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.
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.
We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards.
Veronese webs are rich geometric structures with deep relationships to various domains of mathematics. The PDEs which determine the Veronese web are overdetermined if dim >3, but in the case dim =3 they reduce to a special flavor of a non-linear wave equation. The symmetries embedded in the definition of a Veronese web…
We present a stochastic numerical method for solving fully non-linear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the non-linearity.
We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of regularization, MOR) approach to reconstruct the estimator of the quantity for the non-…
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.
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 …
Non-linear source separation is a challenging open problem with many applications. We extend a recently proposed Adversarial Non-linear ICA (ANICA) model, and introduce Cramer-Wold ICA (CW-ICA). In contrast to ANICA we use a simple, closed--form optimization target instead of a discriminator--based independence measure…
We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant extension of the "anchored regression" method formulated and analyzed in [10] f…
We study two inverse problems on a globally hyperbolic Lorentzian manifold (M,g). The problems are: 1. Passive observations in spacetime: Consider observations in a neighborhood V⊂M of a time-like geodesic μ. Under natural causality conditions, we reconstruct the conformal type of the unknown open, relativ…
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 K objectives combined with a concave L-Lipschitz function.
In this paper, we propose an efficient Monte Carlo implementation of non-linear FBSDEs as a system of interacting particles inspired by the ideas of branching diffusion method. It will be particularly useful to investigate large and complex systems, and hence it is a good complement of our previous work presenting an a…
Capacity analysis has been recently introduced as a way to analyze how linear models distribute their modelling capacity across the input space. In this paper, we extend the notion of capacity allocation to the case of neural networks with non-linear layers. We show that under some hypotheses the problem is equivalent …
We consider a model of linear market impact, and address the problem of replicating a contingent claim in this framework. We derive a non-linear Black-Scholes Equation that provides an exact replication strategy. This equation is fully non-linear and singular, but we show that it is well posed, and we prove existence o…
The goal of a recommendation system is to predict the interest of a user in a given item by exploiting the existing set of ratings as well as certain user/item features. A standard approach to modeling this problem is Inductive Matrix Completion where the predicted rating is modeled as an inner product of the user and …
The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range constraints. Split feasibility generalizes important inverse problems including con…
In this work, we have presented a simple analytical approximation scheme for generic non-linear FBSDEs. By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out a recursive approximation to an arbitrarily highe…
This paper considers method of creation of an advisor and indicator based on the spectral stochastic analysis model, both with linear and non-linear approximation. The problem of entrance to one or another trade position is solved on the basis of combined analysis of dynamics of quotations of all currency pairs, what a…