arXiv research

Paper develops MRCs for supervised classification using generalized maximum entropy.

There is a rapidly increasing interest in crowdsourcing for data labeling. By crowdsourcing, a large number of labels can be often quickly gathered at low cost. However, the labels provided by the crowdsourcing workers are usually not of high quality. In this paper, we propose a minimax conditional entropy principle to…

Given a task of predicting $Y$ from $X$, a loss function $L$, and a set of probability distributions $Γ$ on $(X,Y)$, what is the optimal decision rule minimizing the worst-case expected loss over $Γ$? In this paper, we address this question by introducing a generalization of the principle of maximum entropy. Applying t…

New findings show many popular bandit algorithms are unstable, contradicting minimax optimality.

A new strategy selects k in k-NN regression without hold-out data.

This paper surveys some recent developments in fundamental limits and optimal algorithms for network analysis. We focus on minimax optimal rates in three fundamental problems of network analysis: graphon estimation, community detection, and hypothesis testing. For each problem, we review state-of-the-art results in the…

UCBVI-γ algorithm minimizes regret in discounted MDPs.

SNGP improves DNNs' uncertainty estimation with minimal changes.

Transformers recall from long distributions with statistical guarantees.

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…

Paper finds periodic orbits for convex Lagrangian systems on noncompact manifolds.

These notes review six lectures given by Prof. Andrea Montanari on the topic of statistical estimation for linear models. The first two lectures cover the principles of signal recovery from linear measurements in terms of minimax risk. Subsequent lectures demonstrate the application of these principles to several pract…

Considering that the Seiberg-Witten functional satisfies the Palais-Smale Condition, up to gauge equivalence, the Minimax Principle can be applied on the moduli space to prove the existence of critical points, which correspond to solutions of the second-order SW-equations, up to gauge equivalence.

MOPI optimizes flexible set-valued mappings to achieve superior shape adaptivity in conformal prediction.

A permutation-based SW test achieves minimax-optimal power for two-sample testing.

FAIRM learns fair and generalizable models by enforcing invariance across different data distributions.

New ranking system balances fairness and user utility.

New method improves robustness in partially observable domains by training against latent distribution shifts.

Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However, without proper tuning, this technique implies a high rejection rate. Several methods h…

We deconstruct the performance of GANs into three components: 1. Formulation: we propose a perturbation view of the population target of GANs. Building on this interpretation, we show that GANs can be viewed as a generalization of the robust statistics framework, and propose a novel GAN architecture, termed as Cascade …

The free energy functional has recently been proposed as a variational principle for bounded rational decision-making, since it instantiates a natural trade-off between utility gains and information processing costs that can be axiomatically derived. Here we apply the free energy principle to general decision trees tha…

Proposes a deep neural network for multi-dimensional functional data classification.

New bounds for LDP with heterogeneous privacy levels guaranteeing high probability of accuracy.

Adapts RKHS methods to estimate density ratios with optimal error.

The paper tackles individualized decision-making under unmeasured confounding, providing a novel minimax solution and a paradox.

Framework selects optimal historical data windows for non-stationary learning.

We address the problem of {\it adaptivity} in the framework of reproducing kernel Hilbert space (RKHS) regression. More precisely, we analyze estimators arising from a linear regularization scheme $g_\lam$. In practical applications, an important task is to choose the regularization parameter $\lam$ appropriately, i.e.…

Paper proposes deep neural networks for nonparametric regression from dependent data.

New metric derived for robust optimization in stochastic control problems.

Data in the form of pairwise comparisons arises in many domains, including preference elicitation, sporting competitions, and peer grading among others. We consider parametric ordinal models for such pairwise comparison data involving a latent vector $w^* \in \mathbb{R}^d$ that represents the "qualities" of the $d$ ite…

Unstable minimal surfaces are the unstable stationary points of the Dirichlet-Integral. In order to obtain unstable solutions, the method of the gradient flow together with the minimax-principle is generally used. The application of this method for minimal surfaces in the Euclidean spacce was presented in \cite{s3}. We…

Paper tackles sparse phase retrieval with a novel Bayesian approach.

Two new algorithms solve nonconvex-strongly concave problems efficiently.

We show a principled way of deriving online learning algorithms from a minimax analysis. Various upper bounds on the minimax value, previously thought to be non-constructive, are shown to yield algorithms. This allows us to seamlessly recover known methods and to derive new ones. Our framework also captures such "unort…

A novel decentralized algorithm improves minimax optimization in federated learning.

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…

Develops a method for kernel ridge regression under covariate shift using pseudo-labels.

Paper analyzes GANs training difficulties and proposes a control framework.

Study optimizes data collection from biased, costly sources to minimize risk.

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.

In this paper we extend the results of "A strong minimax property of nondegenerate minimal submanifolds" by White, where it is proved that any smooth, compact submanifold, which is a strictly stable critical point for an elliptic parametric functional, is the unique minimizer in a certain geodesic tubular neighbourhood…

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

A new method solves complex constrained minimax problems.

Developing classification methods with high accuracy that also avoid unfair treatment of different groups has become increasingly important for data-driven decision making in social applications. Many existing methods enforce fairness constraints on a selected classifier (e.g., logistic regression) by directly forming …

The study provides theoretical guarantees for the statistical performance of optimal decision trees.

New algorithm solves federated minimax optimization problems.

Paper proposes an algorithm to solve complex minimax problems efficiently.