arXiv research

The paper identifies network bottlenecks using minimax paths in stochastic networks.

New algorithms minimize regret in SSP with optimal sparse updates.

In this paper we give sufficient conditions guaranteeing the validity of the well-known minimax theorem for the lower Snell envelope with respect to a family of absolutely continuous probability measures. Such minimax results play an important role in the characterisation of arbitrage-free prices of American contingent…

New algorithm reduces regret in linear mixture SSPs without cost bounds.

Paper develops approximation and statistical theory for signature-based path regression.

Combinatorial optimization problems for clustering are known to be NP-hard. Most optimization methods are not able to find the global optimum solution for all datasets. To solve this problem, we propose a global optimal path-based clustering (GOPC) algorithm in this paper. The GOPC algorithm is based on two facts: (1) …

Given a smooth manifold $M$ and a totally nonholonomic distribution $Δ\subset TM$ of rank $d$, we study the effect of singular curves on the topology of the space of horizontal paths joining two points on $M$. Singular curves are critical points of the endpoint map $F:γ\mapstoγ(1)$ defined on the space $Ω$ of horizonta…

Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or decided data-adaptively. Traditional computational methods rely on solving a set o…

Paper tackles offline SSP with value iteration for policy evaluation and learning.

In this paper, we recover sparse signals from their noisy linear measurements by solving nonlinear differential inclusions, which is based on the notion of inverse scale space (ISS) developed in applied mathematics. Our goal here is to bring this idea to address a challenging problem in statistics, \emph{i.e.} finding …

Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $θ$ in an individualized linear threshold $θ^T Z$ for a continuous variable $X$, which minimizes the disagreement between $\text{sign}(X-θ^TZ)$ and a binary response $Y$. While the problem can be formulated into the M-est…

Study tackles non-stationary bandit convex optimization with new algorithms.

This paper analyzes shallow ReLU networks in L^p and Sobolev spaces, focusing on approximation and generalization.

Boosting as gradient descent algorithms is one popular method in machine learning. In this paper a novel Boosting-type algorithm is proposed based on restricted gradient descent with structural sparsity control whose underlying dynamics are governed by differential inclusions. In particular, we present an iterative reg…

Fast accumulation of large amounts of complex data has created a need for more sophisticated statistical methodologies to discover interesting patterns and better extract information from these data. The large scale of the data often results in challenging high-dimensional estimation problems where only a minority of t…

Testing-by-betting strategies almost surely go bankrupt under null hypotheses.

Two new algorithms solve nonconvex-strongly concave problems efficiently.

A novel decentralized algorithm improves minimax optimization in federated learning.

The paper tackles model failure detection and refitting in real-world systems.

Proximal Mediation Analysis with Hidden Recanting Witnesses

We investigate the use of Minimax distances to extract in a nonparametric way the features that capture the unknown underlying patterns and structures in the data. We develop a general-purpose and computationally efficient framework to employ Minimax distances with many machine learning methods that perform on numerica…

New method reduces regret for sparse adversarial SSP problems.

Many tasks in modern machine learning can be formulated as finding equilibria in \emph{sequential} games. In particular, two-player zero-sum sequential games, also known as minimax optimization, have received growing interest. It is tempting to apply gradient descent to solve minimax optimization given its popularity a…

This paper analyzes saddle points and minimax points in non-convex smooth games.

Paper explores generalization of minimax learners, proposing a new metric.

A new method solves complex constrained minimax problems.

New matrix completion method for arbitrary sampling patterns using network flows.

New algorithm solves federated minimax optimization problems.

Paper proposes an algorithm to solve complex minimax problems efficiently.

A new decentralized method solves minimax problems with reduced communication and sample complexity.

Paper studies early-stopped mirror descent for noisy sparse phase retrieval.

Efficient sampling reduces memory usage for Minimax distance analysis.

Study on estimating invertible functions with minimax analysis.

Minimax defense improves neural network security against gradient-based attacks.

Minimax linkage was first introduced by Ao et al. [3] in 2004, as an alternative to standard linkage methods used in hierarchical clustering. Minimax linkage relies on distances to a prototype for each cluster; this prototype can be thought of as a representative object in the cluster, hence improving the interpretabil…

Study non-parametric value function estimation from a single path.

New bounds on minimax regret for sequential probability assignment using logarithmic loss.

Paper proposes algorithms for solving nonconvex-nonconcave problems with complexity guarantees.

New algorithm AG-OG optimizes separable convex-concave problems efficiently.

Develops shuffling gradient-based methods for nonconvex-concave minimax optimization.

Paper improves risk bounds for nonconvex-strongly-concave minimax problems.

Optimally estimate distances on surfaces using reconstructed meshes.

Study minimax linear regression under quantile risk, improving existing bounds and providing new results.

The paper analyzes generalization bounds for NC-SC/NC-C stochastic minimax optimization.

This paper analyzes how machine learning models resist adversarial attacks in nonparametric regression.

Develops high-probability minimax quantile bounds for statistical problems.

TiAda adapts adaptive gradient methods for nonconvex minimax optimization.

New algorithms solve nonconvex-nonconcave minimax optimization problems.