Recurrent neural networks (RNNs) are instrumental in modelling sequential and time-series data. Yet, when using RNNs to inform decision-making, predictions by themselves are not sufficient; we also need estimates of predictive uncertainty. Existing approaches for uncertainty quantification in RNNs are based predominantly on Bayesian methods; these are computationally prohibitive, and require major alterations to the RNN architecture and training. Capitalizing on ideas from classical jackknife resampling, we develop a frequentist alternative that: (a) does not interfere with model training or compromise its accuracy, (b) applies to any RNN architecture, and (c) provides theoretical coverage guarantees on the estimated uncertainty intervals. Our method derives predictive uncertainty from the variability of the (jackknife) sampling distribution of the RNN outputs, which is estimated by repeatedly deleting blocks of (temporally-correlated) training data, and collecting the predictions of the RNN re-trained on the remaining data. To avoid exhaustive re-training, we utilize influence functions to estimate the effect of removing training data blocks on the learned RNN parameters. Using data from a critical care setting, we demonstrate the utility of uncertainty quantification in sequential decision-making.

Type 2 diabetes (T2DM), one of the most prevalent chronic diseases, affects the glucose metabolism of the human body, which decreases the quantity of life and brings a heavy burden on social medical care. Patients with T2DM are more likely to suffer bone fragility fracture as diabetes affects bone mineral density (BMD). However, the discovery of the determinant factors of BMD in a medical way is expensive and time-consuming. In this paper, we propose a novel algorithm, Prior-Knowledge-driven local Causal structure Learning (PKCL), to discover the underlying causal mechanism between BMD and its factors from the clinical data. Since there exist limited data but redundant prior knowledge for medicine, PKCL adequately utilize the prior knowledge to mine the local causal structure for the target relationship. Combining the medical prior knowledge with the discovered causal relationships, PKCL can achieve more reliable results without long-standing medical statistical experiments. Extensive experiments are conducted on a newly provided clinical data set. The experimental study of PKCL on the data is proved to highly corresponding with existing medical knowledge, which demonstrates the superiority and effectiveness of PKCL. To illustrate the importance of prior knowledge, the result of the algorithm without prior knowledge is also investigated.

High-dimensional generative models have many applications including image compression, multimedia generation, anomaly detection and data completion. State-of-the-art estimators for natural images are autoregressive, decomposing the joint distribution over pixels into a product of conditionals parameterized by a deep neural network, e.g. a convolutional neural network such as the PixelCNN. However, PixelCNNs only model a single decomposition of the joint, and only a single generation order is efficient. For tasks such as image completion, these models are unable to use much of the observed context. To generate data in arbitrary orders, we introduce LMConv: a simple modification to the standard 2D convolution that allows arbitrary masks to be applied to the weights at each location in the image. Using LMConv, we learn an ensemble of distribution estimators that share parameters but differ in generation order, achieving improved performance on whole-image density estimation (2.89 bpd on unconditional CIFAR10), as well as globally coherent image completions. Our code is available at https://ajayjain.github.io/lmconv.

We consider the problem of learning a sparse graph under Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the precision matrix under Laplacian structural constraints. Like in the classical graphical lasso problem, recent works made use of the $\ell_1$-norm regularization with the goal of promoting sparsity in Laplacian structural precision matrix estimation. However, we find that the widely used $\ell_1$-norm is not effective in imposing a sparse solution in this problem. Through empirical evidence, we observe that the number of nonzero graph weights grows with the increase of the regularization parameter. From a theoretical perspective, we prove that a large regularization parameter will surprisingly lead to a fully connected graph. To address this issue, we propose a nonconvex estimation method by solving a sequence of weighted $\ell_1$-norm penalized sub-problems and prove that the statistical error of the proposed estimator matches the minimax lower bound. To solve each sub-problem, we develop a projected gradient descent algorithm that enjoys a linear convergence rate. Numerical experiments involving synthetic and real-world data sets from the recent COVID-19 pandemic and financial stock markets demonstrate the effectiveness of the proposed method. An open source $\mathsf{R}$ package containing the code for all the experiments is available at https://github.com/mirca/sparseGraph.

Connectionist models such as neural networks suffer from catastrophic forgetting. In this work, we study this problem from the perspective of information theory and define forgetting as the increase of description lengths of previous data when they are compressed with a sequentially learned model. In addition, we show that continual learning approaches based on variational posterior approximation and generative replay can be considered as approximations to two prequential coding methods in compression, namely, the Bayesian mixture code and maximum likelihood (ML) plug-in code. We compare these approaches in terms of both compression and forgetting and empirically study the reasons that limit the performance of continual learning methods based on variational posterior approximation. To address these limitations, we propose a new continual learning method that combines ML plug-in and Bayesian mixture codes.

Modern neural networks have proven to be powerful function approximators, providing state-of-the-art performance in a multitude of applications. They however fall short in their ability to quantify confidence in their predictions - this is crucial in high-stakes applications that involve critical decision-making. Bayesian neural networks (BNNs) aim at solving this problem by placing a prior distribution over the network's parameters, thereby inducing a posterior distribution that encapsulates predictive uncertainty. While existing variants of BNNs based on Monte Carlo dropout produce reliable (albeit approximate) uncertainty estimates over in-distribution data, they tend to exhibit over-confidence in predictions made on target data whose feature distribution differs from the training data, i.e., the covariate shift setup. In this paper, we develop an approximate Bayesian inference scheme based on posterior regularisation, wherein unlabelled target data are used as "pseudo-labels" of model confidence that are used to regularise the model's loss on labelled source data. We show that this approach significantly improves the accuracy of uncertainty quantification on covariate-shifted data sets, with minimal modification to the underlying model architecture. We demonstrate the utility of our method in the context of transferring prognostic models of prostate cancer across globally diverse populations.

Set classification aims to classify a set of observations as a whole, as opposed to classifying individual observations separately. To formally understand the unfamiliar concept of binary set classification, we first investigate the optimal decision rule under the normal distribution, which utilizes the empirical covariance of the set to be classified. We show that the number of observations in the set plays a critical role in bounding the Bayes risk. Under this framework, we further propose new methods of set classification. For the case where only a few parameters of the model drive the difference between two classes, we propose a computationally-efficient approach to parameter estimation using linear programming, leading to the Covariance-engaged LInear Programming Set (CLIPS) classifier. Its theoretical properties are investigated for both independent case and various (short-range and long-range dependent) time series structures among observations within each set. The convergence rates of estimation errors and risk of the CLIPS classifier are established to show that having multiple observations in a set leads to faster convergence rates, compared to the standard classification situation in which there is only one observation in the set. The applicable domains in which the CLIPS performs better than competitors are highlighted in a comprehensive simulation study. Finally, we illustrate the usefulness of the proposed methods in classification of real image data in histopathology.

Automated machine learning (AutoML) can produce complex model ensembles by stacking, bagging, and boosting many individual models like trees, deep networks, and nearest neighbor estimators. While highly accurate, the resulting predictors are large, slow, and opaque as compared to their constituents. To improve the deployment of AutoML on tabular data, we propose FAST-DAD to distill arbitrarily complex ensemble predictors into individual models like boosted trees, random forests, and deep networks. At the heart of our approach is a data augmentation strategy based on Gibbs sampling from a self-attention pseudolikelihood estimator. Across 30 datasets spanning regression and binary/multiclass classification tasks, FAST-DAD distillation produces significantly better individual models than one obtains through standard training on the original data. Our individual distilled models are over 10x faster and more accurate than ensemble predictors produced by AutoML tools like H2O/AutoSklearn.

Active search refers to the problem of efficiently locating targets in an unknown environment by actively making data-collection decisions, and has many applications including detecting gas leaks, radiation sources or human survivors of disasters using aerial and/or ground robots (agents). Existing active search methods are in general only amenable to a single agent, or if they extend to multi agent they require a central control system to coordinate the actions of all agents. However, such control systems are often impractical in robotics applications. In this paper, we propose two distinct active search algorithms called SPATS (Sparse Parallel Asynchronous Thompson Sampling) and LATSI (LAplace Thompson Sampling with Information gain) that allow for multiple agents to independently make data-collection decisions without a central coordinator. Throughout we consider that targets are sparsely located around the environment in keeping with compressive sensing assumptions and its applicability in real world scenarios. Additionally, while most common search algorithms assume that agents can sense the entire environment (e.g. compressive sensing) or sense point-wise (e.g. Bayesian Optimization) at all times, we make a realistic assumption that each agent can only sense a contiguous region of space at a time. We provide simulation results as well as theoretical analysis to demonstrate the efficacy of our proposed algorithms.

In this paper, we present a new idea for Transfer Learning (TL) based on Gibbs Sampling. Gibbs sampling is an algorithm in which instances are likely to transfer to a new state with a higher possibility with respect to a probability distribution. We find that such an algorithm can be employed to transfer instances between domains. Restricted Boltzmann Machine (RBM) is an energy based model that is very feasible for being trained to represent a data distribution and also for performing Gibbs sampling. We used RBM to capture data distribution of the source domain and use it in order to cast target instances into new data with a distribution similar to the distribution of source data. Using datasets that are commonly used for evaluation of TL methods, we show that our method can successfully enhance target classification by a considerable ratio. Additionally, the proposed method has the advantage over common DA methods that it needs no target data during the process of training of models.