Related papers: Efficiently Searching for Frustrated Cycles in MAP…

MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network given some evidence. Unlike computing posterior probabilities, or MPE (a special case of MAP), the time and space complexity of…

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…

A large number of computational and scientific methods commonly require decomposing a sparse matrix into triangular factors as LU decomposition. A common problem faced during this decomposition is that even though the given matrix may be…

We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…

Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…

A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…

The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact…

In subspace clustering, a group of data points belonging to a union of subspaces are assigned membership to their respective subspaces. This paper presents a new approach dubbed Innovation Pursuit (iPursuit) to the problem of subspace…

Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…

Scientists in many fields have the common and basic need of dimensionality reduction: visualizing the underlying structure of the massive multivariate data in a low-dimensional space. However, many dimensionality reduction methods confront…

Clustering under pairwise constraints is an important knowledge discovery tool that enables the learning of appropriate kernels or distance metrics to improve clustering performance. These pairwise constraints, which come in the form of…

Considering the worst-case scenario, junction tree algorithm remains the most general solution for exact MAP inference with polynomial run-time guarantees. Unfortunately, its main tractability assumption requires the treewidth of a…

Generative models based on flow matching have attracted significant attention for their simplicity and superior performance in high-resolution image synthesis. By leveraging the instantaneous change-of-variables formula, one can directly…

Correlation clustering is a central topic in unsupervised learning, with many applications in ML and data mining. In correlation clustering, one receives as input a signed graph and the goal is to partition it to minimize the number of…

Markov random fields (MRFs) are a powerful tool for modelling statistical dependencies for a set of random variables using a graphical representation. An important computational problem related to MRFs, called maximum a posteriori (MAP)…

Given a graphical model, one essential problem is MAP inference, that is, finding the most likely configuration of states according to the model. Although this problem is NP-hard, large instances can be solved in practice. A major open…

Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new…

Sparsity is a common issue in many trajectory datasets, including human mobility data. This issue frequently brings more difficulty to relevant learning tasks, such as trajectory imputation and prediction. Nowadays, little existing work…

A Hamiltonian decomposition of a regular graph is a partition of its edge set into Hamiltonian cycles. The problem of finding edge-disjoint Hamiltonian cycles in a given regular graph has many applications in combinatorial optimization and…

We consider the problem of detecting a cycle in a directed graph that grows by arc insertions, and the related problems of maintaining a topological order and the strong components of such a graph. For these problems, we give two…