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We derive approximation algorithms for the nonnegative matrix factorization problem, i.e. the problem of factorizing a matrix as the product of two matrices with nonnegative coefficients. We form convex approximations of this problem which…
I describe how real quantum annealers may be used to perform local (in state space) searches around specified states, rather than the global searches traditionally implemented in the quantum annealing algorithm. Such protocols will have…
D-Wave quantum annealers represent a novel computational architecture and have attracted significant interest, but have been used for few real-world computations. Machine learning has been identified as an area where quantum annealing may…
The aim of this paper is to solve linear semidefinite programs arising from higher-order Lasserre relaxations of unconstrained binary quadratic optimization problems. For this we use an interior point method with a preconditioned conjugate…
In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on…
Classical and quantum annealing are computing paradigms that have been proposed to solve a wide range of optimization problems. In this paper, we aim to enhance the performance of annealing algorithms by introducing the technique of…
In the rapidly advancing domain of quantum optimization, the confluence of quantum algorithms such as Quantum Annealing (QA) and the Quantum Approximate Optimization Algorithm (QAOA) with robust optimization methodologies presents a…
Clustering is a powerful machine learning technique that groups "similar" data points based on their characteristics. Many clustering algorithms work by approximating the minimization of an objective function, namely the sum of…
Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and…
Matrix factorization techniques have been widely used as a method for collaborative filtering for recommender systems. In recent times, different variants of deep learning algorithms have been explored in this setting to improve the task of…
Noisy intermediate-scale quantum (NISQ) devices are spearheading the second quantum revolution. Of these, quantum annealers are the only ones currently offering real world, commercial applications on as many as 5000 qubits. The size of…
The increasing size of transformer-based models in NLP makes the question of compressing them important. In this work, we present a comprehensive analysis of factorization based model compression techniques. Specifically, we focus on…
A collaborative convex framework for factoring a data matrix $X$ into a non-negative product $AS$, with a sparse coefficient matrix $S$, is proposed. We restrict the columns of the dictionary matrix $A$ to coincide with certain columns of…
Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…
We propose a method for low-rank semidefinite programming in application to the semidefinite relaxation of unconstrained binary quadratic problems. The method improves an existing solution of the semidefinite programming relaxation to…
Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks. The study of its fundamental…
Quantum annealing was originally proposed as an approach for solving combinatorial optimisation problems using quantum effects. D-Wave Systems has released a production model of quantum annealing hardware. However, the inherent noise and…
There have been multiple attempts to demonstrate that quantum annealing and, in particular, quantum annealing on quantum annealing machines, has the potential to outperform current classical optimization algorithms implemented on CMOS…
Nonnegative matrix factorization (NMF) has become a very popular technique in machine learning because it automatically extracts meaningful features through a sparse and part-based representation. However, NMF has the drawback of being…
We solve robot trajectory planning problems at industry-relevant scales. Our end-to-end solution integrates highly versatile random-key algorithms with model stacking and ensemble techniques, as well as path relinking for solution…