相关论文: Efficient Optimization of Dominant Set Clustering …
We study a stochastic program where the probability distribution of the uncertain problem parameters is unknown and only indirectly observed via finitely many correlated samples generated by an unknown Markov chain with $d$ states. We…
In this project, we reviewed a paper that deals graph-structured convex optimization (GSCO) problem with the approximate Frank-Wolfe (FW) algorithm. We analyzed and implemented the original algorithm and introduced some extensions based on…
We propose a novel generalization of the conditional gradient (CG / Frank-Wolfe) algorithm for minimizing a smooth function $f$ under an intersection of compact convex sets, using a first-order oracle for $\nabla f$ and linear minimization…
We present a new proximal bundle method for Maximum-A-Posteriori (MAP) inference in structured energy minimization problems. The method optimizes a Lagrangean relaxation of the original energy minimization problem using a multi plane…
Model merging has emerged as a promising approach for multi-task learning (MTL), offering a data-efficient alternative to conventional fine-tuning. However, with the rapid development of the open-source AI ecosystem and the increasing…
We demonstrate how to scalably solve a class of constrained self-concordant minimization problems using linear minimization oracles (LMO) over the constraint set. We prove that the number of LMO calls of our method is nearly the same as…
Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning. In theory, under certain conditions, this problem can be…
Clustering is a crucial component of many data mining systems involving the analysis and exploration of various data. Data diversity calls for clustering algorithms to be accurate while providing stable (i.e., deterministic and robust)…
We consider convex optimization problems which are widely used as convex relaxations for low-rank matrix recovery problems. In particular, in several important problems, such as phase retrieval and robust PCA, the underlying assumption in…
Clustering (or community detection) on multilayer graphs poses several additional complications with respect to standard graphs as different layers may be characterized by different structures and types of information. One of the major…
We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…
We present and analyze a new generalized Frank-Wolfe method for the composite optimization problem $(P):{\min}_{x\in\mathbb{R}^n}\; f(\mathsf{A} x) + h(x)$, where $f$ is a $\theta$-logarithmically-homogeneous self-concordant barrier,…
We consider the problem of learning a high-dimensional but low-rank matrix from a large-scale dataset distributed over several machines, where low-rankness is enforced by a convex trace norm constraint. We propose DFW-Trace, a distributed…
We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…
We consider smooth convex minimization over compact convex sets, i.e., $\min_{x \in C} f(x)$ with the (vanilla) Frank-Wolfe algorithm. Well-known lower bounds establish a worst-case $\Omega(1/t)$ primal-gap barrier in the general smooth…
Recently ensemble selection for consensus clustering has emerged as a research problem in Machine Intelligence. Normally consensus clustering algorithms take into account the entire ensemble of clustering, where there is a tendency of…
In this paper, we study the problem of finding the Euclidean distance to a convex cone generated by a set of discrete points in $\mathbb{R}^n_+$. In particular, we are interested in problems where the discrete points are the set of feasible…
We present two first-order primal-dual algorithms for solving saddle point formulations of linear programs, namely FWLP (Frank-Wolfe Linear Programming) and FWLP-P. The former iteratively applies the Frank-Wolfe algorithm to both the primal…
Suppose an agent is in a (possibly unknown) Markov Decision Process in the absence of a reward signal, what might we hope that an agent can efficiently learn to do? This work studies a broad class of objectives that are defined solely as…
Algorithms for clustering points in metric spaces is a long-studied area of research. Clustering has seen a multitude of work both theoretically, in understanding the approximation guarantees possible for many objective functions such as…