We propose a new framework for how to use sequential Monte Carlo (SMC) algorithms for inference in probabilistic graphical models (PGM). Via a sequential decomposition of the PGM we find a sequence of auxiliary distributions defined on a monotonically increasing sequence of probability spaces. By targeting these auxiliary distributions using SMC we are able to approximate the full joint distribution defined by the PGM. One of the key merits of the SMC sampler is that it provides an unbiased estimate of the partition function of the model. We also show how it can be used within a particle Markov chain Monte Carlo framework in order to construct high-dimensional block-sampling algorithms for general PGMs.

EDIT: After reading the author's rebuttal, I changed my assessment of the paper to an accept. The paper is well written and it does a good job at explaining the intuition behind the proposed algorithm. I appreciated the inclusion of the small dimensional toy example as it illustrates in a simple and clear manner the adaptability property of the algorithm. My main concern with the proposed algorithm is that, in my opinion, it is most suitable for small dimensional problems only. The provided examples further justify my impression given that posterior distribution to sample from is of reduced dimension. Consequently, I'm having a hard time justifying the interest of the ML community with respect to the proposed sampling algorithm considering its perceived limited scope.

We propose a novel method for scalable parallelization of SMC algorithms, Entangled Monte Carlo simulation (EMC). EMC avoids the transmission of particles between nodes, and instead reconstructs them from the particle genealogy. In particular, we show that we can reduce the communication to the particle weights for each machine while efficiently maintaining implicit global coherence of the parallel simulation. We explain methods to efficiently maintain a genealogy of particles from which any particle can be reconstructed. We demonstrate using examples from Bayesian phylogenetic that the computational gain from parallelization using EMC significantly outweighs the cost of particle reconstruction. The timing experiments show that reconstruction of particles is indeed much more efficient as compared to transmission of particles.

We propose a new framework for how to use sequential Monte Carlo (SMC) algorithms for inference in probabilistic graphical models (PGM). Via a sequential decomposition of the PGM we find a sequence of auxiliary distributions defined on a monotonically increasing sequence of probability spaces. By targeting these auxiliary distributions using SMC we are able to approximate the full joint distribution defined by the PGM. One of the key merits of the SMC sampler is that it provides an unbiased estimate of the partition function of the model. We also show how it can be used within a particle Markov chain Monte Carlo framework in order to construct high-dimensional block-sampling algorithms for general PGMs.

Sampling from a target probability distribution whose density is known up to a normalization constant is a fundamental task in computational statistics and machine learning. It can be naturally formulated as optimizing a functional measuring the dissimilarity to the target probability distribution, typically the Kullback-Leibler (KL) divergence. From there, it is natural to consider optimization schemes over the space of probability distributions, to design a sequence of distributions approximating the target one. Depending on the chosen geometry over the search space and the time discretization, one may obtain different schemes. For instance, one possible framework is to restrict the search space to the Wasserstein space, i.e. probability distributions with bounded second moments equipped with the Wasserstein-2 distance (Ambrosio et al., 2008). The latter is equipped with a rich Riemannian structure (Otto and Villani, 2000) that enables to define Wasserstein-2 gradient flows, i.e. paths of distributions decreasing the objective functional of steepest descent according to this metric. It is well-known that the Wasserstein gradient flow of the KL can be implemented by a Langevin diffusion on the ambient space (Jordan et al., 1998) and easily discretized in time, resulting in the Langevin Monte Carlo (or Unadjusted Langevin) algorithm (Roberts and Tweedie, 1996). The latter is one of the most famous Markov Chain Monte Carlo (MCMC) algorithms - maybe the most canonical - that generate Markov chains in the ambient space, whose law approximates the target distribution for a large time horizon. Many other time discretizations of the KL Wasserstein gradient flow (Salim et al., 2020; Mou et al., 2021) or its gradient flow with respect to similar optimal transport geometries have been considered in the literature (Liu, 2017; Garbuno-Inigo et al., 2020).

Approximating integrals with respect to a complicated, highdimensional probability distribution π is an important problem spanning multiple disciplines, such as Bayesian statistical inference, machine learning, statistical physics, and theoretical computer science [13, 17]. Sequential Monte Carlo (SMC) methods are a large class of stochastic approximation algorithms designed to solve these problems by combining Markov chain Monte Carlo (MCMC) methods and resampling strategies to sequentially sample from a series of probability distributions. Some examples of SMC algorithms include population Monte Carlo methods [2], annealed importance sampling [27], sequential particle filters [3], and population annealing [40], among many others [15]. Closely related - but purely MCMC - methods include parallel tempering (PT) [14] and simulated tempering (ST) [23], which have been referred to as population-based MCMC methods [15]. An SMC sampler is generally constructed as follows.

A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as expectations with respect to the posterior distribution. The key challenge is to approximate these intractable expectations. In this tutorial, we review sequential Monte Carlo (SMC), a random-sampling-based class of methods for approximate inference. First, we explain the basics of SMC, discuss practical issues, and review theoretical results. We then examine two of the main user design choices: the proposal distributions and the so called intermediate target distributions. We review recent results on how variational inference and amortization can be used to learn efficient proposals and target distributions. Next, we discuss the SMC estimate of the normalizing constant, how this can be used for pseudo-marginal inference and inference evaluation. Throughout the tutorial we illustrate the use of SMC on various models commonly used in machine learning, such as stochastic recurrent neural networks, probabilistic graphical models, and probabilistic programs.

Approximate inference in probabilistic graphical models (PGMs) can be grouped into deterministic methods and Monte-Carlo-based methods. The former can often provide accurate and rapid inferences, but are typically associated with biases that are hard to quantify. The latter enjoy asymptotic consistency, but can suffer from high computational costs. In this paper we present a way of bridging the gap between deterministic and stochastic inference. Specifically, we suggest an efficient sequential Monte Carlo (SMC) algorithm for PGMs which can leverage the output from deterministic inference methods. While generally applicable, we show explicitly how this can be done with loopy belief propagation, expectation propagation, and Laplace approximations. The resulting algorithm can be viewed as a post-correction of the biases associated with these methods and, indeed, numerical results show clear improvements over the baseline deterministic methods as well as over "plain" SMC.

The investment on the stock market is prone to be affected by the Internet. For the purpose of improving the prediction accuracy, we propose a multi-task stock prediction model that not only considers the stock correlations but also supports multi-source data fusion. Our proposed model first utilizes tensor to integrate the multi-sourced data, including financial Web news, investors' sentiments extracted from the social network and some quantitative data on stocks. In this way, the intrinsic relationships among different information sources can be captured, and meanwhile, multi-sourced information can be complemented to solve the data sparsity problem. Secondly, we propose an improved sub-mode coordinate algorithm (SMC). SMC is based on the stock similarity, aiming to reduce the variance of their subspace in each dimension produced by the tensor decomposition. The algorithm is able to improve the quality of the input features, and thus improves the prediction accuracy. And the paper utilizes the Long Short-Term Memory (LSTM) neural network model to predict the stock fluctuation trends. Finally, the experiments on 78 A-share stocks in CSI 100 and thirteen popular HK stocks in the year 2015 and 2016 are conducted. The results demonstrate the improvement on the prediction accuracy and the effectiveness of the proposed model.

Bayesian inference for models that have an intractable partition function is known as a doubly intractable problem, where standard Monte Carlo methods are not applicable. The past decade has seen the development of auxiliary variable Monte Carlo techniques (M{\o}ller et al., 2006; Murray et al., 2006) for tackling this problem; these approaches being members of the more general class of pseudo-marginal, or exact-approximate, Monte Carlo algorithms (Andrieu and Roberts, 2009), which make use of unbiased estimates of intractable posteriors. Everitt et al. (2017) investigated the use of exact-approximate importance sampling (IS) and sequential Monte Carlo (SMC) in doubly intractable problems, but focussed only on SMC algorithms that used data-point tempering. This paper describes SMC samplers that may use alternative sequences of distributions, and describes ways in which likelihood estimates may be improved adaptively as the algorithm progresses, building on ideas from Moores et al. (2015). This approach is compared with a number of alternative algorithms for doubly intractable problems, including approximate Bayesian computation (ABC), which we show is closely related to the method of M{\o}ller et al. (2006).