Related papers: Efficient Lipschitz Extensions for High-Dimensiona…
Node embedding learns a low-dimensional representation for each node in the graph. Recent progress on node embedding shows that proximity matrix factorization methods gain superb performance and scale to large graphs with millions of nodes.…
Graph data is used in a wide range of applications, while analyzing graph data without protection is prone to privacy breach risks. To mitigate the privacy risks, we resort to the standard technique of differential privacy to publish a…
Random projections are able to perform dimension reduction efficiently for datasets with nonlinear low-dimensional structures. One well-known example is that random matrices embed sparse vectors into a low-dimensional subspace nearly…
Classical assumptions like strong convexity and Lipschitz smoothness often fail to capture the nature of deep learning optimization problems, which are typically non-convex and non-smooth, making traditional analyses less applicable. This…
This paper deals with composite optimization problems having the objective function formed as the sum of two terms, one has Lipschitz continuous gradient along random subspaces and may be nonconvex and the second term is simple and…
Evolving networks are more widely existed in real world than static networks, and studying their statistical characteristics is vital to recognize and explore them further. But for the networks with nodes preferential deletion, there are…
This paper presents new deterministic and distributed low-diameter decomposition algorithms for weighted graphs. In particular, we show that if one can efficiently compute approximate distances in a parallel or a distributed setting, one…
Local differential privacy (LDP) can provide each user with strong privacy guarantees under untrusted data curators while ensuring accurate statistics derived from privatized data. Due to its powerfulness, LDP has been widely adopted to…
We propose graph-dependent implicit regularisation strategies for distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity,…
This paper deals with an optimization problem over a network of agents, where the cost function is the sum of the individual objectives of the agents and the constraint set is the intersection of local constraints. Most existing methods…
The application of graph analytics to various domains has yielded tremendous societal and economical benefits in recent years. However, the increasingly widespread adoption of graph analytics comes with a commensurate increase in the need…
The individualization-refinement paradigm provides a strong toolbox for testing isomorphism of two graphs and indeed, the currently fastest implementations of isomorphism solvers all follow this approach. While these solvers are fast in…
We consider statistical inference for a finite-dimensional parameter in a regular semiparametric model under a distributed setting with blockwise missingness, where entire blocks of variables are unavailable at certain sites and sharing…
We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot…
We present a numerical method for rigorous over-approximation of a reachable set of differential inclusions. The method gives high-order error bounds for single step approximations and a uniform bound on the error over the finite time…
We demonstrate two new important properties of the 1-path-norm of shallow neural networks. First, despite its non-smoothness and non-convexity it allows a closed form proximal operator which can be efficiently computed, allowing the use of…
We give improved pseudorandom generators (PRGs) for Lipschitz functions of low-degree polynomials over the hypercube. These are functions of the form psi(P(x)), where P is a low-degree polynomial and psi is a function with small Lipschitz…
In this paper, we investigate the differentially private estimation of data depth functions and their associated medians. We introduce several methods for privatizing depth values at a fixed point, and show that for some depth functions,…
Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and…
Tackling semi-supervised learning problems with graph-based methods has become a trend in recent years since graphs can represent all kinds of data and provide a suitable framework for studying continuum limits, e.g., of differential…