the Inverse Gamma (IGa) stochastic volatility model with time-dependent parameters, defined by the volatility dynamics dVt=κt(θt−Vt)dt+λtVtdBt. This non-affine model is much more realistic than classical affine models like the Heston stochastic volatility model, e…
The paper uses moment matching method for pricing spread options under Lévy models.
problem Pricing spread options under Lévy models with mean-variance mixture.
method Moment matching method applied to Lévy models with mean-variance mixture.
result Obtains semi-closed form formulas for spread option prices.
Paper finds maximum curvature of Bézier-spline curves.
problem Finding maximum curvature of Bézier-spline curves.
method Modified B-spline solutions for inverse interpolation problem.
result Determined maximum curvature of Bézier-spline curves.
Deep models memorize training data in geophysical inversion, leading to biased posterior distributions.
problem Memorization of training data biases learned priors in geophysical inverse problems.
method Casting generative models' training as maximum likelihood, we show memorization results in a reweighted empirical distribution for diffusion models, leading to Gaussian mixture priors and posteriors.
result Memorization leads to posterior distributions that are likelihood-weighted lookup among stored training examples, affecting full waveform inversion outcomes.
Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn the structure of the graph by estimating a sparse inverse covariance matrix from…
A fast method approximates likelihood scores for noisy linear inverse problems.
problem Solving noisy linear inverse problems efficiently.
method Proposes a simple closed-form approximation to the likelihood score for diffusion and flow-based models.
result Significantly faster than baseline methods while maintaining competitive or better reconstruction performances.
This paper presents a methodology for selecting the mini-batch size that minimizes Stochastic Gradient Descent (SGD) learning time for single and multiple learner problems. By decoupling algorithmic analysis issues from hardware and software implementation details, we reveal a robust empirical inverse law between mini-…
We construct radial fundamental solutions for the differential form Laplacian on negatively curved symmetric spaces. At least one of these Green's functions also yields a Biot-Savart Opearator, i.e. a right inverse of the exterior differential on closed forms with image in the kernel of the codifferential. Any Biot-Sav…
NF-ULA combines Langevin Monte Carlo with normalizing flows for imaging inverse problems.
problem Solving inverse problems in imaging with uncertainty quantification.
method Langevin Monte Carlo with normalizing flow prior.
result NF-ULA outperforms competing methods for severely ill-posed inverse problems.
Develops a new method to compute risk-sharing allocations using Laplace transforms.
problem Complex integrals in computing conditional mean risk-sharing allocations.
method Uses Laplace-Stieltjes transforms to compute risk-sharing allocations from joint transforms.
result Provides closed-form or semi-analytic solutions for a broad class of distributions.
Efficiently solves inverse classification problems for logistic and softmax models.
problem Finding instances that change classifier predictions.
method Closed-form solution for logistic regression, iterative optimization for softmax.
result Fast, exact solutions for high-dimensional instances and many classes.
Sparse transformer architecture improves accuracy and speed in generative modeling and inverse problems.
problem Improving accuracy and speed in generative modeling and inverse problems.
method Proposes a sparse transformer architecture using regularized Wasserstein proximal operator with L1 prior. result Sparse transformer achieves higher accuracy and faster convergence than classical methods.
Exact posterior score estimation for solving linear inverse problems
problem Solving linear inverse problems
method Derive the exact posterior score and use it as a denoising training objective
result EPS outperforms training-free and training-based baselines on various metrics
New algorithms speed up inverse reinforcement learning by solving MDPs once.
problem Slow convergence in Maximum Entropy Inverse Reinforcement Learning.
method Deep Inverse Q-learning with constraints exploiting Q-learning.
result Up to several orders of magnitude speedup compared to existing methods.
Modeling bone microarchitecture adaptation using geometric flows.
problem Bone microarchitecture adaptation modeling.
method Advection and mean curvature flow model with a sphere as a test case.
result Closed-form solution for sphere under advection and mean curvature flow.
Develops flexible non-parametric ACFs using B-spline kernels.
problem Flexible modelling of the autocovariance function (ACF) in time-series, spatial, and spatio-temporal analysis.
method Derives the inverse Fourier transform of B-spline spectral bases to create a general class of non-parametric ACFs.
result Provides a provably dense, flexible, and general class of non-parametric ACFs for various types of processes.
Efficiently optimizes hyperparameters for PDE and inverse problems using Gaussian processes.
problem Hyperparameter optimization for scientific computing and inference methods.
method Bilevel optimization with Gauss-Newton linearization for efficient hyperparameter updates.
result Significant improvements in accuracy and robustness compared to random initialization.
We stabilize the Kumaraswamy distribution for efficient sampling and differentiation.
problem Numerical instabilities in the Kumaraswamy distribution's inverse CDF and log-pdf.
method Identified and resolved numerical issues, introduced a stabilized KS distribution.
result Stabilized Kumaraswamy distribution supports efficient sampling and differentiation.
We focus on the maximum regularization parameter for anisotropic total-variation denoising. It corresponds to the minimum value of the regularization parameter above which the solution remains constant. While this value is well know for the Lasso, such a critical value has not been investigated in details for the total…
Closed-form formulas for path-independent options in a specific Lévy model.
problem Valuation of path-independent options in the exponential NIG model.
method Closed-form pricing formulas derived using a factorized representation in Mellin space and complex analysis.
result Valid closed-form formulas with quickly convergent series for various options.
We construct a data-driven statistical indicator for quantifying the tail risk perceived by the EURGBP option market surrounding Brexit-related events. We show that under lognormal SABR dynamics this tail risk is closely related to the so-called martingale defect and provide a closed-form expression for this defect whi…
In this paper we study a class of insurance products where the policy holder has the option to insure k of its annual Operational Risk losses in a horizon of T years. This involves a choice of k out of T years in which to apply the insurance policy coverage by making claims against losses in the given year. The…
GNet uses Gaussian processes for scalable, flexible neural networks.
problem Large-scale predictive modeling with high computational and storage costs.
method GNet employs Gaussian processes with nonparametric activation functions and a fast algorithm for training and predictions.
result GNet achieves competitive performance across various test problems, including nonlinear function prediction and real-world data regression.
GNet uses Gaussian processes for scalable, flexible neural networks.
problem Large-scale predictive modeling with high computational and storage costs.
method GNet employs Gaussian processes with nonparametric activation functions and a fast algorithm for efficient training and predictions.
result GNet achieves competitive performance across various test problems, including nonlinear function prediction and real-world data regression.
C-DPS improves diffusion posterior sampling for inverse problems without projection or likelihood approximation.
problem Inaccurate and unstable solutions in inverse problems due to complex or high-noise conditions.
method C-DPS introduces a forward stochastic process in measurement space evolving in parallel with data-space diffusion, leading to a closed-form posterior.
result C-DPS consistently outperforms existing methods across multiple inverse problem benchmarks.
This research reverses feature visualization in neural networks to optimize for specific feature objectives.
problem The invertibility of feature visualization in neural networks is not well understood.
method The approach involves optimizing for the feature objective that generates the input used in feature visualization, using the gradient of a specific objective function.
result A closed-form solution is found to minimize the gradient, providing an alternative view on network sensitivity.
In this paper, we consider the Graphical Lasso (GL), a popular optimization problem for learning the sparse representations of high-dimensional datasets, which is well-known to be computationally expensive for large-scale problems. Recently, we have shown that the sparsity pattern of the optimal solution of GL is equiv…
The L1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In this paper, a proximal gradient method (G-ISTA) for performing L1-regularized co…
A new model for pricing ultra-short-term options with complex volatility patterns.
problem Complex pricing of ultra-short-term options due to oscillations in implied volatility.
method Edgeworth++ model with nonparametric stochastic volatility and deterministic shift extension.
result Fast and accurate closed-form option pricing for ultra-short-term options.
Enhances reinforcement learning uncertainty estimation with a generalized Gaussian error model.
problem Inaccurate error representations and compromised uncertainty estimation in conventional uncertainty-aware TD learning.
method Introduces a novel framework for generalized Gaussian error modeling in deep reinforcement learning, incorporating higher-order moments, particularly kurtosis, to improve uncertainty estimation and mitigation.
result Significant performance gains in policy gradient algorithms with the proposed framework.
The paper teaches robots to navigate by learning costs from expert demonstrations.
problem Teaching robots to navigate autonomously using only expert observations.
method Developed a map encoder and cost encoder to infer semantic class probabilities and a cost function from expert observations.
result Robots can learn to follow traffic rules in a simulator using only semantic observations.
A new nonparametric approach for system identification has been recently proposed where the impulse response is seen as the realization of a zero--mean Gaussian process whose covariance, the so--called stable spline kernel, guarantees that the impulse response is almost surely stable. Maximum entropy properties of the …
We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that a certain number of generic rank-one or generic linear measurements are suffici…
Iteratively reweighted least squares (IRLS) is a widely-used method in machine learning to estimate the parameters in the generalised linear models. In particular, IRLS for L1 minimisation under the linear model provides a closed-form solution in each step, which is a simple multiplication between the inverse of the we…
Graphical Lasso (GL) is a popular method for learning the structure of an undirected graphical model, which is based on an l1 regularization technique. The objective of this paper is to compare the computationally-heavy GL technique with a numerically-cheap heuristic method that is based on simply thresholding the s…
IKD uses eigen-decomposition for nonlinear dimensionality reduction.
problem Lack of sophisticated and nonlinear dimensionality reduction methods.
method Inverse Kernel Decomposition (IKD) based on eigen-decomposition of sample covariance matrix.
result IKD achieves comparable performance to optimization-based methods with faster running speeds.
New insights into learning for blind inverse problems with theoretical guarantees.
problem Learning in blind inverse problems where both signal and operator are unknown.
method Data-driven approaches using Linear Minimum Mean Square Estimators (LMMSEs) with theoretical analysis.
result Established equivalences with Tikhonov-regularized formulations and derived finite-sample error bounds.
Unified method for deriving ridgelet transforms for various neural network architectures.
problem Deriving closed-form expressions for ridgelet transforms in modern neural network architectures.
method Unified Fourier slice method to derive ridgelet transforms for diverse neural network types.
result Systematic method to derive ridgelet transforms for various neural network architectures.
We investigate the Student-t process as an alternative to the Gaussian process as a nonparametric prior over functions. We derive closed form expressions for the marginal likelihood and predictive distribution of a Student-t process, by integrating away an inverse Wishart process prior over the covariance kernel of a G…
The Wiener-Hopf factorization is obtained in closed form for a phase type approximation to the CGMY Lévy process. This allows, for the approximation, exact computation of first passage times to barrier levels via Laplace transform inversion. Calibration of the CGMY model to market option prices defines the risk neutral…
Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and theoretical results demonstrating both greater efficacy and greater stability c…
Two formulae estimate sensitivity of random vectors to distributional parameters.
problem Estimating sensitivity of random vectors to distributional parameters.
method Two analytical formulae and four numerical algorithms.
result Validated numerical algorithms and demonstrated effectiveness.
Established PFPPs in complete markets, solving integral equations.
problem Existence of Predictable Forward Performance Processes in complete markets.
method Solving a one-period integral equation using Fourier transform for tempered distributions.
result Closed-form solutions for PFPPs with inverse marginal functions that are completely monotonic.
Innovative extensions to option pricing models using asymmetric Brownian motion and random walk approaches.
problem Capturing empirical phenomena like return skewness, heavy tails, and volatility asymmetry in option pricing models.
method Developing the Geometric Asymmetric Brownian Motion (GABM) within the Bachelier--Black--Scholes--Merton framework.
result Deriving closed-form option pricing formulas and a discrete-time binomial tree algorithm that converges to the GABM limit.
A Bayesian treatment of latent directed graph structure for non-iid data is provided where each child datum is sampled with a directed conditional dependence on a single unknown parent datum. The latent graph structure is assumed to lie in the family of directed out-tree graphs which leads to efficient Bayesian inferen…