arXiv research

Paper proposes new Langevin samplers for sampling from log-concave distributions with superlinear gradient growth.

Improved stability for matrix recovery from rank-one measurements.

Paper improves a method for fast global and local convergence in optimization.

New methods optimize functions faster with less gradient accuracy needed.

New algorithm TUSLA improves learning of non-convex neural networks.

Study random walks on groups with superlinear divergent geodesics.

New method achieves superlinear convergence rate with limited memory.

New quasi-Newton method guarantees global superlinear convergence.

OSGM uses online learning to adapt stepsize for faster convergence.

We study some qualitative properties of ancient solutions of superlinear heat equations on a Riemannian manifold, with particular interest in positivity and constancy in space.

New averaging technique speeds up Newton method convergence.

New algorithm samples superlinearly growing log-gradient distributions.

The paper studies the solution of stochastic optimization problems in which approximations to the gradient and Hessian are obtained through subsampling. We first consider Newton-like methods that employ these approximations and discuss how to coordinate the accuracy in the gradient and Hessian to yield a superlinear ra…

We study an optimal liquidation problem under the ambiguity with respect to price impact parameters. Our main results show that the value function and the optimal trading strategy can be characterized by the solution to a semi-linear PDE with superlinear gradient, monotone generator and singular terminal value. We also…

New sampling algorithms for complex distributions without log-concavity.

Memory-constrained algorithms need superlinear memory for efficient convex optimization.

Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions (which form a nonlinear space), equivalently, on random closed sets. …

The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and adaptive control. A new point of view is offered for the constrained optimization prob…

New method improves smoothness of minimizing currents near singular points.

KSS method converges and recovers correct clustering under certain conditions.

Paper proposes a pre-conditioning technique to speed up gradient-descent convergence in distributed linear least-squares problems.

New tool for parallel and private stochastic convex optimization reduces query complexity.

EM algorithm converges in KL divergence for exponential families via mirror descent.

Paper proposes a new method to efficiently incorporate curvature information in stochastic optimization.

New algorithm tames non-linear growth in stochastic optimization.

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data, standard strategies for sparsifying the model can prevent the approximation of …

Study shows income inequality increases with city size, affecting only the wealthiest deciles.

In a continuous-time model with multiple assets described by càdlàg processes, this paper characterizes superhedging prices, absence of arbitrage, and utility maximizing strategies, under general frictions that make execution prices arbitrarily unfavorable for high trading intensity. Such frictions induce a duality bet…

The techniques and analysis presented in this paper provide new methods to solve optimization problems posed on Riemannian manifolds. A new point of view is offered for the solution of constrained optimization problems. Some classical optimization techniques on Euclidean space are generalized to Riemannian manifolds. S…

The paper develops efficient estimators for semi-parametric binary models in distributed computing.

Enhanced VMC methods improve neural wavefunction training.

Deep learning algorithms often require solving a highly non-linear and nonconvex unconstrained optimization problem. Methods for solving optimization problems in large-scale machine learning, such as deep learning and deep reinforcement learning (RL), are generally restricted to the class of first-order algorithms, lik…

Reinforcement Learning (RL) algorithms allow artificial agents to improve their action selections so as to increase rewarding experiences in their environments. Deep Reinforcement Learning algorithms require solving a nonconvex and nonlinear unconstrained optimization problem. Methods for solving the optimization probl…

We consider a class of fractional stochastic volatility models (including the so-called rough Bergomi model), where the volatility is a superlinear function of a fractional Gaussian process. We show that the stock price is a true martingale if and only if the correlation $ρ$ between the driving Brownian motions of the …

Study PL bordism theories with quantitative bounds on filling simplices.

We give a group theoretic characterization of geodesics with superlinear divergence in the Cayley graph of a right-angled Artin group A(G) with connected defining graph G. We use this to determine when two points in an asymptotic cone of A(G) are separated by a cut-point. As an application, we show that if G does not d…

Gaussian processes (GPs) provide a powerful non-parametric framework for reasoning over functions. Despite appealing theory, its superlinear computational and memory complexities have presented a long-standing challenge. State-of-the-art sparse variational inference methods trade modeling accuracy against complexity. H…

State of the art methods in astronomical image reconstruction rely on the resolution of a regularized or constrained optimization problem. Solving this problem can be computationally intensive and usually leads to a quadratic or at least superlinear complexity w.r.t. the number of pixels in the image. We investigate in…

We generalize the notion of cusp excursion of geodesic rays by introducing for any $k \geq 1$ the $k^{th}$ excursion in the cusps of a hyperbolic $N$-manifold of finite volume. We show that on one hand, this excursion is at most linear for geodesics that are generic with respect to the hitting measure of a random walk.…

Study on nonlinear elliptic equations with variable exponents, proving existence and multiplicity of solutions.

Let a $A$ be the 1-skeleton of a triangulated topological annulus. We establish bounds on the combinatorial modulus of a refinement $A'$, formed by attaching new vertices and edges to $A$, that depend only on the refinement and not on the structure of $A$ itself. This immediately applies to showing that a disk triangul…

NR retraction approximates geodesics on submanifolds efficiently.

Artificial Neural Networks (ANNs) have received increasing attention in recent years with applications that span a wide range of disciplines including vital domains such as medicine, network security and autonomous transportation. However, neural network architectures are becoming increasingly complex and with an incre…

Research examines correlations of complex logarithms of lattice points, showing level repulsion and Poissonian behavior.

We are interested in strong approximations of one-dimensional SDEs which have non-Lipschitz coefficients and which take values in a domain. Under a set of general assumptions we derive an implicit scheme that preserves the domain of the SDEs and is strongly convergent with rate one. Moreover, we show that this general …

The study examines correlations of logarithms of integers at different scalings.

We define two non-linear operations with random (not necessarily closed) sets in Banach space: the conditional core and the conditional convex hull. While the first is sublinear, the second one is superlinear (in the reverse set inclusion ordering). Furthermore, we introduce the generalised conditional expectation of r…

A new algorithm estimates mean adaptively to covariance, faster and more flexible than existing methods.