Related papers: A Compact Linear Programming Relaxation for Binary…
This paper introduces a general multi-class approach to weakly supervised classification. Inferring the labels and learning the parameters of the model is usually done jointly through a block-coordinate descent algorithm such as…
In the era of deep learning, loss functions determine the range of tasks available to models and algorithms. To support the application of deep learning in multi-label classification (MLC) tasks, we propose the ZLPR (zero-bounded…
In this paper we address the problem of finding the most probable state of a discrete Markov random field (MRF), also known as the MRF energy minimization problem. The task is known to be NP-hard in general and its practical importance…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
Energy minimization algorithms, such as graph cuts, enable the computation of the MAP solution under certain probabilistic models such as Markov random fields. However, for many computer vision problems, the MAP solution under the model is…
Given labeled points in a high-dimensional vector space, we seek a low-dimensional subspace such that projecting onto this subspace maintains some prescribed distance between points of differing labels. Intended applications include…
We consider the general polynomial optimization problem $P: f^*=\min \{f(x)\,:\,x\in K\}$ where $K$ is a compact basic semi-algebraic set. We first show that the standard Lagrangian relaxation yields a lower bound as close as desired to the…
Multi-label recognition with partial labels (MLR-PL), in which only some labels are known while others are unknown for each image, is a practical task in computer vision, since collecting large-scale and complete multi-label datasets is…
This work addresses the challenge of training supervised machine or deep learning models on orbiting platforms where we are generally constrained by limited on-board hardware capabilities and restricted uplink bandwidths to upload. We aim…
In this paper, we propose some new semidefinite relaxations for a class of nonconvex complex quadratic programming problems, which widely appear in the areas of signal processing and power system. By deriving new valid constraints to the…
We develop a general framework for MAP estimation in discrete and Gaussian graphical models using Lagrangian relaxation techniques. The key idea is to reformulate an intractable estimation problem as one defined on a more tractable graph,…
An enhanced label propagation (LP) method called GraphHop was proposed recently. It outperforms graph convolutional networks (GCNs) in the semi-supervised node classification task on various networks. Although the performance of GraphHop…
We present the first method to handle curvature regularity in region-based image segmentation and inpainting that is independent of initialization. To this end we start from a new formulation of length-based optimization schemes, based on…
This two-part paper is concerned with the problem of minimizing a linear objective function subject to a bilinear matrix inequality (BMI) constraint. In this part, we first consider a family of convex relaxations which transform BMI…
In recent years, bilevel approaches have become very popular to efficiently estimate high-dimensional hyperparameters of machine learning models. However, to date, binary parameters are handled by continuous relaxation and rounding…
Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…
Fully connected layers are a primary source of memory and computational overhead in deep neural networks due to their dense, often redundant parameterization. While various compression techniques exist, they frequently introduce complex…
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)…
A linear programming (LP) based framework is presented for obtaining converses for finite blocklength lossy joint source-channel coding problems. The framework applies for any loss criterion, generalizes certain previously known converses,…
In this chapter, an integer linear programming formulation for the problem of obtaining task-relevant, multi-resolution, environment abstractions for resource-constrained autonomous agents is presented. The formulation leverages concepts…