We propose Continual Repeated Annealed Flow Transport Monte Carlo (CRAFT), a method that combines a sequential Monte Carlo (SMC) sampler (itself a generalization of Annealed Importance Sampling) with variational inference using normalizing flows. The normalizing flows are directly trained to transport between annealing temperatures using a KL divergence for each transition. This optimization objective is itself estimated using the normalizing flow/SMC approximation. We show conceptually and using multiple empirical examples that CRAFT improves on Annealed Flow Transport Monte Carlo (Arbel et al., 2021), on which it builds and also on Markov chain Monte Carlo (MCMC) based Stochastic Normalizing Flows (Wu et al., 2020). By incorporating CRAFT within particle MCMC, we show that such learnt samplers can achieve impressively accurate results on a challenging lattice field theory example.
Many interesting tasks in image restoration can be cast as linear inverse problems. A recent family of approaches for solving these problems uses stochastic algorithms that sample from the posterior distribution of natural images given the measurements. However, efficient solutions often require problem-specific supervised training to model the posterior, whereas unsupervised methods that are not problem-specific typically rely on inefficient iterative methods. This work addresses these issues by introducing Denoising Diffusion Restoration Models (DDRM), an efficient, unsupervised posterior sampling method. Motivated by variational inference, DDRM takes advantage of a pre-trained denoising diffusion generative model for solving any linear inverse problem. We demonstrate DDRM's versatility on several image datasets for super-resolution, deblurring, inpainting, and colorization under various amounts of measurement noise. DDRM outperforms the current leading unsupervised methods on the diverse ImageNet dataset in reconstruction quality, perceptual quality, and runtime, being 5x faster than the nearest competitor. DDRM also generalizes well for natural images out of the distribution of the observed ImageNet training set.
Graph Convolutional Networks (GCNs) have recently attracted vast interest and achieved state-of-the-art performance on graphs, but its success could typically hinge on careful training with amounts of expensive and time-consuming labeled data. To alleviate labeled data scarcity, self-training methods have been widely adopted on graphs by labeling high-confidence unlabeled nodes and then adding them to the training step. In this line, we empirically make a thorough study for current self-training methods on graphs. Surprisingly, we find that high-confidence unlabeled nodes are not always useful, and even introduce the distribution shift issue between the original labeled dataset and the augmented dataset by self-training, severely hindering the capability of self-training on graphs. To this end, in this paper, we propose a novel Distribution Recovered Graph Self-Training framework (DR-GST), which could recover the distribution of the original labeled dataset. Specifically, we first prove the equality of loss function in self-training framework under the distribution shift case and the population distribution if each pseudo-labeled node is weighted by a proper coefficient. Considering the intractability of the coefficient, we then propose to replace the coefficient with the information gain after observing the same changing trend between them, where information gain is respectively estimated via both dropout variational inference and dropedge variational inference in DR-GST. However, such a weighted loss function will enlarge the impact of incorrect pseudo labels. As a result, we apply the loss correction method to improve the quality of pseudo labels. Both our theoretical analysis and extensive experiments on five benchmark datasets demonstrate the effectiveness of the proposed DR-GST, as well as each well-designed component in DR-GST.
As a structured prediction task, scene graph generation aims to build a visually-grounded scene graph to explicitly model objects and their relationships in an input image. Currently, the mean field variational Bayesian framework is the de facto methodology used by the existing methods, in which the unconstrained inference step is often implemented by a message passing neural network. However, such formulation fails to explore other inference strategies, and largely ignores the more general constrained optimization models. In this paper, we present a constrained structure learning method, for which an explicit constrained variational inference objective is proposed. Instead of applying the ubiquitous message-passing strategy, a generic constrained optimization method - entropic mirror descent - is utilized to solve the constrained variational inference step. We validate the proposed generic model on various popular scene graph generation benchmarks and show that it outperforms the state-of-the-art methods.
We propose a general Variational Embedding Learning Framework (VELF) for alleviating the severe cold-start problem in CTR prediction. VELF addresses the cold start problem via alleviating over-fits caused by data-sparsity in two ways: learning probabilistic embedding, and incorporating trainable and regularized priors which utilize the rich side information of cold start users and advertisements (Ads). The two techniques are naturally integrated into a variational inference framework, forming an end-to-end training process. Abundant empirical tests on benchmark datasets well demonstrate the advantages of our proposed VELF. Besides, extended experiments confirmed that our parameterized and regularized priors provide more generalization capability than traditional fixed priors.
We revisit the theory of importance weighted variational inference (IWVI), a promising strategy for learning latent variable models. IWVI uses new variational bounds, known as Monte Carlo objectives (MCOs), obtained by replacing intractable integrals by Monte Carlo estimates -- usually simply obtained via importance sampling. Burda, Grosse and Salakhutdinov (2016) showed that increasing the number of importance samples provably tightens the gap between the bound and the likelihood. Inspired by this simple monotonicity theorem, we present a series of nonasymptotic results that link properties of Monte Carlo estimates to tightness of MCOs. We challenge the rationale that smaller Monte Carlo variance leads to better bounds. We confirm theoretically the empirical findings of several recent papers by showing that, in a precise sense, negative correlation reduces the variational gap. We also generalise the original monotonicity theorem by considering non-uniform weights. We discuss several practical consequences of our theoretical results. Our work borrows many ideas and results from the theory of stochastic orders.
Inference is crucial in modern astronomical research, where hidden astrophysical features and patterns are often estimated from indirect and noisy measurements. Inferring the posterior of hidden features, conditioned on the observed measurements, is essential for understanding the uncertainty of results and downstream scientific interpretations. Traditional approaches for posterior estimation include sampling-based methods and variational inference. However, sampling-based methods are typically slow for high-dimensional inverse problems, while variational inference often lacks estimation accuracy. In this paper, we propose alpha-DPI, a deep learning framework that first learns an approximate posterior using alpha-divergence variational inference paired with a generative neural network, and then produces more accurate posterior samples through importance re-weighting of the network samples. It inherits strengths from both sampling and variational inference methods: it is fast, accurate, and scalable to high-dimensional problems. We apply our approach to two high-impact astronomical inference problems using real data: exoplanet astrometry and black hole feature extraction.
Lesions or organ boundaries visible through medical imaging data are often ambiguous, thus resulting in significant variations in multi-reader delineations, i.e., the source of aleatoric uncertainty. In particular, quantifying the inter-observer variability of manual annotations with Magnetic Resonance (MR) Imaging data plays a crucial role in establishing a reference standard for various diagnosis and treatment tasks. Most segmentation methods, however, simply model a mapping from an image to its single segmentation map and do not take the disagreement of annotators into consideration. In order to account for inter-observer variability, without sacrificing accuracy, we propose a novel variational inference framework to model the distribution of plausible segmentation maps, given a specific MR image, which explicitly represents the multi-reader variability. Specifically, we resort to a latent vector to encode the multi-reader variability and counteract the inherent information loss in the imaging data. Then, we apply a variational autoencoder network and optimize its evidence lower bound (ELBO) to efficiently approximate the distribution of the segmentation map, given an MR image. Experimental results, carried out with the QUBIQ brain growth MRI segmentation datasets with seven annotators, demonstrate the effectiveness of our approach.
Machine learning techniques typically applied to dementia forecasting lack in their capabilities to jointly learn several tasks, handle time dependent heterogeneous data and missing values. In this paper, we propose a framework using the recently presented SSHIBA model for jointly learning different tasks on longitudinal data with missing values. The method uses Bayesian variational inference to impute missing values and combine information of several views. This way, we can combine different data-views from different time-points in a common latent space and learn the relations between each time-point while simultaneously modelling and predicting several output variables. We apply this model to predict together diagnosis, ventricle volume, and clinical scores in dementia. The results demonstrate that SSHIBA is capable of learning a good imputation of the missing values and outperforming the baselines while simultaneously predicting three different tasks.
Traditional recommender systems aim to estimate a user's rating to an item based on observed ratings from the population. As with all observational studies, hidden confounders, which are factors that affect both item exposures and user ratings, lead to a systematic bias in the estimation. Consequently, a new trend in recommender system research is to negate the influence of confounders from a causal perspective. Observing that confounders in recommendations are usually shared among items and are therefore multi-cause confounders, we model the recommendation as a multi-cause multi-outcome (MCMO) inference problem. Specifically, to remedy confounding bias, we estimate user-specific latent variables that render the item exposures independent Bernoulli trials. The generative distribution is parameterized by a DNN with factorized logistic likelihood and the intractable posteriors are estimated by variational inference. Controlling these factors as substitute confounders, under mild assumptions, can eliminate the bias incurred by multi-cause confounders. Furthermore, we show that MCMO modeling may lead to high variance due to scarce observations associated with the high-dimensional causal space. Fortunately, we theoretically demonstrate that introducing user features as pre-treatment variables can substantially improve sample efficiency and alleviate overfitting. Empirical studies on simulated and real-world datasets show that the proposed deep causal recommender shows more robustness to unobserved confounders than state-of-the-art causal recommenders. Codes and datasets are released at https://github.com/yaochenzhu/deep-deconf.
Value function factorization via centralized training and decentralized execution is promising for solving cooperative multi-agent reinforcement tasks. One of the approaches in this area, QMIX, has become state-of-the-art and achieved the best performance on the StarCraft II micromanagement benchmark. However, the monotonic-mixing of per agent estimates in QMIX is known to restrict the joint action Q-values it can represent, as well as the insufficient global state information for single agent value function estimation, often resulting in suboptimality. To this end, we present LSF-SAC, a novel framework that features a variational inference-based information-sharing mechanism as extra state information to assist individual agents in the value function factorization. We demonstrate that such latent individual state information sharing can significantly expand the power of value function factorization, while fully decentralized execution can still be maintained in LSF-SAC through a soft-actor-critic design. We evaluate LSF-SAC on the StarCraft II micromanagement challenge and demonstrate that it outperforms several state-of-the-art methods in challenging collaborative tasks. We further set extensive ablation studies for locating the key factors accounting for its performance improvements. We believe that this new insight can lead to new local value estimation methods and variational deep learning algorithms. A demo video and code of implementation can be found at https://sites.google.com/view/sacmm.
In this work we use variational inference to quantify the degree of uncertainty in deep learning model predictions of radio galaxy classification. We show that the level of model posterior variance for individual test samples is correlated with human uncertainty when labelling radio galaxies. We explore the model performance and uncertainty calibration for different weight priors and suggest that a sparse prior produces more well-calibrated uncertainty estimates. Using the posterior distributions for individual weights, we demonstrate that we can prune 30% of the fully-connected layer weights without significant loss of performance by removing the weights with the lowest signal-to-noise ratio. A larger degree of pruning can be achieved using a Fisher information based ranking, but both pruning methods affect the uncertainty calibration for Fanaroff-Riley type I and type II radio galaxies differently. Like other work in this field, we experience a cold posterior effect, whereby the posterior must be down-weighted to achieve good predictive performance. We examine whether adapting the cost function to accommodate model misspecification can compensate for this effect, but find that it does not make a significant difference. We also examine the effect of principled data augmentation and find that this improves upon the baseline but also does not compensate for the observed effect. We interpret this as the cold posterior effect being due to the overly effective curation of our training sample leading to likelihood misspecification, and raise this as a potential issue for Bayesian deep learning approaches to radio galaxy classification in future.
Information field theory (IFT), the information theory for fields, is a mathematical framework for signal reconstruction and non-parametric inverse problems. Artificial intelligence (AI) and machine learning (ML) aim at generating intelligent systems including such for perception, cognition, and learning. This overlaps with IFT, which is designed to address perception, reasoning, and inference tasks. Here, the relation between concepts and tools in IFT and those in AI and ML research are discussed. In the context of IFT, fields denote physical quantities that change continuously as a function of space (and time) and information theory refers to Bayesian probabilistic logic equipped with the associated entropic information measures. Reconstructing a signal with IFT is a computational problem similar to training a generative neural network (GNN) in ML. In this paper, the process of inference in IFT is reformulated in terms of GNN training. In contrast to classical neural networks, IFT based GNNs can operate without pre-training thanks to incorporating expert knowledge into their architecture. Furthermore, the cross-fertilization of variational inference methods used in IFT and ML are discussed. These discussions suggests that IFT is well suited to address many problems in AI and ML research and application.
In the modern age of social media and networks, graph representations of real-world phenomena have become an incredibly useful source to mine insights. Often, we are interested in understanding how entities in a graph are interconnected. The Graph Neural Network (GNN) has proven to be a very useful tool in a variety of graph learning tasks including node classification, link prediction, and edge classification. However, in most of these tasks, the graph data we are working with may be noisy and may contain spurious edges. That is, there is a lot of uncertainty associated with the underlying graph structure. Recent approaches to modeling uncertainty have been to use a Bayesian framework and view the graph as a random variable with probabilities associated with model parameters. Introducing the Bayesian paradigm to graph-based models, specifically for semi-supervised node classification, has been shown to yield higher classification accuracies. However, the method of graph inference proposed in recent work does not take into account the structure of the graph. In this paper, we propose a novel algorithm called Bayesian Graph Convolutional Network using Neighborhood Random Walk Sampling (BGCN-NRWS), which uses a Markov Chain Monte Carlo (MCMC) based graph sampling algorithm utilizing graph structure, reduces overfitting by using a variational inference layer, and yields consistently competitive classification results compared to the state-of-the-art in semi-supervised node classification.
Variational inference is a powerful paradigm for approximate Bayesian inference with a number of appealing properties, including support for model learning and data subsampling. By contrast MCMC methods like Hamiltonian Monte Carlo do not share these properties but remain attractive since, contrary to parametric methods, MCMC is asymptotically unbiased. For these reasons researchers have sought to combine the strengths of both classes of algorithms, with recent approaches coming closer to realizing this vision in practice. However, supporting data subsampling in these hybrid methods can be a challenge, a shortcoming that we address by introducing a surrogate likelihood that can be learned jointly with other variational parameters. We argue theoretically that the resulting algorithm permits the user to make an intuitive trade-off between inference fidelity and computational cost. In an extensive empirical comparison we show that our method performs well in practice and that it is well-suited for black-box inference in probabilistic programming frameworks.
The finite invert Beta-Liouville mixture model (IBLMM) has recently gained some attention due to its positive data modeling capability. Under the conventional variational inference (VI) framework, the analytically tractable solution to the optimization of the variational posterior distribution cannot be obtained, since the variational object function involves evaluation of intractable moments. With the recently proposed extended variational inference (EVI) framework, a new function is proposed to replace the original variational object function in order to avoid intractable moment computation, so that the analytically tractable solution of the IBLMM can be derived in an elegant way. The good performance of the proposed approach is demonstrated by experiments with both synthesized data and a real-world application namely text categorization.
Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection process in deep learning models to some extent. However, they lack the much-required uncertainty modelling and robustness capabilities which are crucial for their use in several real-world applications such as autonomous driving and healthcare. We propose a novel and unique approach to model uncertainty in NODE by considering a distribution over the end-time $T$ of the ODE solver. The proposed approach, latent time NODE (LT-NODE), treats $T$ as a latent variable and apply Bayesian learning to obtain a posterior distribution over $T$ from the data. In particular, we use variational inference to learn an approximate posterior and the model parameters. Prediction is done by considering the NODE representations from different samples of the posterior and can be done efficiently using a single forward pass. As $T$ implicitly defines the depth of a NODE, posterior distribution over $T$ would also help in model selection in NODE. We also propose, adaptive latent time NODE (ALT-NODE), which allow each data point to have a distinct posterior distribution over end-times. ALT-NODE uses amortized variational inference to learn an approximate posterior using inference networks. We demonstrate the effectiveness of the proposed approaches in modelling uncertainty and robustness through experiments on synthetic and several real-world image classification data.
Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection process in deep learning models to some extent. However, they lack the much-required uncertainty modelling and robustness capabilities which are crucial for their use in several real-world applications such as autonomous driving and healthcare. We propose a novel and unique approach to model uncertainty in NODE by considering a distribution over the end-time $T$ of the ODE solver. The proposed approach, latent time NODE (LT-NODE), treats $T$ as a latent variable and apply Bayesian learning to obtain a posterior distribution over $T$ from the data. In particular, we use variational inference to learn an approximate posterior and the model parameters. Prediction is done by considering the NODE representations from different samples of the posterior and can be done efficiently using a single forward pass. As $T$ implicitly defines the depth of a NODE, posterior distribution over $T$ would also help in model selection in NODE. We also propose, adaptive latent time NODE (ALT-NODE), which allow each data point to have a distinct posterior distribution over end-times. ALT-NODE uses amortized variational inference to learn an approximate posterior using inference networks. We demonstrate the effectiveness of the proposed approaches in modelling uncertainty and robustness through experiments on synthetic and several real-world image classification data.
Neural memory enables fast adaptation to new tasks with just a few training samples. Existing memory models store features only from the single last layer, which does not generalize well in presence of a domain shift between training and test distributions. Rather than relying on a flat memory, we propose a hierarchical alternative that stores features at different semantic levels. We introduce a hierarchical prototype model, where each level of the prototype fetches corresponding information from the hierarchical memory. The model is endowed with the ability to flexibly rely on features at different semantic levels if the domain shift circumstances so demand. We meta-learn the model by a newly derived hierarchical variational inference framework, where hierarchical memory and prototypes are jointly optimized. To explore and exploit the importance of different semantic levels, we further propose to learn the weights associated with the prototype at each level in a data-driven way, which enables the model to adaptively choose the most generalizable features. We conduct thorough ablation studies to demonstrate the effectiveness of each component in our model. The new state-of-the-art performance on cross-domain and competitive performance on traditional few-shot classification further substantiates the benefit of hierarchical variational memory.
Learning the dynamics of spatiotemporal events is a fundamental problem. Neural point processes enhance the expressivity of point process models with deep neural networks. However, most existing methods only consider temporal dynamics without spatial modeling. We propose Deep Spatiotemporal Point Process (\ours{}), a deep dynamics model that integrates spatiotemporal point processes. Our method is flexible, efficient, and can accurately forecast irregularly sampled events over space and time. The key construction of our approach is the nonparametric space-time intensity function, governed by a latent process. The intensity function enjoys closed form integration for the density. The latent process captures the uncertainty of the event sequence. We use amortized variational inference to infer the latent process with deep networks. Using synthetic datasets, we validate our model can accurately learn the true intensity function. On real-world benchmark datasets, our model demonstrates superior performance over state-of-the-art baselines. Our code and data can be found at the https://github.com/Rose-STL-Lab/DeepSTPP.