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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

169,291 papers · 148 categories

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48 results for non-linear problems

Study Tikhonov regularization for non-linear inverse problems to improve image reconstruction accuracy.

problem Reconstructing quantities from noisy, non-linearly transformed observations.
method Tikhonov regularization using reproducing kernel Hilbert spaces.
result Developed optimal convergence rates for the estimator.

Efficient estimator for non-linear regression problems using convex programming.

problem Non-linear regression problems with difference of convex (DC) non-linearities.
method Formulated as a convex program, using an approximation oracle for gradients.
result Produces accurate estimates with high probability under certain assumptions.

DualIV simplifies non-linear IV regression via dual formulation.

problem Non-linear instrumental variable regression with potential first-stage regression bottleneck.
method Dual formulation of non-linear IV regression as a convex-concave saddle-point problem, leading to a kernel-based algorithm with analytic solution.
result Empirical results show competitive performance compared to existing algorithms.

Solves Dirichlet problem for elliptic equations on Hermitian manifolds.

problem Solving Dirichlet problem for fully non-linear elliptic equations on Hermitian manifolds.
method Establishing a quantitative boundary estimate under a subsolution assumption.
result Derives solvability and regularity of the Dirichlet problem.

New approach to ODEs using Gaussian processes and Bayesian filtering.

problem Solving ordinary differential equations (ODEs) with probabilistic methods.
method Formulate ODE solutions as Gaussian process regression problems with non-linear measurement functions.
result Developed novel Gaussian solvers with favourable stability properties.

New classifier combines locally linear kernels for fast and accurate non-linear classification.

problem Developing a fast and accurate non-linear classifier.
method Combines locally linear classifiers using a 1\ell_1 Multiple Kernel Learning (MKL) problem with scalable MKL training for streaming kernels.
result The resulting classifier achieves high accuracy with fast inference time.

The paper establishes boundary estimates for solutions to elliptic equations on Hermitian manifolds.

problem Boundary estimates for solutions to fully non-linear elliptic equations on Hermitian manifolds.
method Unified approach using quantitative boundary estimates, gradient estimates, and existence results.
result Established gradient estimates and unified approach to Dirichlet problem solutions.

Study non-linear combinatorial bandits with polynomial rewards, finding significant differences from linear cases.

problem Adversarial combinatorial bandits with general non-linear reward functions.
method Extending existing work on adversarial linear combinatorial bandits, analyzing minimax optimal regret for polynomial and non-polynomial reward functions.
result Minimax optimal regret bounds for adversarial combinatorial bandits with general non-linear reward functions.

Elliptic theory explains indicial weights for non-linear geometry problems.

problem Understanding indicial weights for elliptic operators on non-compact manifolds.
method Developed an elliptic theory for indicial weights, proving Fredholm conditions.
result An elliptic theory exists even when the weight is indicial.

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

problem Estimating non-linear functionals of probability distributions.
method Proposes a quantum-inside-quantum Monte Carlo algorithm for a broad class of non-linear estimation problems.
result Achieves a quadratic speedup for non-linear estimation problems, including nested conditional expectations and stochastic optimization.

Broadens Jourdain and Martini's method to non-linear stochastic processes.

problem Applying pricing methods to non-linear stochastic processes.
method Analyzes from probabilistic and analytic viewpoints, extending Jourdain and Martini's method.
result Broadens applicability of pricing methods to non-linear frameworks.

Improved regret bound for multinomial logistic bandits with non-linearity.

problem Maximizing rewards in multinomial logistic bandits with non-linear feedback.
method Extended the definition of κκ_* to multinomial setting and proposed an efficient algorithm.
result Minimax-optimal regret bound of O~(RdKT/κ) \smash{\widetilde{\mathcal{O}}( R d \sqrt{ {KT}/{κ_*}} ) } , improving over existing guarantees.

Matrix completion works well for smooth non-linear structures, even without low-rank assumptions.

problem Matrix completion for smooth non-linear structures.
method Nuclear-norm penalization for matrices lying in a low-dimensional non-linear manifold.
result Nuclear-norm penalization is minimax rate optimal for recovering smooth non-linear matrices with missing data.

Improves recommendation systems by adding non-linearity to matrix completion.

problem Predicting user interests from ratings and features using bilinear models is limiting.
method Applies non-linear activation functions on top of projected user/item features using gradient descent.
result Gradient descent can solve non-linear Inductive Matrix Completion problems effectively.

CRCCA framework improves non-linear CCA with compressed representations.

problem Non-linear CCA for multi-view data with limited samples.
method Information-theoretic compressed representation framework (CRCCA) based on lattice quantization.
result The CRCCA framework provides theoretical bounds and optimality conditions, offering a flexible and computationally efficient solution.

Extends capacity analysis to neural networks, showing how capacity is distributed across layers.

problem How capacity is distributed in neural networks with non-linear layers.
method Introduces layer decoupling to quantify non-linear activation's impact, and uses a markovian rule for capacity propagation in deep networks.
result Shows that under certain conditions, capacity allocation in neural networks is equivalent to linear capacity allocation in an extended input space.

Paper uses black-box inference to estimate non-linear latent force models.

problem Estimating posterior state and forcing term in non-linear systems with unknown forcing terms.
method Black-box variational inference with local inverse autoregressive flows.
result Demonstrates effectiveness of approximation on known posterior systems and non-linear dynamics.

DART optimizes subset selection in non-linear bandit problems.

problem Optimizing subset selection in non-linear bandit problems with correlated rewards.
method DART algorithm for combinatorial bandits without individual arm feedback or linearity assumption.
result DART achieves a regret bound of ildeO(KKNT) ilde{\mathcal{O}}(K\sqrt{KNT}).

Proposes a new method for feature selection in non-linear functions.

problem Feature selection for non-linear functions in high-dimensional data.
method Continuous relaxation of Bernoulli distributions to learn feature selection indicators via gradient descent.
result Demonstrates the effectiveness of the approach on synthetic and real-life applications.

Improved disability insurance model with collective health claims.

problem Enhance disability insurance model with collective health claims.
method Expand classic semi-Markov model with collective health claims, solve many-body problem using mean-field approach.
result Mean-field approach simplifies complex model into a transparent pricing method.

This paper tackles non-linear reward optimization in resource allocation problems.

problem Optimizing a non-linear function of long-term average rewards in resource allocation problems.
method Proposes model-based and model-free algorithms to learn optimal policies.
result Model-based algorithm achieves a regret of $\Tilde{O}\left(LKDS\sqrt{\frac{A}{T}} ight)$ for KK objectives combined with a concave LL-Lipschitz function.

Develops inverse EKF for non-linear systems with stability guarantees and learning unknown dynamics.

problem Estimating adversary's Kalman-filtered estimates in highly non-linear systems.
method Proposes inverse extended Kalman filter (I-EKF) for second-order, Gaussian sum, and dithered forward models. Uses reproducing kernel Hilbert space for learning unknown dynamics.
result Derives theoretical stability guarantees for inverse second-order EKF.

This work proposes a new algorithm for efficient reduced modeling of non-linear dynamical systems.

problem Reduced modeling of computationally demanding dynamical systems to balance accuracy and complexity.
method Embedding trajectories in a RKHS, solving low-rank constraint optimization problems, and exploiting kernel-based computations.
result The proposed algorithm achieves a gain in approximation accuracy and computational efficiency.

Proves energy estimates for tensorial wave equations, decoupling components for stability proof.

problem Proving stability of (1+3)(1+3)-Minkowski space-time with various non-linearities.
method Decouples energy estimates for tensorial wave equations, exploiting tensorial structure and Lie derivatives.
result Decoupled energy estimates for tensorial solutions, allowing new stability proofs.

The paper analyzes portfolio selection with non-linear wealth dynamics and random coefficients.

problem Mean-variance portfolio selection with non-linear wealth dynamics and random coefficients.
method Solves an auxiliary stochastic control problem to construct a candidate portfolio, verifies optimality using convex duality, and provides the efficient frontier.
result Obtains the efficient frontier in closed form, showing people prefer riskless assets over classical linear markets.

ENIAC method optimizes and explores complex RL problems with non-linear policies.

problem Theoretical understanding of non-linear policies in RL with strategic exploration.
method ENIAC, an actor-critic method for non-linear function approximation.
result ENIAC finds near-optimal policies in polynomial exploration rounds under bounded eluder dimension.