相关论文: Generalization Bounds for Semi-supervised Matrix C…

Serendipity in recommender systems (RSs) has attracted increasing attention as a concept that enhances user satisfaction by presenting unexpected and useful items. However, evaluating serendipitous performance remains challenging because…

Recommender systems are essential tools in the digital landscape for connecting users with content that more closely aligns with their preferences. Matrix completion is a widely used statistical framework for such systems, aiming to predict…

Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…

Human ratings have become a crucial resource for training and evaluating machine learning systems. However, traditional elicitation methods for absolute and comparative rating suffer from issues with consistency and often do not distinguish…

Matrix completion aims to estimate missing entries in a data matrix, using the assumption of a low-complexity structure (e.g., low rank) so that imputation is possible. While many effective estimation algorithms exist in the literature,…

The goal of recommender systems is to help users find useful items from a large catalog of items by producing a list of item recommendations for every user. Data sets based on implicit data collection have a number of special…

Matrix factorization models have been extensively studied as a valuable test-bed for understanding the implicit biases of overparameterized models. Although both low nuclear norm and low rank regularization have been studied for these…

We consider the problem of exact low-rank matrix completion from a geometric viewpoint: given a partially filled matrix M, we keep the positions of specified and unspecified entries fixed, and study how the minimal completion rank depends…

The inference of a large symmetric signal-matrix $\mathbf{S} \in \mathbb{R}^{N\times N}$ corrupted by additive Gaussian noise, is considered for two regimes of growth of the rank $M$ as a function of $N$. For sub-linear ranks…

In this paper, we study a general low-rank matrix recovery problem with linear measurements corrupted by some noise. The objective is to understand under what conditions on the restricted isometry property (RIP) of the problem local search…

This paper explores the generalization characteristics of iterative learning algorithms with bounded updates for non-convex loss functions, employing information-theoretic techniques. Our key contribution is a novel bound for the…

In this work, we study the generalization capability of algorithms from an information-theoretic perspective. It has been shown that the expected generalization error of an algorithm is bounded from above by a function of the relative…

We derive a novel information-theoretic analysis of the generalization property of meta-learning algorithms. Concretely, our analysis proposes a generic understanding of both the conventional learning-to-learn framework and the modern…

In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two…

Gradient descent for matrix factorization exhibits an implicit bias toward approximately low-rank solutions. While existing theories often assume the boundedness of iterates, empirically the bias persists even with unbounded sequences. This…

It has been recently observed in much of the literature that neural networks exhibit a bottleneck rank property: for larger depths, the activation and weights of neural networks trained with gradient-based methods tend to be of…

Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching…

The problem of low-rank matrix completion has recently generated a lot of interest leading to several results that offer exact solutions to the problem. However, in order to do so, these methods make assumptions that can be quite…

Large language models (LLMs) are increasingly deployed in settings where the available context is incomplete or degraded. We argue that an LLM generating answers under incomplete context can be viewed as an implicit imputer, and evaluated…

In the present paper, we consider the problem of matrix completion with noise. Unlike previous works, we consider quite general sampling distribution and we do not need to know or to estimate the variance of the noise. Two new nuclear-norm…