Related papers: The only admissible way of merging arbitrary e-val…
We use valid inequalities (cuts) of the binary integer program for winner determination in a combinatorial auction (CA) as "artificial items" that can be interpreted intuitively and priced to generate Artificial Walrasian Equilibria. We…
Let $G$ be a simple graph with the Laplacian matrix $L(G)$ and let $e(G)$ be the number of edges of $G$. A conjecture by Brouwer and a conjecture by Grone and Merris state that the sum of the $k$ largest Laplacian eigenvalues of $G$ is at…
We study a two-alternative voting game where voters' preferences depend on an unobservable world state and each voter receives a private signal correlated to the true world state. We consider the collective decision when voters can…
Model merging under unseen test-time distribution shifts often renders naive strategies, such as mean averaging unreliable. This challenge is especially acute in medical imaging, where models are fine-tuned locally at clinics on private…
The averaged alternating modified reflections (AAMR) method is a projection algorithm for finding the closest point in the intersection of convex sets to any arbitrary point in a Hilbert space. This method can be seen as an adequate…
We consider redundant binary joint digital expansions of integer vectors. The redundancy is used to minimize the Hamming weight, i.e., the number of nonzero digit vectors. This leads to efficient linear combination algorithms in abelian…
The estimation of normalizing constants is a fundamental step in probabilistic model comparison. Sequential Monte Carlo methods may be used for this task and have the advantage of being inherently parallelizable. However, the standard…
We apply the Min-Sum message-passing protocol to solve the consensus problem in distributed optimization. We show that while the ordinary Min-Sum algorithm does not converge, a modified version of it known as Splitting yields convergence to…
Training large neural networks and merging task-specific models both exploit low-rank structure and require parameter importance estimation, yet these challenges have been pursued in isolation. Current workflows compute curvature…
Compared to p-values, e-values provably guarantee safe, valid inference. If the goal is to test multiple hypotheses simultaneously, one can construct e-values for each individual test and then use the recently developed e-BH procedure to…
Optimal transport on a graph focuses on finding the most efficient way to transfer resources from one distribution to another while considering the graph's structure. This paper introduces a new distributed algorithm that solves the optimal…
We show that for any concave utility, the expected utility of an e-variable can only increase after conditioning on a sufficient statistic. The simplest form of the result has an extremely straightforward proof, which follows from a single…
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
Rating aggregation plays a crucial role in various fields, such as product recommendations, hotel rankings, and teaching evaluations. However, traditional averaging methods can be affected by participation bias, where some raters do not…
We show that integrating a polynomial of degree t on an arbitrary simplex (with respect to Lebesgue measure) reduces to evaluating t homogeneous polynomials of degree j = 1, 2,. .. , t, each at a unique point $\xi$ j of the simplex. This…
We propose a distributed algorithm based on Alternating Direction Method of Multipliers (ADMM) to minimize the sum of locally known convex functions using communication over a network. This optimization problem emerges in many applications…
Our previous experiments demonstrated that subsets collections of (short) documents (with several hundred entries) share a common normalized in some way eigenvalue spectrum of combinatorial Laplacian. Based on this insight, we propose a…
Consider a graph whose vertices are colored in one of two colors, say black or white. A white vertex is called integrated if it has at least as many black neighbors as white neighbors, and similarly for a black vertex. The coloring as a…
The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this…
Many real-world problems rely on finding eigenvalues and eigenvectors of a matrix. The power iteration algorithm is a simple method for determining the largest eigenvalue and associated eigenvector of a general matrix. This algorithm relies…