相关论文: Difference of Submodular Minimization via DC Progr…
In this paper, the optimization problem of the supervised distance preserving projection (SDPP) for data dimension reduction (DR) is considered, which is equivalent to a rank constrained least squares semidefinite programming (RCLSSDP). In…
Many combinatorial problems arising in machine learning can be reduced to the problem of minimizing a submodular function. Submodular functions are a natural discrete analog of convex functions, and can be minimized in strongly polynomial…
In this article, we focus on solving a class of distributed optimization problems involving $n$ agents with the local objective function at every agent $i$ given by the difference of two convex functions $f_i$ and $g_i$…
Submodular functions are relevant to machine learning for at least two reasons: (1) some problems may be expressed directly as the optimization of submodular functions and (2) the lovasz extension of submodular functions provides a useful…
The difference-of-convex (DC) program is an important model in nonconvex optimization due to its structure, which encompasses a wide range of practical applications. In this paper, we aim to tackle a generalized class of DC programs, where…
Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…
Dimensionality reduction is a classical technique widely used for data analysis. One foundational instantiation is Principal Component Analysis (PCA), which minimizes the average reconstruction error. In this paper, we introduce the…
We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…
We present the Multi-Block DC (BDC) class, a rich class of structured nonconvex functions that admit a DC ("difference-of-convex") decomposition across parameter blocks. This multi-block class not only subsumes the usual DC programming, but…
Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…
In this work, we study decentralized convex constrained optimization problems in networks. We focus on the dual averaging-based algorithmic framework that is well-documented to be superior in handling constraints and complex communication…
We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and…
We introduce a new approach to decomposable submodular function minimization (DSFM) that exploits incidence relations. Incidence relations describe which variables effectively influence the component functions, and when properly utilized,…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
A wide range of fundamental machine learning tasks that are addressed by the maximum a posteriori estimation can be reduced to a general minimum conical hull problem. The best-known solution to tackle general minimum conical hull problems…
We propose a new approach to perform the boosted difference of convex functions algorithm (BDCA) on non-smooth and non-convex problems involving the difference of convex (DC) functions. The recently proposed BDCA uses an extrapolation step…
Principal Component Analysis (PCA) is known to be the most widely applied dimensionality reduction approach. A lot of improvements have been done on the traditional PCA, in order to obtain optimal results in the dimensionality reduction of…
This paper introduces an efficient perturbed difference-of-convex algorithm (pDCA) for computing d-stationary points of an important class of structured nonsmooth difference-of-convex problems. Compared to the principal algorithms…
DR-submodular continuous functions are important objectives with wide real-world applications spanning MAP inference in determinantal point processes (DPPs), and mean-field inference for probabilistic submodular models, amongst others.…
In dual decomposition, the dual to an optimization problem with a specific structure is solved in distributed fashion using (sub)gradient and recently also fast gradient methods. The traditional dual decomposition suffers from two main…