Related papers: Generalization bounds for learning under graph-dep…

This paper studies how to capture dependency graph structures from real data which may not be Gaussian. Starting from marginal loss functions not necessarily derived from probability distributions, we utilize an additive…

Statistical learning relies upon data sampled from a distribution, and we usually do not care what actually generated it in the first place. From the point of view of causal modeling, the structure of each distribution is induced by…

Recent advancements in graph learning have revolutionized the way to understand and analyze data with complex structures. Notably, Graph Neural Networks (GNNs), i.e. neural network architectures designed for learning graph representations,…

This work initiates a general study of learning and generalization without the i.i.d. assumption, starting from first principles. While the traditional approach to statistical learning theory typically relies on standard assumptions from…

Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…

Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled…

We study the fundamental problem of learning with respect to the squared loss in a convex class. The state-of-the-art sample complexity estimates in this setting rely on Rademacher complexities, which are generally difficult to control. We…

Existing generalization bounds for deep neural networks require data to be independent and identically distributed (iid). This assumption may not hold in real-life applications such as evolutionary biology, infectious disease epidemiology,…

Many machine learning algorithms are based on the assumption that training examples are drawn independently. However, this assumption does not hold anymore when learning from a networked sample because two or more training examples may…

Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their…

We propose new bounds on the error of learning algorithms in terms of a data-dependent notion of complexity. The estimates we establish give optimal rates and are based on a local and empirical version of Rademacher averages, in the sense…

Pac-Bayes bounds are among the most accurate generalization bounds for classifiers learned from independently and identically distributed (IID) data, and it is particularly so for margin classifiers: there have been recent contributions…

We develop a general framework for conducting inference on the mean of dependent random variables given constraints on their dependency graph. We establish the consistency of an oracle variance estimator of the mean when the dependency…

Desirable random graph models (RGMs) should (i) reproduce common patterns in real-world graphs (e.g., power-law degrees, small diameters, and high clustering), (ii) generate variable (i.e., not overly similar) graphs, and (iii) remain…

Dependency knowledge of the form "x is independent of y once z is known" invariably obeys the four graphoid axioms, examples include probabilistic and database dependencies. Often, such knowledge can be represented efficiently with…

In this paper, we establish generalization bounds for transductive learning algorithms in the context of information theory and PAC-Bayes, covering both the random sampling and the random splitting setting. First, we show that the…

Continual learning (CL) has emerged as a dominant paradigm for acquiring knowledge from sequential tasks while avoiding catastrophic forgetting. Although many CL methods have been proposed to show impressive empirical performance, the…

Distribution shifts on graphs -- the data distribution discrepancies between training and testing a graph machine learning model, are often ubiquitous and unavoidable in real-world scenarios. Such shifts may severely deteriorate the…

In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…

We present a nonparametric graphical model. Our model uses an undirected graph that represents conditional independence for general random variables defined by the conditional dependence coefficient (Azadkia and Chatterjee (2021)). The set…