In this paper we study Meta learning of Gaussian graphical models. In our setup, each task has a different true precision matrix, each with a possibly different support (i.e., set of edges in the graph). We assume that the union of the supports of all the true precision matrices (i.e., the true support union) is small in size, which relates to sparse graphs. We propose to pool all the samples from different tasks, and estimate a single precision matrix by $\ell_1$-regularized maximum likelihood estimation. We show that with high probability, the support of the estimated single precision matrix is equal to the true support union, provided a sufficient number of samples per task $n \in O((\log N)/K)$, for $N$ nodes and $K$ tasks. That is, one requires less samples per task when more tasks are available. We prove a matching information-theoretic lower bound for the necessary number of samples, which is $n \in \Omega((\log N)/K)$, and thus, our algorithm is minimax optimal. Synthetic experiments validate our theory.

The James-Stein (JS) shrinkage estimator is a biased estimator that captures the mean of Gaussian random vectors.While it has a desirable statistical property of dominance over the maximum likelihood estimator (MLE) in terms of mean squared error (MSE), not much progress has been made on extending the estimator onto manifold-valued data. We propose C-SURE, a novel Stein's unbiased risk estimate (SURE) of the JS estimator on the manifold of complex-valued data with a theoretically proven optimum over MLE. Adapting the architecture of the complex-valued SurReal classifier, we further incorporate C-SURE into a prototype convolutional neural network (CNN) classifier. We compare C-SURE with SurReal and a real-valued baseline on complex-valued MSTAR and RadioML datasets. C-SURE is more accurate and robust than SurReal, and the shrinkage estimator is always better than MLE for the same prototype classifier. Like SurReal, C-SURE is much smaller, outperforming the real-valued baseline on MSTAR (RadioML) with less than 1 percent (3 percent) of the baseline size

Background: The expanding research in the field of long non-coding RNAs(lncRNAs) showed abnormal expression of lncRNAs in many complex diseases. Accurately identifying lncRNA-disease association is essential in understanding lncRNA functionality and disease mechanism. There are many machine learning techniques involved in the prediction of lncRNA-disease association which use different biological interaction networks and associated features. Feature learning from the network structured data is one of the limiting factors of machine learning-based methods. Graph neural network based techniques solve this limitation by unsupervised feature learning. Deep belief networks (DBN) are recently used in biological network analysis to learn the latent representations of network features. Method: In this paper, we propose a DBN based lncRNA-disease association prediction model (DBNLDA) from lncRNA, disease and miRNA interactions. The architecture contains three major modules-network construction, DBN based feature learning and neural network-based prediction. First, we constructed three heterogeneous networks such as lncRNA-miRNA similarity (LMS), disease-miRNA similarity (DMS) and lncRNA-disease association (LDA) network. From the node embedding matrices of similarity networks, lncRNA-disease representations were learned separately by two DBN based subnetworks. The joint representation of lncRNA-disease was learned by a third DBN from outputs of the two subnetworks mentioned. This joint feature representation was used to predict the association score by an ANN classifier. Result: The proposed method obtained AUC of 0.96 and AUPR of 0.967 when tested against standard dataset used by the state-of-the-art methods. Analysis on breast, lung and stomach cancer cases also affirmed the effectiveness of DBNLDA in predicting significant lncRNA-disease associations.

In the absence of large labelled datasets, self-supervised learning techniques can boost performance by learning useful representations from unlabelled data, which is often more readily available. However, there is often a domain shift between the unlabelled collection and the downstream target problem data. We show that by learning Bayesian instance weights for the unlabelled data, we can improve the downstream classification accuracy by prioritising the most useful instances. Additionally, we show that the training time can be reduced by discarding unnecessary datapoints. Our method, BetaDataWeighter is evaluated using the popular self-supervised rotation prediction task on STL-10 and Visual Decathlon. We compare to related instance weighting schemes, both hand-designed heuristics and meta-learning, as well as conventional self-supervised learning. BetaDataWeighter achieves both the highest average accuracy and rank across datasets, and on STL-10 it prunes up to 78% of unlabelled images without significant loss in accuracy, corresponding to over 50% reduction in training time.

When working with multimodal Bayesian posterior distributions, Markov chain Monte Carlo (MCMC) algorithms can have difficulty moving between modes, and default variational or mode-based approximate inferences will understate posterior uncertainty. And, even if the most important modes can be found, it is difficult to evaluate their relative weights in the posterior. Here we propose an alternative approach, using parallel runs of MCMC, variational, or mode-based inference to hit as many modes or separated regions as possible, and then combining these using importance sampling based Bayesian stacking, a scalable method for constructing a weighted average of distributions so as to maximize cross-validated prediction utility. The result from stacking is not necessarily equivalent, even asymptotically, to fully Bayesian inference, but it serves many of the same goals. Under misspecified models, stacking can give better predictive performance than full Bayesian inference, hence the multimodality can be considered a blessing rather than a curse. We explore with an example where the stacked inference approximates the true data generating process from the misspecified model, an example of inconsistent inference, and non-mixing samplers. We elaborate the practical implantation in the context of latent Dirichlet allocation, Gaussian process regression, hierarchical model, variational inference in horseshoe regression, and neural networks.

We propose Deep Residual Mixture Models (DRMMs) which share the many desirable properties of Gaussian Mixture Models (GMMs), but with a crucial benefit: The modeling capacity of a DRMM can grow exponentially with depth, while the number of model parameters only grows quadratically. DRMMs allow for extremely flexible conditional sampling, as the conditioning variables can be freely selected without re-training the model, and it is easy to combine the sampling with priors and (in)equality constraints. DRMMs should be applicable where GMMs are traditionally used, but as demonstrated in our experiments, DRMMs scale better to complex, high-dimensional data. We demonstrate the approach in constrained multi-limb inverse kinematics and image completion.

Neural Networks (NNs) have provided state-of-the-art results for many challenging machine learning tasks such as detection, regression and classification across the domains of computer vision, speech recognition and natural language processing. Despite their success, they are often implemented in a frequentist scheme, meaning they are unable to reason about uncertainty in their predictions. This article introduces Bayesian Neural Networks (BNNs) and the seminal research regarding their implementation. Different approximate inference methods are compared, and used to highlight where future research can improve on current methods.

Many democratic countries use district-based elections where there is a "seat" for each district in the governing body. In each district, the party whose candidate gets the maximum number of votes wins the corresponding seat. The result of the election is decided based on the number of seats won by the different parties. The electors (voters) can cast their votes only in the district of their residence. Thus, locations of the electors and boundaries of the districts may severely affect the election result even if the proportion of popular support (number of electors) of different parties remains unchanged. This has led to significant amount of research on whether the districts may be redrawn or electors may be moved to maximize seats for a particular party. In this paper, we frame the spatial distribution of electors in a probabilistic setting, and explore different models to capture the intra-district polarization of electors in favour of a party, or the spatial concentration of supporters of different parties. Our models are inspired by elections in India, where supporters of different parties tend to be concentrated in certain districts. We show with extensive simulations that our model can capture different statistical properties of real elections held in India. We frame parameter estimation problems to fit our models to the observed election results. Since analytical calculation of the likelihood functions are infeasible for our complex models, we use Likelihood-free Inference methods under the Approximate Bayesian Computation framework. Since this approach is highly time-consuming, we explore how supervised regression using Logistic Regression or Deep Neural Networks can be used to speed it up. We also explore how the election results can change by varying the spatial distributions of the voters, even when the proportions of popular support of the parties remain constant.

Bayesian meta-learning enables robust and fast adaptation to new tasks with uncertainty assessment. The key idea behind Bayesian meta-learning is empirical Bayes inference of hierarchical model. In this work, we extend this framework to include a variety of existing methods, before proposing our variant based on gradient-EM algorithm. Our method improves computational efficiency by avoiding back-propagation computation in the meta-update step, which is exhausting for deep neural networks. Furthermore, it provides flexibility to the inner-update optimization procedure by decoupling it from meta-update. Experiments on sinusoidal regression, few-shot image classification, and policy-based reinforcement learning show that our method not only achieves better accuracy with less computation cost, but is also more robust to uncertainty.

The model uncertainty obtained by variational Bayesian inference with Monte Carlo dropout is prone to miscalibration. In this paper, different logit scaling methods are extended to dropout variational inference to recalibrate model uncertainty. Expected uncertainty calibration error (UCE) is presented as a metric to measure miscalibration. The effectiveness of recalibration is evaluated on CIFAR-10/100 and SVHN for recent CNN architectures. Experimental results show that logit scaling considerably reduce miscalibration by means of UCE. Well-calibrated uncertainty enables reliable rejection of uncertain predictions and robust detection of out-of-distribution data.