Multi-sensor systems are proliferating the asset management industry and by proxy, the structural health management community. Asset managers are beginning to require a prognostics and health management system to predict and assess maintenance decisions. These systems handle big machinery data and multi-sensor fusion and integrate remaining useful life prognostic capabilities. We introduce a deep adversarial learning approach to damage prognostics. A non-Markovian variational inference-based model incorporating an adversarial training algorithm framework was developed. The proposed framework was applied to a public multi-sensor data set of turbofan engines to demonstrate its ability to predict remaining useful life. We find that using the deep adversarial based approach results in higher performing remaining useful life predictions.
In this paper, we measure systematic risk with a new nonparametric factor model, the neural network factor model. The suitable factors for systematic risk can be naturally found by inserting daily returns on a wide range of assets into the bottleneck network. The network-based model does not stick to a probabilistic structure unlike parametric factor models, and it does not need feature engineering because it selects notable features by itself. In addition, we compare performance between our model and the existing models using 20-year data of S&P 100 components. Although the new model can not outperform the best ones among the parametric factor models due to limitations of the variational inference, the estimation method used for this study, it is still noteworthy in that it achieves the performance as best the comparable models could without any prior knowledge.
We propose a novel Coupled Hidden Markov Model to detect epileptic seizures in multichannel electroencephalography (EEG) data. Our model defines a network of seizure propagation paths to capture both the temporal and spatial evolution of epileptic activity. To address the intractability introduced by the coupled interactions, we derive a variational inference procedure to efficiently infer the seizure evolution from spectral patterns in the EEG data. We validate our model on EEG aquired under clinical conditions in the Epilepsy Monitoring Unit of the Johns Hopkins Hospital. Using 5-fold cross validation, we demonstrate that our model outperforms three baseline approaches which rely on a classical detection framework. Our model also demonstrates the potential to localize seizure onset zones in focal epilepsy.
This work combines the free energy principle from cognitive neuroscience and the ensuing active inference dynamics with recent advances in variational inference in deep generative models, and evolution strategies to introduce the "deep active inference" agent. This agent minimises a variational free energy bound on the average surprise of its sensations, which is motivated by a homeostatic argument. It does so by optimising the parameters of a generative latent variable model of its sensory inputs, together with a variational density approximating the posterior distribution over the latent variables, given its observations, and by acting on its environment to actively sample input that is likely under this generative model. The internal dynamics of the agent are implemented using deep and recurrent neural networks, as used in machine learning, making the deep active inference agent a scalable and very flexible class of active inference agent. Using the mountain car problem, we show how goal directed behaviour can be implemented by defining appropriate priors on the latent states in the agent's model. Furthermore, we show that the deep active inference agent can learn a generative model of the environment, which can be sampled from to understand the agent's beliefs about the environment and its interaction therewith.
Most human protein-coding genes can be transcribed into multiple possible distinct mRNA isoforms. These alternative splicing patterns encourage molecular diversity and dysregulation of isoform expression plays an important role in disease etiology. However, isoforms are difficult to characterize from short-read RNA-seq data because they share identical subsequences and exist in tissue- and sample-specific frequencies. Here, we develop BIISQ, a Bayesian nonparametric model to discover Isoforms and Individual Specific Quantification from RNA-seq data. BIISQ does not require known isoform reference sequences but instead estimates isoform composition directly with an isoform catalog shared across samples. We develop a stochastic variational inference approach for efficient and robust posterior inference and demonstrate superior precision and recall for short read RNA-seq simulations and simulated short read data from PacBio long read sequencing when compared to state-of-the-art isoform reconstruction methods. BIISQ achieves the most significant gains for longer (in terms of exons) isoforms and isoforms that are lowly expressed (over 500% more transcripts correctly inferred at low coverage in simulations). Finally, we estimate isoforms in the GEUVADIS RNA-seq data, identify genetic variants that regulate transcript ratios, and demonstrate variant enrichment in functional elements related to mRNA splicing regulation.
Social graphs, representing online friendships among users, are one of the fundamental types of data for many applications, such as recommendation, virality prediction and marketing in social media. However, this data may be unavailable due to the privacy concerns of users, or kept private by social network operators, which makes such applications difficult. Inferring user interests and discovering user connections through their shared multimedia content has attracted more and more attention in recent years. This paper proposes a Gaussian relational topic model for connection discovery using user shared images in social media. The proposed model not only models user interests as latent variables through their shared images, but also considers the connections between users as a result of their shared images. It explicitly relates user shared images to user connections in a hierarchical, systematic and supervisory way and provides an end-to-end solution for the problem. This paper also derives efficient variational inference and learning algorithms for the posterior of the latent variables and model parameters. It is demonstrated through experiments with over 200k images from Flickr that the proposed method significantly outperforms the methods in previous works.
Continual learning deals with training models on new tasks and datasets in an online fashion. One strand of research has used probabilistic regularization for continual learning, with two of the main approaches in this vein being Online Elastic Weight Consolidation (Online EWC) and Variational Continual Learning (VCL). VCL employs variational inference, which in other settings has been improved empirically by applying likelihood-tempering. We show that applying this modification to VCL recovers Online EWC as a limiting case, allowing for interpolation between the two approaches. We term the general algorithm Generalized VCL (GVCL). In order to mitigate the observed overpruning effect of VI, we take inspiration from a common multi-task architecture, neural networks with task-specific FiLM layers, and find that this addition leads to significant performance gains, specifically for variational methods. In the small-data regime, GVCL strongly outperforms existing baselines. In larger datasets, GVCL with FiLM layers outperforms or is competitive with existing baselines in terms of accuracy, whilst also providing significantly better calibration.
This paper investigates the problem of designing data-driven stochastic Model Predictive Control (MPC) for linear time-invariant systems under additive stochastic disturbance, whose probability distribution is unknown but can be partially inferred from data. We propose a novel online learning based risk-averse stochastic MPC framework in which Conditional Value-at-Risk (CVaR) constraints on system states are required to hold for a family of distributions called an ambiguity set. The ambiguity set is constructed from disturbance data by leveraging a Dirichlet process mixture model that is self-adaptive to the underlying data structure and complexity. Specifically, the structural property of multimodality is exploit-ed, so that the first- and second-order moment information of each mixture component is incorporated into the ambiguity set. A novel constraint tightening strategy is then developed based on an equivalent reformulation of distributionally ro-bust CVaR constraints over the proposed ambiguity set. As more data are gathered during the runtime of the controller, the ambiguity set is updated online using real-time disturbance data, which enables the risk-averse stochastic MPC to cope with time-varying disturbance distributions. The online variational inference algorithm employed does not require all collected data be learned from scratch, and therefore the proposed MPC is endowed with the guaranteed computational complexity of online learning. The guarantees on recursive feasibility and closed-loop stability of the proposed MPC are established via a safe update scheme. Numerical examples are used to illustrate the effectiveness and advantages of the proposed MPC.
Semi-supervised variational autoencoders (VAEs) have obtained strong results, but have also encountered the challenge that good ELBO values do not always imply accurate inference results. In this paper, we investigate and propose two causes of this problem: (1) The ELBO objective cannot utilize the label information directly. (2) A bottleneck value exists and continuing to optimize ELBO after this value will not improve inference accuracy. On the basis of the experiment results, we propose SHOT-VAE to address these problems without introducing additional prior knowledge. The SHOT-VAE offers two contributions: (1) A new ELBO approximation named smooth-ELBO that integrates the label predictive loss into ELBO. (2) An approximation based on optimal interpolation that breaks the ELBO value bottleneck by reducing the margin between ELBO and the data likelihood. The SHOT-VAE achieves good performance with a 25.30% error rate on CIFAR-100 with 10k labels and reduces the error rate to 6.11% on CIFAR-10 with 4k labels.
We develop variational Laplace for Bayesian neural networks (BNNs) which exploits a local approximation of the curvature of the likelihood to estimate the ELBO without the need for stochastic sampling of the neural-network weights. The Variational Laplace objective is simple to evaluate, as it is (in essence) the log-likelihood, plus weight-decay, plus a squared-gradient regularizer. Variational Laplace gave better test performance and expected calibration errors than maximum a-posteriori inference and standard sampling-based variational inference, despite using the same variational approximate posterior. Finally, we emphasise care needed in benchmarking standard VI as there is a risk of stopping before the variance parameters have converged. We show that early-stopping can be avoided by increasing the learning rate for the variance parameters.
Recent work has attempted to directly approximate the `function-space' or predictive posterior distribution of Bayesian models, without approximating the posterior distribution over the parameters. This is appealing in e.g. Bayesian neural networks, where we only need the former, and the latter is hard to represent. In this work, we highlight some advantages and limitations of employing the Kullback-Leibler divergence in this setting. For example, we show that minimizing the KL divergence between a wide class of parametric distributions and the posterior induced by a (non-degenerate) Gaussian process prior leads to an ill-defined objective function. Then, we propose (featurized) Bayesian linear regression as a benchmark for `function-space' inference methods that directly measures approximation quality. We apply this methodology to assess aspects of the objective function and inference scheme considered in Sun, Zhang, Shi, and Grosse (2018), emphasizing the quality of approximation to Bayesian inference as opposed to predictive performance.
Inference networks of traditional Variational Autoencoders (VAEs) are typically amortized, resulting in relatively inaccurate posterior approximation compared to instance-wise variational optimization. Recent semi-amortized approaches were proposed to address this drawback; however, their iterative gradient update procedures can be computationally demanding. To address these issues, in this paper we introduce an accurate amortized inference algorithm. We propose a novel recursive mixture estimation algorithm for VAEs that iteratively augments the current mixture with new components so as to maximally reduce the divergence between the variational and the true posteriors. Using the functional gradient approach, we devise an intuitive learning criteria for selecting a new mixture component: the new component has to improve the data likelihood (lower bound) and, at the same time, be as divergent from the current mixture distribution as possible, thus increasing representational diversity. Compared to recently proposed boosted variational inference (BVI), our method relies on amortized inference in contrast to BVI's non-amortized single optimization instance. A crucial benefit of our approach is that the inference at test time requires a single feed-forward pass through the mixture inference network, making it significantly faster than the semi-amortized approaches. We show that our approach yields higher test data likelihood than the state-of-the-art on several benchmark datasets.
Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep learning algorithms are lacking of theoretical support. On the other hand, another line of works have proposed theoretical frameworks that are computationally infeasible. In this paper, we train sparse deep neural networks with a fully Bayesian treatment under spike-and-slab priors, and develop a set of computationally efficient variational inferences via continuous relaxation of Bernoulli distribution. The variational posterior contraction rate is provided, which justifies the consistency of the proposed variational Bayes method. Notably, our empirical results demonstrate that this variational procedure provides uncertainty quantification in terms of Bayesian predictive distribution and is also capable to accomplish consistent variable selection by training a sparse multi-layer neural network.
We introduce Dirichlet pruning, a novel post-processing technique to transform a large neural network model into a compressed one. Dirichlet pruning is a form of structured pruning that assigns the Dirichlet distribution over each layer's channels in convolutional layers (or neurons in fully-connected layers) and estimates the parameters of the distribution over these units using variational inference. The learned distribution allows us to remove unimportant units, resulting in a compact architecture containing only crucial features for a task at hand. The number of newly introduced Dirichlet parameters is only linear in the number of channels, which allows for rapid training, requiring as little as one epoch to converge. We perform extensive experiments, in particular on larger architectures such as VGG and ResNet (45% and 58% compression rate, respectively) where our method achieves the state-of-the-art compression performance and provides interpretable features as a by-product.
Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address one limitation of sparse GPs, which is due to the challenge in dealing with a large number of inducing variables without imposing a special structure on the inducing inputs. In particular, we introduce a novel hierarchical prior, which imposes sparsity on the set of inducing variables. We treat our model variationally, and we experimentally show considerable computational gains compared to standard sparse GPs when sparsity on the inducing variables is realized considering the nearest inducing inputs of a random mini-batch of the data. We perform an extensive experimental validation that demonstrates the effectiveness of our approach compared to the state-of-the-art. Our approach enables the possibility to use sparse GPs using a large number of inducing points without incurring a prohibitive computational cost.
The aim of this paper is to study the reward based policy exploration problem in a supervised learning approach and enable robots to form complex movement trajectories in challenging reward settings and search spaces. For this, the experience of the robot, which can be bootstrapped from demonstrated trajectories, is used to train a novel Neural Processes-based deep network that samples from its latent space and generates the required trajectories given desired rewards. Our framework can generate progressively improved trajectories by sampling them from high reward landscapes, increasing the reward gradually. Variational inference is used to create a stochastic latent space to sample varying trajectories in generating population of trajectories given target rewards. We benefit from Evolutionary Strategies and propose a novel crossover operation, which is applied in the self-organized latent space of the individual policies, allowing blending of the individuals that might address different factors in the reward function. Using a number of tasks that require sequential reaching to multiple points or passing through gaps between objects, we showed that our method provides stable learning progress and significant sample efficiency compared to a number of state-of-the-art robotic reinforcement learning methods. Finally, we show the real-world suitability of our method through real robot execution involving obstacle avoidance.
Continuous-time event data are common in applications such as individual behavior data, financial transactions, and medical health records. Modeling such data can be very challenging, in particular for applications with many different types of events, since it requires a model to predict the event types as well as the time of occurrence. Recurrent neural networks that parameterize time-varying intensity functions are the current state-of-the-art for predictive modeling with such data. These models typically assume that all event sequences come from the same data distribution. However, in many applications event sequences are generated by different sources, or users, and their characteristics can be very different. In this paper, we extend the broad class of neural marked point process models to mixtures of latent embeddings, where each mixture component models the characteristic traits of a given user. Our approach relies on augmenting these models with a latent variable that encodes user characteristics, represented by a mixture model over user behavior that is trained via amortized variational inference. We evaluate our methods on four large real-world datasets and demonstrate systematic improvements from our approach over existing work for a variety of predictive metrics such as log-likelihood, next event ranking, and source-of-sequence identification.
Prediction of events such as part replacement and failure events plays a critical role in reliability engineering. Event stream data are commonly observed in manufacturing and teleservice systems. Designing predictive models for individual units based on such event streams is challenging and an under-explored problem. In this work, we propose a non-parametric prognostic framework for individualized event prediction based on the inhomogeneous Poisson processes with a multivariate Gaussian convolution process (MGCP) prior on the intensity functions. The MGCP prior on the intensity functions of the inhomogeneous Poisson processes maps data from similar historical units to the current unit under study which facilitates sharing of information and allows for analysis of flexible event patterns. To facilitate inference, we derive a variational inference scheme for learning and estimation of parameters in the resulting MGCP modulated Poisson process model. Experimental results are shown on both synthetic data as well as real-world data for fleet based event prediction.
We present Quantized Variational Inference, a new algorithm for Evidence Lower Bound maximization. We show how Optimal Voronoi Tesselation produces variance free gradients for ELBO optimization at the cost of introducing asymptotically decaying bias. Subsequently, we propose a Richardson extrapolation type method to improve the asymptotic bound. We show that using the Quantized Variational Inference framework leads to fast convergence for both score function and the reparametrized gradient estimator at a comparable computational cost. Finally, we propose several experiments to assess the performance of our method and its limitations.
We propose to learn a probabilistic motion model from a sequence of images for spatio-temporal registration. Our model encodes motion in a low-dimensional probabilistic space - the motion matrix - which enables various motion analysis tasks such as simulation and interpolation of realistic motion patterns allowing for faster data acquisition and data augmentation. More precisely, the motion matrix allows to transport the recovered motion from one subject to another simulating for example a pathological motion in a healthy subject without the need for inter-subject registration. The method is based on a conditional latent variable model that is trained using amortized variational inference. This unsupervised generative model follows a novel multivariate Gaussian process prior and is applied within a temporal convolutional network which leads to a diffeomorphic motion model. Temporal consistency and generalizability is further improved by applying a temporal dropout training scheme. Applied to cardiac cine-MRI sequences, we show improved registration accuracy and spatio-temporally smoother deformations compared to three state-of-the-art registration algorithms. Besides, we demonstrate the model's applicability for motion analysis, simulation and super-resolution by an improved motion reconstruction from sequences with missing frames compared to linear and cubic interpolation.