We present a new algorithm for amortized inference in sparse probabilistic graphical models (PGMs), which we call $\Delta$-amortized inference ($\Delta$-AI). Our approach is based on the observation that when the sampling of variables in a PGM is seen as a sequence of actions taken by an agent, sparsity of the PGM enables local credit assignment in the agent's policy learning objective. This yields a local constraint that can be turned into a local loss in the style of generative flow networks (GFlowNets) that enables off-policy training but avoids the need to instantiate all the random variables for each parameter update, thus speeding up training considerably. The $\Delta$-AI objective matches the conditional distribution of a variable given its Markov blanket in a tractable learned sampler, which has the structure of a Bayesian network, with the same conditional distribution under the target PGM. As such, the trained sampler recovers marginals and conditional distributions of interest and enables inference of partial subsets of variables. We illustrate $\Delta$-AI's effectiveness for sampling from synthetic PGMs and training latent variable models with sparse factor structure.

In estimation theory, the Kushner equation provides the evolution of the probability density of the state of a dynamical system given continuous-time observations. Building upon our recent work, we propose a new way to approximate the solution of the Kushner equation through tractable variational Gaussian approximations of two proximal losses associated with the propagation and Bayesian update of the probability density. The first is a proximal loss based on the Wasserstein metric and the second is a proximal loss based on the Fisher metric. The solution to this last proximal loss is given by implicit updates on the mean and covariance that we proposed earlier. These two variational updates can be fused and shown to satisfy a set of stochastic differential equations on the Gaussian's mean and covariance matrix. This Gaussian flow is consistent with the Kalman-Bucy and Riccati flows in the linear case and generalize them in the nonlinear one.

In Simulation-based Inference, the goal is to solve the inverse problem when the likelihood is only known implicitly. Neural Posterior Estimation commonly fits a normalized density estimator as a surrogate model for the posterior. This formulation cannot easily fit unnormalized surrogates because it optimizes the Kullback-Leibler divergence. We propose to optimize a generalized Kullback-Leibler divergence that accounts for the normalization constant in unnormalized distributions. The objective recovers Neural Posterior Estimation when the model class is normalized and unifies it with Neural Ratio Estimation, combining both into a single objective. We investigate a hybrid model that offers the best of both worlds by learning a normalized base distribution and a learned ratio. We also present benchmark results.

Point processes offer a versatile framework for sequential event modeling. However, the computational challenges and constrained representational power of the existing point process models have impeded their potential for wider applications. This limitation becomes especially pronounced when dealing with event data that is associated with multi-dimensional or high-dimensional marks such as texts or images. To address this challenge, this study proposes a novel event generative framework for modeling point processes with high-dimensional marks. We aim to capture the distribution of events without explicitly specifying the conditional intensity or probability density function. Instead, we use a conditional generator that takes the history of events as input and generates the high-quality subsequent event that is likely to occur given the prior observations. The proposed framework offers a host of benefits, including considerable representational power to capture intricate dynamics in multi- or even high-dimensional event space, as well as exceptional efficiency in learning the model and generating samples. Our numerical results demonstrate superior performance compared to other state-of-the-art baselines.

In this paper, we introduce an innovative approach for addressing Bayesian inverse problems through the utilization of physics-informed invertible neural networks (PI-INN). The PI-INN framework encompasses two sub-networks: an invertible neural network (INN) and a neural basis network (NB-Net). The primary role of the NB-Net lies in modeling the spatial basis functions characterizing the solution to the forward problem dictated by the underlying partial differential equation. Simultaneously, the INN is designed to partition the parameter vector linked to the input physical field into two distinct components: the expansion coefficients representing the forward problem solution and the Gaussian latent noise. If the forward mapping is precisely estimated, and the statistical independence between expansion coefficients and latent noise is well-maintained, the PI-INN offers a precise and efficient generative model for Bayesian inverse problems, yielding tractable posterior density estimates. As a particular physics-informed deep learning model, the primary training challenge for PI-INN centers on enforcing the independence constraint, which we tackle by introducing a novel independence loss based on estimated density. We support the efficacy and precision of the proposed PI-INN through a series of numerical experiments, including inverse kinematics, 1-dimensional and 2-dimensional diffusion equations, and seismic traveltime tomography. Specifically, our experimental results showcase the superior performance of the proposed independence loss in comparison to the commonly used but computationally demanding kernel-based maximum mean discrepancy loss.

The fast growth of social networks and their data access limitations in recent years has led to increasing difficulty in obtaining the complete topology of these networks. However, diffusion information over these networks is available, and many algorithms have been proposed to infer the underlying networks using this information. The previously proposed algorithms only focus on inferring more links and ignore preserving the critical topological characteristics of the underlying social networks. In this paper, we propose a novel method called DANI to infer the underlying network while preserving its structural properties. It is based on the Markov transition matrix derived from time series cascades, as well as the node-node similarity that can be observed in the cascade behavior from a structural point of view. In addition, the presented method has linear time complexity (increases linearly with the number of nodes, number of cascades, and square of the average length of cascades), and its distributed version in the MapReduce framework is also scalable. We applied the proposed approach to both real and synthetic networks. The experimental results showed that DANI has higher accuracy and lower run time while maintaining structural properties, including modular structure, degree distribution, connected components, density, and clustering coefficients, than well-known network inference methods.

Despite the remarkable advances in language modeling, current mainstream decoding methods still struggle to generate texts that align with human texts across different aspects. In particular, sampling-based methods produce less-repetitive texts which are often disjunctive in discourse, while search-based methods maintain topic coherence at the cost of increased repetition. Overall, these methods fall short in achieving holistic alignment across a broad range of aspects. In this work, we frame decoding from a language model as an optimization problem with the goal of strictly matching the expected performance with human texts measured by multiple metrics of desired aspects simultaneously. The resulting decoding distribution enjoys an analytical solution that scales the input language model distribution via a sequence-level energy function defined by these metrics. And most importantly, we prove that this induced distribution is guaranteed to improve the perplexity on human texts, which suggests a better approximation to the underlying distribution of human texts. To facilitate tractable sampling from this globally normalized distribution, we adopt the Sampling-Importance-Resampling technique. Experiments on various domains and model scales demonstrate the superiority of our method in metrics alignment with human texts and human evaluation over strong baselines.

We present a sequential Bayesian learning method for tracking non-stationary signal-to-noise ratios in LDPC codes using probabilistic graphical models. We represent the LDPC code as a cluster graph using a general purpose cluster graph construction algorithm called the layered trees running intersection property (LTRIP) algorithm. The channel noise estimator is a global Gamma cluster, which we extend to allow for Bayesian tracking of non-stationary noise variation. We evaluate our proposed model on real-world 5G drive test data. Our results show that our model is capable of tracking non-stationary channel noise, which outperforms an LDPC code with a fixed knowledge of the actual average channel noise.

The cold posterior effect (CPE) (Wenzel et al., 2020) in Bayesian deep learning shows that, for posteriors with a temperature T < 1, the resulting posterior predictive could have better performances than the Bayesian posterior (T = 1). As the Bayesian posterior is known to be optimal under perfect model specification, many recent works have studied the presence of CPE as a model misspecification problem, arising from the prior and/or from the likelihood function. In this work, we provide a more nuanced understanding of the CPE as we show that misspecification leads to CPE only when the resulting Bayesian posterior underfits. In fact, we theoretically show that if there is no underfitting, there is no CPE. In Bayesian deep learning, the cold posterior effect (CPE) (Wenzel et al., 2020) refers to the phenomenon in which if we artificially "temper" the posterior by either p(θ|D) (p(D|θ)p(θ)) The discovery of the CPE has sparked debates in the community about its potential contributing factors. If the prior and likelihood are properly specified, the Bayesian solution (i.e., T = 1) should be optimal (Gelman et al., 2013), assuming approximate inference is properly working. Hence, the presence of the CPE implies either the prior (Wenzel et al., 2020; Fortuin et al., 2022), the likelihood (Aitchison, 2021; Kapoor et al., 2022), or both are misspecified. This has been, so far, the main argument of many works trying to explain the CPE. One line of research examines the impact of the prior misspecification on the CPE (Wenzel et al., 2020; Fortuin et al., 2022). The priors of modern Bayesian neural networks are often selected for tractability. Consequently, the quality of the selected priors in relation to the CPE is a natural concern.

We present VBPI-Mixtures, an algorithm designed to enhance the accuracy of phylogenetic posterior distributions, particularly for tree-topology and branchlength approximations. Despite the Variational Bayesian Phylogenetic Inference (VBPI), a leading-edge black-box variational inference (BBVI) framework, achieving remarkable approximations of these distributions, the multimodality of the tree-topology posterior presents a formidable challenge to sampling-based learning techniques such as BBVI. Advanced deep learning methodologies such as normalizing flows and graph neural networks have been explored to refine the branch-length posterior approximation, yet efforts to ameliorate the posterior approximation over tree topologies have been lacking. As a result, VBPI-Mixtures is capable of capturing distributions over tree-topologies that VBPI fails to model. We deliver state-ofthe-art performance on difficult density estimation tasks across numerous real phylogenetic datasets. Phylogenetic inference has a wide range of applications in various fields, such as molecular evolution, epidemiology, ecology, and tumor progression, making it an essential tool for modern evolutionary research. Bayesian phylogenetics allows researchers to reason about uncertainty in their findings about the evolutionary relationship between species. The posterior distribution over phylogenetic trees given the species data is, however, challenging to infer, since the latent space is a Cartesian product of the discrete tree-topology space and the continuous branch-length space. Furthermore, the cardinality of the tree-topology space grows as a double factorial of the number of species (taxa), making the marginal likelihood computationally intractable in most interesting problem settings.