arXiv subjects

Ali Sheikholeslami

Publications and source records attributed to Ali Sheikholeslami.

4 recordsLinked to original sources

arXiv2026

Adaptive Importance Tempering: A flexible approach to improve computational efficiency of Metropolis Coupled Markov Chain Monte Carlo algorithms on binary spaces

Based on the algorithm Informed Importance Tempering (IIT) proposed by Li et al. (2023) we propose an algorithm that uses an adaptive bounded balancing function. We argue why implementing parallel tempering where each replica uses a rejection free MCMC algorithm can be inefficient in high dimensional spaces and show how the proposed adaptive algorithm can overcome these computational inefficiencies. We present two equivalent versions of the adaptive algorithm (A-IIT and SS-IIT) and establish that both have the same limiting distribution, making either suitable for use within a parallel tempering framework. To evaluate performance, we benchmark the adaptive algorithm against several MCMC methods: IIT, Rejection free Metropolis-Hastings (RF-MH) and RF-MH using a multiplicity list. Simulation results demonstrate that Adaptive IIT identifies high-probability states more efficiently than these competing algorithms in high-dimensional binary spaces with multiple modes.

stat.CO↗

arXiv2022

Sampling via Rejection-Free Partial Neighbor Search

The Metropolis algorithm involves producing a Markov chain to converge to a specified target density $π$. In order to improve its efficiency, we can use the Rejection-Free version of the Metropolis algorithm, which avoids the inefficiency of rejections by evaluating all neighbors. Rejection-Free can be made more efficient through the use of parallelism hardware. However, for some specialized hardware, such as Digital Annealing Unit, the number of units will limit the number of neighbors being considered at each step. Hence, we propose an enhanced version of Rejection-Free known as Partial Neighbor Search, which only considers a portion of the neighbors while using the Rejection-Free technique. This method will be tested on several examples to demonstrate its effectiveness and advantages under different circumstances.

stat.CO↗

arXiv2022

Optimization via Rejection-Free Partial Neighbor Search

Simulated Annealing using Metropolis steps at decreasing temperatures is widely used to solve complex combinatorial optimization problems. In order to improve its efficiency, we can use the Rejection-Free version of the Metropolis algorithm, which avoids the inefficiency of rejections by considering all the neighbors at every step. As a solution to avoid the algorithm from becoming stuck in local extreme areas, we propose an enhanced version of Rejection-Free called Partial Neighbor Search (PNS), which only considers random parts of the neighbors while applying Rejection-Free. We demonstrate the superior performance of the Rejection-Free PNS algorithm by applying these methods to several examples, such as the QUBO question, the Knapsack problem, the 3R3XOR problem, and the quadratic programming.

math.OC↗

arXiv2022

Graph clustering with Boltzmann machines

Graph clustering is the process of grouping vertices into densely connected sets called clusters. We tailor two mathematical programming formulations from the literature, to this problem. In doing so, we obtain a heuristic approximation to the intra-cluster density maximization problem. We use two variations of a Boltzmann machine heuristic to obtain numerical solutions. For benchmarking purposes, we compare solution quality and computational performances to those obtained using a commercial solver, Gurobi. We also compare clustering quality to the clusters obtained using the popular Louvain modularity maximization method. Our initial results clearly demonstrate the superiority of our problem formulations. They also establish the superiority of the Boltzmann machine over the traditional exact solver. In the case of smaller less complex graphs, Boltzmann machines provide the same solutions as Gurobi, but with solution times that are orders of magnitude lower. In the case of larger and more complex graphs, Gurobi fails to return meaningful results within a reasonable time frame. Finally, we also note that both our clustering formulations, the distance minimization and $K$-medoids, yield clusters of superior quality to those obtained with the Louvain algorithm.

cs.LG↗