Data unfolding -- the removal of noise or artifacts from measurements -- is a fundamental task across the experimental sciences. Of particular interest in the present work are applications of data unfolding in physics, in which context the dominant approach is RichardsonLucy (RL) deconvolution. The classical RL approach aims to find denoised data that, once passed through the noise model, is as close as possible to the measured data, in terms of Kullback-Leibler (KL) divergence. Fundamental to this approach is the hypothesis that the support of the measured data overlaps with the output of the noise model, so that the KL divergence correctly captures their similarity. In practice, this hypothesis is typically enforced by binning the measured data and noise model, introducing numerical error into the unfolding process. As a counterpoint to classical binned methods for unfolding, the present work studies an alternative formulation of the unfolding problem, using a Wasserstein loss instead of the KL divergence to quantify the similarity between the measured data and the output of the noise model. We establish sharp conditions for existence and uniqueness of optimizers; as a consequence we answer open questions of Li, et al. [23], regarding necessary conditions for existence and uniqueness in the case of transport map noise models. Following these theoretical results, we then develop a provably convergent generalized Sinkhorn algorithm to compute approximate optimizers. Our algorithm requires only empirical observations of the noise model and measured data and scales with the size of the data, rather than the ambient dimension.

Achieving valid conditional coverage in conformal prediction is challenging due to the theoretical difficulty of satisfying pointwise constraints in finite samples. Building upon the characterization of conditional coverage through marginal moment restrictions, we introduce Minimax Optimization Predictive Inference (MOPI), a framework that generalizes prior work by optimizing over a flexible class of set-valued mappings during the calibration phase, rather than simply calibrating a fixed sublevel set. This minimax formulation effectively circumvents the structural constraints of predefined score functions, achieving superior shape adaptivity while maintaining a principled connection to the minimization of mean squared coverage error. Theoretically, we provide non-asymptotic oracle inequalities and show that the convergence rate of the coverage error attains the optimal order under regular conditions. The MOPI also enables valid inference conditional on sensitive attributes that are available during calibration but unobserved at test time. Empirical results on complex, non-standard conditional distributions demonstrate that MOPI produces more efficient prediction sets than existing baselines.

The Riesz representer is a central object in semiparametric statistics and debiased/doubly-robust estimation. Two literatures in econometrics have highlighted the role for directly estimating Riesz representers: the automatic debiased machine learning literature (as in Chernozhukov et al., 2022b), and an independent literature on sieve methods for conditional moment models (as in Chen et al., 2014). These two literatures solve distinct optimization problems that in the population both have the Riesz representer as their solution. We show that with unregularized or ridge-regularized linear, sieve, or RKHS models, the two resulting estimators are numerically equivalent. However, for other regularization schemes such as the Lasso, or more general machine learning function classes including neural networks, the estimators are not necessarily equivalent. In the latter case, the Chen et al. (2014) formulation yields a novel constrained optimization problem for directly estimating Riesz representers with machine learning. Drawing on results from Birrell et al. (2022), we conjecture that this approach may offer statistical advantages at the cost of greater computational complexity.

Recommendation and collaborative filtering systems are important in modern information and e-commerce applications. As these systems are becoming increasingly popular in the industry, their outputs could affect business decision making, introducing incentives for an adversarial party to compromise the availability or integrity of such systems. We introduce a data poisoning attack on collaborative filtering systems. We demonstrate how a powerful attacker with full knowledge of the learner can generate malicious data so as to maximize his/her malicious objectives, while at the same time mimicking normal user behavior to avoid being detected. While the complete knowledge assumption seems extreme, it enables a robust assessment of the vulnerability of collaborative filtering schemes to highly motivated attacks.

Neural Information Processing Systems http://nips.cc/

Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems. Simple non-convex optimization algorithms are popular and effective in practice. Despite recent progress in proving various non-convex algorithms converge from a good initial point, it remains unclear why random or arbitrary initialization suffices in practice. We prove that the commonly used non-convex objective function for positive semidefinite matrix completion has no spurious local minima - all local minima must also be global. Therefore, many popular optimization algorithms such as (stochastic) gradient descent can provably solve positive semidefinite matrix completion with arbitrary initialization in polynomial time. The result can be generalized to the setting when the observed entries contain noise. We believe that our main proof strategy can be useful for understanding geometric properties of other statistical problems involving partial or noisy observations.

Many applications of machine learning involve structured outputs with large domains, where learning of a structured predictor is prohibitive due to repetitive calls to an expensive inference oracle. In this work, we show that by decomposing training of a Structural Support Vector Machine (SVM) into a series of multiclass SVM problems connected through messages, one can replace an expensive structured oracle with Factorwise Maximization Oracles (FMOs) that allow efficient implementation of complexity sublinear to the factor domain. AGreedy Direction Method of Multiplier (GDMM) algorithm is then proposed to exploit the sparsity of messages while guarantees convergence tosub-optimality after O(log(1/)) passes of FMOs over every factor. We conduct experiments on chain-structured and fully-connected problems of large output domains, where the proposed approach is orders-of-magnitude faster than current state-of-the-art algorithms for training Structural SVMs.

We consider cooperative multi-agent consensus optimization problems over anundirected network of agents, where only those agents connected by an edgecan directly communicate. The objective is to minimize the sum of agent-specific composite convex functions over agent-specific private conic constraintsets; hence, the optimal consensus decision should lie in the intersection of theseprivate sets. We provide convergence rates in sub-optimality, infeasibility andconsensus violation; examine the effect of underlying network topology on theconvergence rates of the proposed decentralized algorithms; and show how to ex-tend these methods to handle time-varying communication networks.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/