Pedestrian detection in a crowd is a challenging task due to a high number of mutually-occluding human instances, which brings ambiguity and optimization difficulties to the current IoU-based ground truth assignment procedure in classical object detection methods. In this paper, we develop a unique perspective of pedestrian detection as a variational inference problem. We formulate a novel and efficient algorithm for pedestrian detection by modeling the dense proposals as a latent variable while proposing a customized Auto Encoding Variational Bayes (AEVB) algorithm. Through the optimization of our proposed algorithm, a classical detector can be fashioned into a variational pedestrian detector. Experiments conducted on CrowdHuman and CityPersons datasets show that the proposed algorithm serves as an efficient solution to handle the dense pedestrian detection problem for the case of single-stage detectors. Our method can also be flexibly applied to two-stage detectors, achieving notable performance enhancement.
Massive Open Online Courses (MOOCs) have become a popular choice for e-learning thanks to their great flexibility. However, due to large numbers of learners and their diverse backgrounds, it is taxing to offer real-time support. Learners may post their feelings of confusion and struggle in the respective MOOC forums, but with the large volume of posts and high workloads for MOOC instructors, it is unlikely that the instructors can identify all learners requiring intervention. This problem has been studied as a Natural Language Processing (NLP) problem recently, and is known to be challenging, due to the imbalance of the data and the complex nature of the task. In this paper, we explore for the first time Bayesian deep learning on learner-based text posts with two methods: Monte Carlo Dropout and Variational Inference, as a new solution to assessing the need of instructor interventions for a learner's post. We compare models based on our proposed methods with probabilistic modelling to its baseline non-Bayesian models under similar circumstances, for different cases of applying prediction. The results suggest that Bayesian deep learning offers a critical uncertainty measure that is not supplied by traditional neural networks. This adds more explainability, trust and robustness to AI, which is crucial in education-based applications. Additionally, it can achieve similar or better performance compared to non-probabilistic neural networks, as well as grant lower variance.
While reinforcement learning algorithms provide automated acquisition of optimal policies, practical application of such methods requires a number of design decisions, such as manually designing reward functions that not only define the task, but also provide sufficient shaping to accomplish it. In this paper, we view reinforcement learning as inferring policies that achieve desired outcomes, rather than as a problem of maximizing rewards. To solve this inference problem, we establish a novel variational inference formulation that allows us to derive a well-shaped reward function which can be learned directly from environment interactions. From the corresponding variational objective, we also derive a new probabilistic Bellman backup operator and use it to develop an off-policy algorithm to solve goal-directed tasks. We empirically demonstrate that this method eliminates the need to hand-craft reward functions for a suite of diverse manipulation and locomotion tasks and leads to effective goal-directed behaviors.
Deep Gaussian processes (DGPs), a hierarchical composition of GP models, have successfully boosted the expressive power of their single-layer counterpart. However, it is impossible to perform exact inference in DGPs, which has motivated the recent development of variational inference-based methods. Unfortunately, either these methods yield a biased posterior belief or it is difficult to evaluate their convergence. This paper introduces a new approach for specifying flexible, arbitrarily complex, and scalable approximate posterior distributions. The posterior distribution is constructed through a normalizing flow (NF) which transforms a simple initial probability into a more complex one through a sequence of invertible transformations. Moreover, a novel convolutional normalizing flow (CNF) is developed to improve the time efficiency and capture dependency between layers. Empirical evaluation shows that CNF DGP outperforms the state-of-the-art approximation methods for DGPs.
Category recommendation for users on an e-Commerce platform is an important task as it dictates the flow of traffic through the website. It is therefore important to surface precise and diverse category recommendations to aid the users' journey through the platform and to help them discover new groups of items. An often understated part in category recommendation is users' proclivity to repeat purchases. The structure of this temporal behavior can be harvested for better category recommendations and in this work, we attempt to harness this through variational inference. Further, to enhance the variational inference based optimization, we initialize the optimizer at better starting points through the well known Metapath2Vec algorithm. We demonstrate our results on two real-world datasets and show that our model outperforms standard baseline methods.
Sparse Bayesian learning (SBL) can be implemented with low complexity based on the approximate message passing (AMP) algorithm. However, it does not work well for a generic measurement matrix, which may cause AMP to diverge. Damped AMP has been used for SBL to alleviate the problem at the cost of reducing convergence speed. In this work, we propose a new SBL algorithm based on structured variational inference, leveraging AMP with a unitary transformation (UAMP). Both single measurement vector and multiple measurement vector problems are investigated. It is shown that, compared to state-of-the-art AMP-based SBL algorithms, the proposed UAMP-SBL is more robust and efficient, leading to remarkably better performance.
Gaussian variational inference and the Laplace approximation are popular alternatives to Markov chain Monte Carlo that formulate Bayesian posterior inference as an optimization problem, enabling the use of simple and scalable stochastic optimization algorithms. However, a key limitation of both methods is that the solution to the optimization problem is typically not tractable to compute; even in simple settings the problem is nonconvex. Thus, recently developed statistical guarantees -- which all involve the (data) asymptotic properties of the global optimum -- are not reliably obtained in practice. In this work, we provide two major contributions: a theoretical analysis of the asymptotic convexity properties of variational inference with a Gaussian family and the maximum a posteriori (MAP) problem required by the Laplace approximation; and two algorithms -- consistent Laplace approximation (CLA) and consistent stochastic variational inference (CSVI) -- that exploit these properties to find the optimal approximation in the asymptotic regime. Both CLA and CSVI involve a tractable initialization procedure that finds the local basin of the optimum, and CSVI further includes a scaled gradient descent algorithm that provably stays locally confined to that basin. Experiments on nonconvex synthetic and real-data examples show that compared with standard variational and Laplace approximations, both CSVI and CLA improve the likelihood of obtaining the global optimum of their respective optimization problems.
Uncertainty quantification provides quantitative measures on the reliability of candidate solutions of ill-posed inverse problems. Due to their sequential nature, Monte Carlo sampling methods require large numbers of sampling steps for accurate Bayesian inference and are often computationally infeasible for large-scale inverse problems, such as seismic imaging. Our main contribution is a data-driven variational inference approach where we train a normalizing flow (NF), a type of invertible neural net, capable of cheaply sampling the posterior distribution given previously unseen seismic data from neighboring surveys. To arrive at this result, we train the NF on pairs of low- and high-fidelity migrated images. In our numerical example, we obtain high-fidelity images from the Parihaka dataset and low-fidelity images are derived from these images through the process of demigration, followed by adding noise and migration. During inference, given shot records from a new neighboring seismic survey, we first compute the reverse-time migration image. Next, by feeding this low-fidelity migrated image to the NF we gain access to samples from the posterior distribution virtually for free. We use these samples to compute a high-fidelity image including a first assessment of the image's reliability. To our knowledge, this is the first attempt to train a conditional network on what we know from neighboring images to improve the current image and assess its reliability.
Federated Bayesian learning offers a principled framework for the definition of collaborative training algorithms that are able to quantify epistemic uncertainty and to produce trustworthy decisions. Upon the completion of collaborative training, an agent may decide to exercise her legal "right to be forgotten", which calls for her contribution to the jointly trained model to be deleted and discarded. This paper studies federated learning and unlearning in a decentralized network within a Bayesian framework. It specifically develops federated variational inference (VI) solutions based on the decentralized solution of local free energy minimization problems within exponential-family models and on local gossip-driven communication. The proposed protocols are demonstrated to yield efficient unlearning mechanisms.
Locally Linear Embedding (LLE) is a nonlinear spectral dimensionality reduction and manifold learning method. It has two main steps which are linear reconstruction and linear embedding of points in the input space and embedding space, respectively. In this work, we propose two novel generative versions of LLE, named Generative LLE (GLLE), whose linear reconstruction steps are stochastic rather than deterministic. GLLE assumes that every data point is caused by its linear reconstruction weights as latent factors. The proposed GLLE algorithms can generate various LLE embeddings stochastically while all the generated embeddings relate to the original LLE embedding. We propose two versions for stochastic linear reconstruction, one using expectation maximization and another with direct sampling from a derived distribution by optimization. The proposed GLLE methods are closely related to and inspired by variational inference, factor analysis, and probabilistic principal component analysis. Our simulations show that the proposed GLLE methods work effectively in unfolding and generating submanifolds of data.
In this paper, we provide a generalized framework for Variational Inference-Stochastic Optimal Control by using thenon-extensive Tsallis divergence. By incorporating the deformed exponential function into the optimality likelihood function, a novel Tsallis Variational Inference-Model Predictive Control algorithm is derived, which includes prior works such as Variational Inference-Model Predictive Control, Model Predictive PathIntegral Control, Cross Entropy Method, and Stein VariationalInference Model Predictive Control as special cases. The proposed algorithm allows for effective control of the cost/reward transform and is characterized by superior performance in terms of mean and variance reduction of the associated cost. The aforementioned features are supported by a theoretical and numerical analysis on the level of risk sensitivity of the proposed algorithm as well as simulation experiments on 5 different robotic systems with 3 different policy parameterizations.
Modelers use automatic differentiation (AD) of computation graphs to implement complex Deep Learning models without defining gradient computations. Stochastic AD extends AD to stochastic computation graphs with sampling steps, which arise when modelers handle the intractable expectations common in Reinforcement Learning and Variational Inference. However, current methods for stochastic AD are limited: They are either only applicable to continuous random variables and differentiable functions, or can only use simple but high variance score-function estimators. To overcome these limitations, we introduce Storchastic, a new framework for AD of stochastic computation graphs. Storchastic allows the modeler to choose from a wide variety of gradient estimation methods at each sampling step, to optimally reduce the variance of the gradient estimates. Furthermore, Storchastic is provably unbiased for estimation of any-order gradients, and generalizes variance reduction techniques to higher-order gradient estimates. Finally, we implement Storchastic as a PyTorch library at https://github.com/HEmile/storchastic.
We present a variational inference (VI) framework that unifies and leverages sequential Monte-Carlo (particle filtering) with \emph{approximate} rejection sampling to construct a flexible family of variational distributions. Furthermore, we augment this approach with a resampling step via Bernoulli race, a generalization of a Bernoulli factory, to obtain a low-variance estimator of the marginal likelihood. Our framework, Variational Rejection Particle Filtering (VRPF), leads to novel variational bounds on the marginal likelihood, which can be optimized efficiently with respect to the variational parameters and generalizes several existing approaches in the VI literature. We also present theoretical properties of the variational bound and demonstrate experiments on various models of sequential data, such as the Gaussian state-space model and variational recurrent neural net (VRNN), on which VRPF outperforms various existing state-of-the-art VI methods.
Integrating robots in complex everyday environments requires a multitude of problems to be solved. One crucial feature among those is to equip robots with a mechanism for teaching them a new task in an easy and natural way. When teaching tasks that involve sequences of different skills, with varying order and number of these skills, it is desirable to only demonstrate full task executions instead of all individual skills. For this purpose, we propose a novel approach that simultaneously learns to segment trajectories into reoccurring patterns and the skills to reconstruct these patterns from unlabelled demonstrations without further supervision. Moreover, the approach learns a skill conditioning that can be used to understand possible sequences of skills, a practical mechanism to be used in, for example, human-robot-interactions for a more intelligent and adaptive robot behaviour. The Bayesian and variational inference based approach is evaluated on synthetic and real human demonstrations with varying complexities and dimensionality, showing the successful learning of segmentations and skill libraries from unlabelled data.
We present d3p, a software package designed to help fielding runtime efficient widely-applicable Bayesian inference under differential privacy guarantees. d3p achieves general applicability to a wide range of probabilistic modelling problems by implementing the differentially private variational inference algorithm, allowing users to fit any parametric probabilistic model with a differentiable density function. d3p adopts the probabilistic programming paradigm as a powerful way for the user to flexibly define such models. We demonstrate the use of our software on a hierarchical logistic regression example, showing the expressiveness of the modelling approach as well as the ease of running the parameter inference. We also perform an empirical evaluation of the runtime of the private inference on a complex model and find a $\sim$10 fold speed-up compared to an implementation using TensorFlow Privacy.
The actor-critic RL is widely used in various robotic control tasks. By viewing the actor-critic RL from the perspective of variational inference (VI), the policy network is trained to obtain the approximate posterior of actions given the optimality criteria. However, in practice, the actor-critic RL may yield suboptimal policy estimates due to the amortization gap and insufficient exploration. In this work, inspired by the previous use of Hamiltonian Monte Carlo (HMC) in VI, we propose to integrate the policy network of actor-critic RL with HMC, which is termed as {\it Hamiltonian Policy}. As such we propose to evolve actions from the base policy according to HMC, and our proposed method has many benefits. First, HMC can improve the policy distribution to better approximate the posterior and hence reduce the amortization gap. Second, HMC can also guide the exploration more to the regions of action spaces with higher Q values, enhancing the exploration efficiency. Further, instead of directly applying HMC into RL, we propose a new leapfrog operator to simulate the Hamiltonian dynamics. Finally, in safe RL problems, we find that the proposed method can not only improve the achieved return, but also reduce safety constraint violations by discarding potentially unsafe actions. With comprehensive empirical experiments on continuous control baselines, including MuJoCo and PyBullet Roboschool, we show that the proposed approach is a data-efficient and easy-to-implement improvement over previous actor-critic methods.
Approximate Bayesian inference methods that scale to very large datasets are crucial in leveraging probabilistic models for real-world time series. Sparse Markovian Gaussian processes combine the use of inducing variables with efficient Kalman filter-like recursions, resulting in algorithms whose computational and memory requirements scale linearly in the number of inducing points, whilst also enabling parallel parameter updates and stochastic optimisation. Under this paradigm, we derive a general site-based approach to approximate inference, whereby we approximate the non-Gaussian likelihood with local Gaussian terms, called sites. Our approach results in a suite of novel sparse extensions to algorithms from both the machine learning and signal processing literature, including variational inference, expectation propagation, and the classical nonlinear Kalman smoothers. The derived methods are suited to large time series, and we also demonstrate their applicability to spatio-temporal data, where the model has separate inducing points in both time and space.
This study presents PRISM, a probabilistic simplex component analysis approach to identifying the vertices of a data-circumscribing simplex from data. The problem has a rich variety of applications, the most notable being hyperspectral unmixing in remote sensing and non-negative matrix factorization in machine learning. PRISM uses a simple probabilistic model, namely, uniform simplex data distribution and additive Gaussian noise, and it carries out inference by maximum likelihood. The inference model is sound in the sense that the vertices are provably identifiable under some assumptions, and it suggests that PRISM can be effective in combating noise when the number of data points is large. PRISM has strong, but hidden, relationships with simplex volume minimization, a powerful geometric approach for the same problem. We study these fundamental aspects, and we also consider algorithmic schemes based on importance sampling and variational inference. In particular, the variational inference scheme is shown to resemble a matrix factorization problem with a special regularizer, which draws an interesting connection to the matrix factorization approach. Numerical results are provided to demonstrate the potential of PRISM.
To adopt neural networks in safety critical domains, knowing whether we can trust their predictions is crucial. Bayesian neural networks (BNNs) provide uncertainty estimates by averaging predictions with respect to the posterior weight distribution. Variational inference methods for BNNs approximate the intractable weight posterior with a tractable distribution, yet mostly rely on sampling from the variational distribution during training and inference. Recent sampling-free approaches offer an alternative, but incur a significant parameter overhead. We here propose a more efficient parameterization of the posterior approximation for sampling-free variational inference that relies on the distribution induced by multiplicative Gaussian activation noise. This allows us to combine parameter efficiency with the benefits of sampling-free variational inference. Our approach yields competitive results for standard regression problems and scales well to large-scale image classification tasks including ImageNet.
Inference is the task of drawing conclusions about unobserved variables given observations of related variables. Applications range from identifying diseases from symptoms to classifying economic regimes from price movements. Unfortunately, performing exact inference is intractable in general. One alternative is variational inference, where a candidate probability distribution is optimized to approximate the posterior distribution over unobserved variables. For good approximations, a flexible and highly expressive candidate distribution is desirable. In this work, we use quantum Born machines as variational distributions over discrete variables. We apply the framework of operator variational inference to achieve this goal. In particular, we adopt two specific realizations: one with an adversarial objective and one based on the kernelized Stein discrepancy. We demonstrate the approach numerically using examples of Bayesian networks, and implement an experiment on an IBM quantum computer. Our techniques enable efficient variational inference with distributions beyond those that are efficiently representable on a classical computer.