Acceleration of MCMC-based algorithms using reconfigurable logic

Monte Carlo (MC) methods such as Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) have emerged as popular tools to sample from high dimensional probability distributions. Because these algorithms can draw samples effectively from arbitrary distributions in Bayesian inference problems, they have been widely used in a range of statistical applications. However, they are often too time consuming due to the prohibitive costly likelihood evaluations, thus they cannot be practically applied to complex models with large-scale datasets. Currently, the lack of sufficiently fast MCMC methods limits their applicability in many modern applications such as genetics and machine learning, and this situation is bound to get worse given the increasing adoption of big data in many fields. The objective of this dissertation is to develop, design and build efficient hardware architectures for MCMC-based algorithms on Field Programmable Gate Arrays (FPGAs), and thereby bring them closer to practical applications. The contributions of this work include: 1) Novel parallel FPGA architectures of the state-of-the-art resampling algorithms for SMC methods. The proposed architectures allow for parallel implementations and thus improve the processing speed. 2) A novel mixed precision MCMC algorithm, along with a tailored FPGA architecture. The proposed design allows for more parallelism and achieves low latency for a given set of hardware resources, while still guaranteeing unbiased estimates. 3) A new variant of subsampling MCMC method based on unequal probability sampling, along with a highly optimized FPGA architecture. The proposed method significantly reduces off-chip memory access and achieves high accuracy in estimates for a given time budget. This work has resulted in the development of hardware accelerators of MCMC and SMC for very large-scale Bayesian tasks by applying the above techniques. Notable speed improvements compared to the respective state-of-the-art CPU and GPU implementations have been achieved in this work.Open Acces

Speeding up MCMC by Efficient Data Subsampling

We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for n observations is estimated from a random subset of m observations. We introduce a general and highly efficient unbiased estimator of the log-likelihood based on control variates obtained from clustering the data. The cost of computing the log-likelihood estimator is much smaller than that of the full log-likelihood used by standard MCMC. The likelihood estimate is bias-corrected and used in two correlated pseudo-marginal algorithms to sample from a perturbed posterior, for which we derive the asymptotic error with respect to n and m, respectively. A practical estimator of the error is proposed and we show that the error is negligible even for a very small m in our applications. We demonstrate that Subsampling MCMC is substantially more efficient than standard MCMC in terms of sampling efficiency for a given computational budget, and that it outperforms other subsampling methods for MCMC proposed in the literature

Speeding Up MCMC by Efficient Data Subsampling

We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for $n$ observations is estimated from a random subset of $m$ observations. We introduce a highly efficient unbiased estimator of the log-likelihood based on control variates, such that the computing cost is much smaller than that of the full log-likelihood in standard MCMC. The likelihood estimate is bias-corrected and used in two dependent pseudo-marginal algorithms to sample from a perturbed posterior, for which we derive the asymptotic error with respect to $n$ and $m$, respectively. We propose a practical estimator of the error and show that the error is negligible even for a very small $m$ in our applications. We demonstrate that Subsampling MCMC is substantially more efficient than standard MCMC in terms of sampling efficiency for a given computational budget, and that it outperforms other subsampling methods for MCMC proposed in the literature.Comment: Main changes: The theory has been significantly revise

Natively probabilistic computation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Brain and Cognitive Sciences, 2009.Includes bibliographical references (leaves 129-135).I introduce a new set of natively probabilistic computing abstractions, including probabilistic generalizations of Boolean circuits, backtracking search and pure Lisp. I show how these tools let one compactly specify probabilistic generative models, generalize and parallelize widely used sampling algorithms like rejection sampling and Markov chain Monte Carlo, and solve difficult Bayesian inference problems. I first introduce Church, a probabilistic programming language for describing probabilistic generative processes that induce distributions, which generalizes Lisp, a language for describing deterministic procedures that induce functions. I highlight the ways randomness meshes with the reflectiveness of Lisp to support the representation of structured, uncertain knowledge, including nonparametric Bayesian models from the current literature, programs for decision making under uncertainty, and programs that learn very simple programs from data. I then introduce systematic stochastic search, a recursive algorithm for exact and approximate sampling that generalizes a popular form of backtracking search to the broader setting of stochastic simulation and recovers widely used particle filters as a special case. I use it to solve probabilistic reasoning problems from statistical physics, causal reasoning and stereo vision. Finally, I introduce stochastic digital circuits that model the probability algebra just as traditional Boolean circuits model the Boolean algebra.(cont.) I show how these circuits can be used to build massively parallel, fault-tolerant machines for sampling and allow one to efficiently run Markov chain Monte Carlo methods on models with hundreds of thousands of variables in real time. I emphasize the ways in which these ideas fit together into a coherent software and hardware stack for natively probabilistic computing, organized around distributions and samplers rather than deterministic functions. I argue that by building uncertainty and randomness into the foundations of our programming languages and computing machines, we may arrive at ones that are more powerful, flexible and efficient than deterministic designs, and are in better alignment with the needs of computational science, statistics and artificial intelligence.by Vikash Kumar Mansinghka.Ph.D