Related papers: Distributional Shrinkage II: Higher-Order Scores E…

Many problems, especially those with a composite structure, can naturally be expressed in higher order logic. From a KR perspective modeling these problems in an intuitive way is a challenging task. In this paper we study the graph mining…

For many learning problems one may not have access to fine grained label information; e.g., an image can be labeled as husky, dog, or even animal depending on the expertise of the annotator. In this work, we formalize these settings and…

Let \phi(G) be the minimum conductance of an undirected graph G, and let 0=\lambda_1 <= \lambda_2 <=... <= \lambda_n <= 2 be the eigenvalues of the normalized Laplacian matrix of G. We prove that for any graph G and any k >= 2, \phi(G) =…

Many inference problems in structured prediction can be modeled as maximizing a score function on a space of labels, where graphs are a natural representation to decompose the total score into a sum of unary (nodes) and pairwise (edges)…

Ranking systems produce ordered lists from scalar scores, yet the ranking itself depends only on pairwise comparisons. We develop a mathematical theory that takes this observation seriously, centering the analysis on pairwise margins rather…

We strengthen the notion of "double samplers", first introduced by Dinur and Kaufman [Proc. 58th FOCS, 2017], which are samplers with additional combinatorial properties, and whose existence we prove using high dimensional expanders. The…

We introduce a new framework for data denoising, partially inspired by martingale optimal transport. For a given noisy distribution (the data), our approach involves finding the closest distribution to it among all distributions which 1)…

Understanding and predicting mobility dynamics in transportation networks is critical for infrastructure planning, resilience analysis, and traffic management. Traditional graph-based models typically assume memoryless movement, limiting…

Conventional unsupervised hashing methods usually take advantage of similarity graphs, which are either pre-computed in the high-dimensional space or obtained from random anchor points. On the one hand, existing methods uncouple the…

By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in \cite{BeiglbockHenry…

When training large models, such as neural networks, the full derivatives of order 2 and beyond are usually inaccessible, due to their computational cost. Therefore, among the second-order optimization methods, it is common to bypass the…

We provide a framework to approximate the 2-Wasserstein distance and the optimal transport map, amenable to efficient training as well as statistical and geometric analysis. With the quadratic cost and considering the Kantorovich dual form…

Deep neural networks (DNNs) trained for image denoising are able to generate high-quality samples with score-based reverse diffusion algorithms. These impressive capabilities seem to imply an escape from the curse of dimensionality, but…

Graph spanners are fundamental graph structures with a wide range of applications in distributed networks. We consider a standard synchronous message passing model where in each round $O(\log n)$ bits can be transmitted over every edge (the…

Entropic Brenier maps are regularized analogues of Brenier maps (optimal transport maps) which converge to Brenier maps as the regularization parameter shrinks. In this work, we prove quantitative stability bounds between entropic Brenier…

We present a method for training a neural network to perform image denoising without access to clean training examples or access to paired noisy training examples. Our method requires only a single noisy realization of each training example…

We study the optimal transport problem in the Euclidean space where the cost function is given by the value function associated with a Linear Quadratic minimization problem. Under appropriate assumptions, we generalize Brenier's Theorem…

We consider a decision network on an undirected graph in which each node corresponds to a decision variable, and each node and edge of the graph is associated with a reward function whose value depends only on the variables of the…

Recently, a new decoding rule called jar decoding was proposed; under jar decoding, a non-asymptotic achievable tradeoff between the coding rate and word error probability was also established for any discrete input memoryless channel with…

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast…