arXiv subjects

Guangyao Zhou

Publications and source records attributed to Guangyao Zhou.

24 records · Page 2Linked to original sources

arXiv2022

Metropolis Augmented Hamiltonian Monte Carlo

Hamiltonian Monte Carlo (HMC) is a powerful Markov Chain Monte Carlo (MCMC) method for sampling from complex high-dimensional continuous distributions. However, in many situations it is necessary or desirable to combine HMC with other Metropolis-Hastings (MH) samplers. The common HMC-within-Gibbs strategy implies a trade-off between long HMC trajectories and more frequent other MH updates. Addressing this trade-off has been the focus of several recent works. In this paper we propose Metropolis Augmented Hamiltonian Monte Carlo (MAHMC), an HMC variant that allows MH updates within HMC and eliminates this trade-off. Experiments on two representative examples demonstrate MAHMC's efficiency and ease of use when compared with within-Gibbs alternatives.

stat.CO↗

arXiv2021

Graphical Models with Attention for Context-Specific Independence and an Application to Perceptual Grouping

Discrete undirected graphical models, also known as Markov Random Fields (MRFs), can flexibly encode probabilistic interactions of multiple variables, and have enjoyed successful applications to a wide range of problems. However, a well-known yet little studied limitation of discrete MRFs is that they cannot capture context-specific independence (CSI). Existing methods require carefully developed theories and purpose-built inference methods, which limit their applications to only small-scale problems. In this paper, we propose the Markov Attention Model (MAM), a family of discrete MRFs that incorporates an attention mechanism. The attention mechanism allows variables to dynamically attend to some other variables while ignoring the rest, and enables capturing of CSIs in MRFs. A MAM is formulated as an MRF, allowing it to benefit from the rich set of existing MRF inference methods and scale to large models and datasets. To demonstrate MAM's capabilities to capture CSIs at scale, we apply MAMs to capture an important type of CSI that is present in a symbolic approach to recurrent computations in perceptual grouping. Experiments on two recently proposed synthetic perceptual grouping tasks and on realistic images demonstrate the advantages of MAMs in sample-efficiency, interpretability and generalizability when compared with strong recurrent neural network baselines, and validate MAM's capabilities to efficiently capture CSIs at scale.

cs.LG↗

arXiv2021

Prepartition: Load Balancing Approach for Virtual Machine Reservations in a Cloud Data Center

Load balancing is vital for the efficient and long-term operation of cloud data centers. With virtualization, post (reactive) migration of virtual machines after allocation is the traditional way for load balancing and consolidation. However, reactive migration is not easy to obtain predefined load balance objectives and may interrupt services and bring instability. Therefore, we provide a new approach, called Prepartition, for load balancing. It partitions a VM request into a few sub-requests sequentially with start time, end time and capacity demands, and treats each sub-request as a regular VM request. In this way, it can proactively set a bound for each VM request on each physical machine and makes the scheduler get ready before VM migration to obtain the predefined load balancing goal, which supports the resource allocation in a fine-grained manner. Simulations with real-world trace and synthetic data show that Prepartition for offline (PrepartitionOff) scheduling has 10%-20% better performance than the existing load balancing algorithms under several metrics, including average utilization, imbalance degree, makespan and Capacity_makespan. We also extend Prepartition to online load balancing. Evaluation results show that our proposed approach also outperforms existing online algorithms.

cs.DC↗

arXiv2021

Mixed Hamiltonian Monte Carlo for Mixed Discrete and Continuous Variables

Hamiltonian Monte Carlo (HMC) has emerged as a powerful Markov Chain Monte Carlo (MCMC) method to sample from complex continuous distributions. However, a fundamental limitation of HMC is that it can not be applied to distributions with mixed discrete and continuous variables. In this paper, we propose mixed HMC (M-HMC) as a general framework to address this limitation. M-HMC is a novel family of MCMC algorithms that evolves the discrete and continuous variables in tandem, allowing more frequent updates of discrete variables while maintaining HMC's ability to suppress random-walk behavior. We establish M-HMC's theoretical properties, and present an efficient implementation with Laplace momentum that introduces minimal overhead compared to existing HMC methods. The superior performances of M-HMC over existing methods are demonstrated with numerical experiments on Gaussian mixture models (GMMs), variable selection in Bayesian logistic regression (BLR), and correlated topic models (CTMs).

stat.CO↗

arXiv2021

Query Training: Learning a Worse Model to Infer Better Marginals in Undirected Graphical Models with Hidden Variables

Probabilistic graphical models (PGMs) provide a compact representation of knowledge that can be queried in a flexible way: after learning the parameters of a graphical model once, new probabilistic queries can be answered at test time without retraining. However, when using undirected PGMS with hidden variables, two sources of error typically compound in all but the simplest models (a) learning error (both computing the partition function and integrating out the hidden variables is intractable); and (b) prediction error (exact inference is also intractable). Here we introduce query training (QT), a mechanism to learn a PGM that is optimized for the approximate inference algorithm that will be paired with it. The resulting PGM is a worse model of the data (as measured by the likelihood), but it is tuned to produce better marginals for a given inference algorithm. Unlike prior works, our approach preserves the querying flexibility of the original PGM: at test time, we can estimate the marginal of any variable given any partial evidence. We demonstrate experimentally that QT can be used to learn a challenging 8-connected grid Markov random field with hidden variables and that it consistently outperforms the state-of-the-art AdVIL when tested on three undirected models across multiple datasets.

stat.ML↗

arXiv2019

Capacities and the Free Passage of Entropic Barriers

We propose an approach for estimating the probability that a given small target, among many, will be the first to be reached in a molecular dynamics simulation. Reaching small targets out of a vast number of possible configurations constitutes an entropic barrier. Experimental evidence suggests that entropic barriers are ubiquitous in biomolecular systems, and often characterize the rate-limiting step of biomolecular processes. Presumably for the same reasons, they often characterize the rate-limiting step in simulations. To the extent that first-passage probabilities can be computed without requiring direct simulation, the process of traversing entropic barriers can replaced by a single choice from the computed ("first-passage") distribution. We will show that in the presence of certain entropic barriers, first-passage probabilities are approximately invariant to the initial configuration, provided that it is modestly far away from each of the targets. We will further show that as a consequence of this invariance, the first-passage distribution can be well-approximated in terms of "capacities" of local sets around the targets. Using these theoretical results and a Monte Carlo mechanism for approximating capacities, we provide a method for estimating the hitting probabilities of small targets in the presence of entropic barriers. In numerical experiments with an idealized ("golf-course") potential, the estimates are as accurate as the results of direct simulations, but far faster to compute.

physics.comp-ph↗