Understanding and quantifying uncertainty in black box Neural Networks (NNs) is critical when deployed in real-world settings such as healthcare. Recent works using Bayesian and non-Bayesian methods have shown how a unified predictive uncertainty can be modelled for NNs. Decomposing this uncertainty to disentangle the granular sources of heteroscedasticity in data provides rich information about its underlying causes. We propose a conceptually simple non-Bayesian approach, deep split ensemble, to disentangle the predictive uncertainties using a multivariate Gaussian mixture model. The NNs are trained with clusters of input features, for uncertainty estimates per cluster. We evaluate our approach on a series of benchmark regression datasets, while also comparing with unified uncertainty methods. Extensive analyses using dataset shits and empirical rule highlight our inherently well-calibrated models. Our work further demonstrates its applicability in a multi-modal setting using a benchmark Alzheimer's dataset and also shows how deep split ensembles can highlight hidden modality-specific biases. The minimal changes required to NNs and the training procedure, and the high flexibility to group features into clusters makes it readily deployable and useful. The source code is available at https://github.com/wazeerzulfikar/deep-split-ensembles

Tensor networks are factorisations of high rank tensors into networks of lower rank tensors and have primarily been used to analyse quantum many-body problems. Tensor networks have seen a recent surge of interest in relation to supervised learning tasks with a focus on image classification. In this work, we improve upon the matrix product state (MPS) tensor networks that can operate on one-dimensional vectors to be useful for working with 2D and 3D medical images. We treat small image regions as orderless, squeeze their spatial information into feature dimensions and then perform MPS operations on these locally orderless regions. These local representations are then aggregated in a hierarchical manner to retain global structure. The proposed locally orderless tensor network (LoTeNet) is compared with relevant methods on three datasets. The architecture of LoTeNet is fixed in all experiments and we show it requires lesser computational resources to attain performance on par or superior to the compared methods.

We show how to use Stein variational gradient descent (SVGD) to carry out inference in Gaussian process (GP) models with non-Gaussian likelihoods and large data volumes. Markov chain Monte Carlo (MCMC) is extremely computationally intensive for these situations, but the parametric assumptions required for efficient variational inference (VI) result in incorrect inference when they encounter the multi-modal posterior distributions that are common for such models. SVGD provides a non-parametric alternative to variational inference which is substantially faster than MCMC but unhindered by parametric assumptions. We prove that for GP models with Lipschitz gradients the SVGD algorithm monotonically decreases the Kullback-Leibler divergence from the sampling distribution to the true posterior. Our method is demonstrated on benchmark problems in both regression and classification, and a real air quality example with 11440 spatiotemporal observations, showing substantial performance improvements over MCMC and VI.

Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known computational burden of Markov Chain Monte Carlo approach for Bayesian regression, we developed a multilevel Gibbs sampler for Bayesian regression of linear mixed models. The level hierarchy of data matrices is created by clustering the features and/or samples of data matrices. Additionally, the use of correlated samples is investigated for variance reduction to improve the convergence of the Markov Chain. Testing on a diverse set of data sets, speed-up is achieved for almost all of them without significant loss in predictive performance.

The success of Deep Neural Networks (DNNs) highly depends on data quality. Moreover, predictive uncertainty makes high performing DNNs risky for real-world deployment. In this paper, we aim to address these two issues by proposing a unified filtering framework leveraging underlying data density, that can effectively denoise training data as well as avoid predicting uncertain test data points. Our proposed framework leverages underlying data distribution to differentiate between noise and clean data samples without requiring any modification to existing DNN architectures or loss functions. Extensive experiments on multiple image classification datasets and multiple CNN architectures demonstrate that our simple yet effective framework can outperform the state-of-the-art techniques in denoising training data and abstaining uncertain test data.

Scientists and engineers are often interested in learning the number of subpopulations (or components) present in a data set. A common suggestion is to use a finite mixture model (FMM) with a prior on the number of components. Past work has shown the resulting FMM component-count posterior is consistent; that is, the posterior concentrates on the true generating number of components. But existing results crucially depend on the assumption that the component likelihoods are perfectly specified. In practice, this assumption is unrealistic, and empirical evidence suggests that the FMM posterior on the number of components is sensitive to the likelihood choice. In this paper, we add rigor to data-analysis folk wisdom by proving that under even the slightest model misspecification, the FMM component-count posterior diverges: the posterior probability of any particular finite number of latent components converges to 0 in the limit of infinite data. We illustrate practical consequences of our theory on simulated and real data sets.

Modern gradient boosting software frameworks, such as XGBoost and LightGBM, implement Newton descent in a functional space. At each boosting iteration, their goal is to find the base hypothesis, selected from some base hypothesis class, that is closest to the Newton descent direction in a Euclidean sense. Typically, the base hypothesis class is fixed to be all binary decision trees up to a given depth. In this work, we study a Heterogeneous Newton Boosting Machine (HNBM) in which the base hypothesis class may vary across boosting iterations. Specifically, at each boosting iteration, the base hypothesis class is chosen, from a fixed set of subclasses, by sampling from a probability distribution. We derive a global linear convergence rate for the HNBM under certain assumptions, and show that it agrees with existing rates for Newton's method when the Newton direction can be perfectly fitted by the base hypothesis at each boosting iteration. We then describe a particular realization of a HNBM, SnapBoost, that, at each boosting iteration, randomly selects between either a decision tree of variable depth or a linear regressor with random Fourier features. We describe how SnapBoost is implemented, with a focus on the training complexity. Finally, we present experimental results, using OpenML and Kaggle datasets, that show that SnapBoost is able to achieve better generalization loss than competing boosting frameworks, without taking significantly longer to tune.

The prototypical network (ProtoNet) is a few-shot learning framework that performs metric learning and classification using the distance to prototype representations of each class. It has attracted a great deal of attention recently since it is simple to implement, highly extensible, and performs well in experiments. However, it only takes into account the mean of the support vectors as prototypes and thus it performs poorly when the support set has high variance. In this paper, we propose to combine ProtoNet with local Fisher discriminant analysis to reduce the local within-class covariance and increase the local between-class covariance of the support set. We show the usefulness of the proposed method by theoretically providing an expected risk bound and empirically demonstrating its superior classification accuracy on miniImageNet and tieredImageNet.

This is part of the Learning path: Get started with IBM Streams. In this developer code pattern, we will be streaming online shopping data and using the data to track the products that each customer has added to the cart. We will build a k-means clustering model with scikit-learn to group customers according to the contents of their shopping carts. The cluster assignment can be used to predict additional products to recommend. Our application will be built using IBM Streams on IBM Cloud Pak for Data.

Machine learning is a field of study in the broad spectrum of artificial intelligence (AI) that can make predictions using data without being explicitly programmed to do so. Machine learning algorithms are used in a wide variety of applications, such as recommendation engines, computer vision, spam filtering and so much more. They perform extraordinary well where it is difficult or infeasible to develop conventional algorithms to perform the needed tasks. While many machine learning algorithms have been around for a long time, the ability to automatically apply complex mathematical calculations to big data-- over and over, faster and faster -- is a recent development. One of the most overwhelmingly represented machine learning techniques is a neural network.