arXiv research

Extends neural network verification to non-linear specifications.

In that paper, we provide a new characterization of the solutions of specific reflected backward stochastic differential equations (or RBSDEs) whose driver $g$ is convex and has quadratic growth in its second variable: this is done by introducing the extended notion of $g$-Snell enveloppe. Then, in a second step, we re…

Detects adversarial examples with non-linear dimensionality reduction.

Defines simplicity of non-linear mappings using information geometry.

Quantum computing offers a quadratic speedup for estimating non-linear functionals.

We derive a priori estimates for solutions of a general class of fully non-linear equations on compact Hermitian manifolds. Our method is based on ideas that have been used for different specific equations, such as the complex Monge-Ampère, Hessian and inverse Hessian equations. As an application we solve a class of He…

A method for constructing explicit Calabi-Yau metrics in six dimensions in terms of an initial hyperkahler structure is presented. The equations to solve are non linear in general, but become linear when the objects describing the metric depend on only one complex coordinate of the hyperkahler 4-dimensional space and i…

Paper studies solutions to a specific equation in conformal geometry with singular sets.

Study confirms complex crypto market dynamics via non-linear potentials.

Gradient descent with growing learning rate enables learning non-linear features in neural networks.

Unified model learns joint and individual features from brain imaging data.

ParamBoost uses gradient boosting to create interpretable non-linear models with constraints.

We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement sequence to consist of the observations of the difference between the derivative …

Improved Kalman filter for non-linear, non-Gaussian data.

We consider that the price of a firm follows a non linear stochastic delay differential equation. We also assume that any claim value whose value depends on firm value and time follows a non linear stochastic delay differential equation. Using self-financed strategy and replication we are able to derive a Random Partia…

This research evaluates learning models for bionic robots, focusing on transfer function identification.

A notion of parabolic C-subsolutions is introduced for parabolic equations, extending the theory of C-subsolutions recently developed by B. Guan and more specifically G. Székelyhidi for elliptic equations. The resulting parabolic theory provides a convenient unified approach for the study of many geometric flows.

Enhances xVA valuation with initial margin and CSA discounting.

In this article we present an approach that enables joint wind speed and wind power forecasts for a wind park. We combine a multivariate seasonal time varying threshold autoregressive moving average (TVARMA) model with a power threshold generalized autoregressive conditional heteroscedastic (power-TGARCH) model. The mo…

New algorithm tackles non-linear utility in MNL bandits with $ilde{O}(\sqrt{T})$ regret.

DPLS improves asset pricing by capturing non-linear risk factor structures.

DGPs learn from multiple tasks using shared and private latent processes.

Layer-wise relevance propagation (LRP) is a recently proposed technique for explaining predictions of complex non-linear classifiers in terms of input variables. In this paper, we apply LRP for the first time to natural language processing (NLP). More precisely, we use it to explain the predictions of a convolutional n…

Deep networks prioritize easier examples over harder ones, leading to faster training.

Tractable model explains market dynamics using Langevin and SUSY QM.

Wiener-Granger causality is a widely used framework of causal analysis for temporally resolved events. We introduce a new measure of Wiener-Granger causality based on kernelization of partial canonical correlation analysis with specific advantages in the context of large high-dimensional data. The introduced measure is…

New algorithm for choosing top-K options efficiently with linear space and non-linear feedback.

A new clustering method handles uncertain covariates efficiently.

Hadwiger's Theorem states that Euclidean-invariant convex-continuous valuations of definable sets are linear combinations of intrinsic volumes. We lift this result from sets to data distributions over sets, specifically, to definable real-valued functions on n-dimensional Euclidean space. This generalizes intrinsic vol…

We consider the task of robust non-linear regression in the presence of both inlier noise and outliers. Assuming that the unknown non-linear function belongs to a Reproducing Kernel Hilbert Space (RKHS), our goal is to estimate the set of the associated unknown parameters. Due to the presence of outliers, common techni…

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation by first embedding the trajectories in a reproducing kernel Hilbert space (RKHS…

Deep learning framework for uncertainty quantification in physics.

We consider the problem of learning fair decision systems in complex scenarios in which a sensitive attribute might affect the decision along both fair and unfair pathways. We introduce a causal approach to disregard effects along unfair pathways that simplifies and generalizes previous literature. Our method corrects …

This work interprets SFA through variational inference, relaxing linearity constraints.

Gradient Boosted Feature Selection (GBFS) selects features reliably and scales well.

Develops a data-driven smoothing technique for high-dimensional, non-linear panel data.

Paper introduces Functional Effects Models to account for individual heterogeneity in panel data.

We propose a novel kernel based post selection inference (PSI) algorithm, which can not only handle non-linearity in data but also structured output such as multi-dimensional and multi-label outputs. Specifically, we develop a PSI algorithm for independence measures, and propose the Hilbert-Schmidt Independence Criteri…

KPCA improves OoD detection by separating InD and OoD data.

A non linear regression approach which consists of a specific regression model incorporating a latent process, allowing various polynomial regression models to be activated preferentially and smoothly, is introduced in this paper. The model parameters are estimated by maximum likelihood performed via a dedicated expeca…

Study of recurrences in earthquakes, climate, financial time-series, etc. is crucial to better forecast disasters and limit their consequences. However, almost all the previous phenomenological studies involved only a long-ranged autocorrelation function, or disregarded the multi-scaling properties induced by potential…

Proposes hedging strategies for mortgage prepayment risk.

New model identifies patient-specific disease root causes.

Paper introduces non-linear discounting models for default compensation and climate valuation.

This paper tackles efficient and scalable estimation of a complex model involving stochastic linear combinations of non-linear regressions.

Study high-dimensional Bayesian linear regression using variational inference.

Paper analyzes dataset distillation for efficient encoding of task-relevant information.

Sparse Bayesian learning improves rational approximations for complex-valued models.