Bayesian inference usually requires running potentially costly inference procedures separately for every new observation. In contrast, the idea of amortized Bayesian inference is to initially invest computational cost in training an inference network on simulated data, which can subsequently be used to rapidly perform inference (i.e., to return estimates of posterior distributions) for new observations. This approach has been applied to many real-world models in the sciences and engineering, but it is unclear how robust the approach is to adversarial perturbations in the observed data. Here, we study the adversarial robustness of amortized Bayesian inference, focusing on simulation-based estimation of multi-dimensional posterior distributions. We show that almost unrecognizable, targeted perturbations of the observations can lead to drastic changes in the predicted posterior and highly unrealistic posterior predictive samples, across several benchmark tasks and a real-world example from neuroscience. We propose a computationally efficient regularization scheme based on penalizing the Fisher information of the conditional density estimator, and show how it improves the adversarial robustness of amortized Bayesian inference.

The intrinsically infinite-dimensional features of the functional observations over multidimensional domains render the standard classification methods effectively inapplicable. To address this problem, we introduce a novel multiclass functional deep neural network (mfDNN) classifier as an innovative data mining and classification tool. Specifically, we consider sparse deep neural network architecture with rectifier linear unit (ReLU) activation function and minimize the cross-entropy loss in the multiclass classification setup. This neural network architecture allows us to employ modern computational tools in the implementation. The convergence rates of the misclassification risk functions are also derived for both fully observed and discretely observed multidimensional functional data. We demonstrate the performance of mfDNN on simulated data and several benchmark datasets from different application domains.

Learning-based methods for blind single image super resolution (SISR) conduct the restoration by a learned mapping between high-resolution (HR) images and their low-resolution (LR) counterparts degraded with arbitrary blur kernels. However, these methods mostly require an independent step to estimate the blur kernel, leading to error accumulation between steps. We propose an end-to-end learning framework for the blind SISR problem, which enables image restoration within a unified Bayesian framework with either full- or semi-supervision. The proposed method, namely SREMN, integrates learning techniques into the generalized expectation-maximization (GEM) algorithm and infers HR images from the maximum likelihood estimation (MLE). Extensive experiments show the superiority of the proposed method with comparison to existing work and novelty in semi-supervised learning.

Deep generative models (DGMs) and their conditional counterparts provide a powerful ability for general-purpose generative modeling of data distributions. However, it remains challenging for existing methods to address advanced conditional generative problems without annotations, which can enable multiple applications like image-to-image translation and image editing. We present a unified Bayesian framework for such problems, which introduces an inference stage on latent variables within the learning process. In particular, we propose a variational Bayesian image translation network (VBITN) that enables multiple image translation and editing tasks. Comprehensive experiments show the effectiveness of our method on unsupervised image-to-image translation, and demonstrate the novel advanced capabilities for semantic editing and mixed domain translation.

We use both Bayesian and neural models to dissect a data set of Chinese learners' pre- and post-interventional responses to two tests measuring their understanding of English prepositions. The results mostly replicate previous findings from frequentist analyses and newly reveal crucial interactions between student ability, task type, and stimulus sentence. Given the sparsity of the data as well as high diversity among learners, the Bayesian method proves most useful; but we also see potential in using language model probabilities as predictors of grammaticality and learnability.

A key challenge of continual reinforcement learning (CRL) in dynamic environments is to promptly adapt the RL agent's behavior as the environment changes over its lifetime, while minimizing the catastrophic forgetting of the learned information. To address this challenge, in this article, we propose DaCoRL, i.e., dynamics-adaptive continual RL. DaCoRL learns a context-conditioned policy using progressive contextualization, which incrementally clusters a stream of stationary tasks in the dynamic environment into a series of contexts and opts for an expandable multihead neural network to approximate the policy. Specifically, we define a set of tasks with similar dynamics as an environmental context and formalize context inference as a procedure of online Bayesian infinite Gaussian mixture clustering on environment features, resorting to online Bayesian inference to infer the posterior distribution over contexts. Under the assumption of a Chinese restaurant process prior, this technique can accurately classify the current task as a previously seen context or instantiate a new context as needed without relying on any external indicator to signal environmental changes in advance. Furthermore, we employ an expandable multihead neural network whose output layer is synchronously expanded with the newly instantiated context, and a knowledge distillation regularization term for retaining the performance on learned tasks. As a general framework that can be coupled with various deep RL algorithms, DaCoRL features consistent superiority over existing methods in terms of the stability, overall performance and generalization ability, as verified by extensive experiments on several robot navigation and MuJoCo locomotion tasks.

Selecting an effective training signal for tasks in natural language processing is difficult: expert annotations are expensive, and crowd-sourced annotations may not be reliable. At the same time, recent work in NLP has demonstrated that learning from a distribution over labels acquired from crowd annotations can be effective. However, there are many ways to acquire such a distribution, and the performance allotted by any one method can fluctuate based on the task and the amount of available crowd annotations, making it difficult to know a priori which distribution is best. This paper systematically analyzes this in the out-of-domain setting, adding to the NLP literature which has focused on in-domain evaluation, and proposes new methods for acquiring soft-labels from crowd-annotations by aggregating the distributions produced by existing methods. In particular, we propose to aggregate multiple-views of crowd annotations via temperature scaling and finding their Jensen-Shannon centroid. We demonstrate that these aggregation methods lead to the most consistent performance across four NLP tasks on out-of-domain test sets, mitigating fluctuations in performance from the individual distributions. Additionally, aggregation results in the most consistently well-calibrated uncertainty estimation. We argue that aggregating different views of crowd-annotations is an effective and minimal intervention to acquire soft-labels which induce robust classifiers despite the inconsistency of the individual soft-labeling methods.

Modern health care systems are conducting continuous, automated surveillance of the electronic medical record (EMR) to identify adverse events with increasing frequency; however, many events such as sepsis do not have elucidated prodromes (i.e., event chains) that can be used to identify and intercept the adverse event early in its course. Clinically relevant and interpretable results require a framework that can (i) infer temporal interactions across multiple patient features found in EMR data (e.g., Labs, vital signs, etc.) and (ii) identify patterns that precede and are specific to an impending adverse event (e.g., sepsis). In this work, we propose a linear multivariate Hawkes process model, coupled with ReLU link function, to recover a Granger Causal (GC) graph with both exciting and inhibiting effects. We develop a scalable two-phase gradient-based method to obtain a maximum surrogate-likelihood estimator, which is shown to be effective via extensive numerical simulation. Our method is subsequently extended to a data set of patients admitted to Grady hospital system in Atlanta, GA, USA, where the estimated GC graph identifies several highly interpretable GC chains that precede sepsis. The code is available at \url{https://github.com/SongWei-GT/two-phase-MHP}.

Uncertainty quantification is a central challenge in reliable and trustworthy machine learning. Naive measures such as last-layer scores are well-known to yield overconfident estimates in the context of overparametrized neural networks. Several methods, ranging from temperature scaling to different Bayesian treatments of neural networks, have been proposed to mitigate overconfidence, most often supported by the numerical observation that they yield better calibrated uncertainty measures. In this work, we provide a sharp comparison between popular uncertainty measures for binary classification in a mathematically tractable model for overparametrized neural networks: the random features model. We discuss a trade-off between classification accuracy and calibration, unveiling a double descent like behavior in the calibration curve of optimally regularized estimators as a function of overparametrization. This is in contrast with the empirical Bayes method, which we show to be well calibrated in our setting despite the higher generalization error and overparametrization.

Existing models in cognitive science typically assume human categorization as graded generalization behavior in a multidimensional psychological space. However, category representations in these models may suffer from the curse of dimensionality in a natural setting. People generally rely on a tractable yet sufficient set of features to understand the complex environment. We propose a rational model of categorization based on a hierarchical mixture of probabilistic principal components, that simultaneously learn category representations and an economical collection of features. The model captures dimensional biases in human categorization and supports zero-shot learning. We further exploit a generative process within a low-dimensional latent space to provide a better account of categorization with high-dimensional stimuli.