THE next time you visit the local hospital for a chest X-ray, scan, or even a check-up, artificial intelligence (AI) could be having more of a role in your health than you might expect. While we are many years away from a completely automated health service, AI can already help clinicians make better decisions and either augment or even replace human judgments in specific areas of healthcare. Researchers at the John Radcliffe Hospital in the UK have developed an AI diagnostics system that is highly accurate in diagnosing heart disease around 80 percent of the time. At Harvard University, researchers have created a microscope that can detect potentially lethal blood infections. Technologically-based systems help physicians by combing through the gigabytes of data available from journals and textbooks, as well as information from real-time clinical practices.

Precision medicine and artificial intelligence (AI) are complicated by design: Both scientific fields rely on extreme specificity, complex equations, and forces that can't be seen. As both fields begin to alter the healthcare landscape, they could plant a number of legal landmines. Can algorithms or biomarkers be patented? Will centers be able to access the large data sets they need to perform accurate AI? What control over their data should patients have?

In this paper we propose a tensor-based nonlinear model for high-order data classification. The advantages of the proposed scheme are that (i) it significantly reduces the number of weight parameters, and hence of required training samples, and (ii) it retains the spatial structure of the input samples. The proposed model, called \textit{Rank}-1 FNN, is based on a modification of a feedforward neural network (FNN), such that its weights satisfy the {\it rank}-1 canonical decomposition. We also introduce a new learning algorithm to train the model, and we evaluate the \textit{Rank}-1 FNN on third-order hyperspectral data. Experimental results and comparisons indicate that the proposed model outperforms state of the art classification methods, including deep learning based ones, especially in cases with small numbers of available training samples.

Stochastic convex optimization algorithms are the most popular way to train machine learning models on large-scale data. Scaling up the training process of these models is crucial in many applications, but the most popular algorithm, Stochastic Gradient Descent (SGD), is a serial algorithm that is surprisingly hard to parallelize. In this paper, we propose an efficient distributed stochastic optimization method based on adaptive step sizes and variance reduction techniques. We achieve a linear speedup in the number of machines, small memory footprint, and only a small number of synchronization rounds -- logarithmic in dataset size -- in which the computation nodes communicate with each other. Critically, our approach is a general reduction than parallelizes any serial SGD algorithm, allowing us to leverage the significant progress that has been made in designing adaptive SGD algorithms. We conclude by implementing our algorithm in the Spark distributed framework and exhibit dramatic performance gains on large-scale logistic regression problems.

Deep neural network architectures designed for application domains other than sound, especially image recognition, may not optimally harness the time-frequency representation when adapted to the sound recognition problem. In this work, we explore the ConditionaL Neural Network (CLNN) and the Masked ConditionaL Neural Network (MCLNN) for multi-dimensional temporal signal recognition. The CLNN considers the inter-frame relationship, and the MCLNN enforces a systematic sparseness over the network's links to enable learning in frequency bands rather than bins allowing the network to be frequency shift invariant mimicking a filterbank. The mask also allows considering several combinations of features concurrently, which is usually handcrafted through exhaustive manual search. We applied the MCLNN to the environmental sound recognition problem using the ESC-10 and ESC-50 datasets. MCLNN achieved competitive performance, using 12% of the parameters and without augmentation, compared to state-of-the-art Convolutional Neural Networks.

Convolutional operator learning is increasingly gaining attention in many signal processing and computer vision applications. Learning kernels has mostly relied on so-called local approaches that extract and store many overlapping patches across training signals. Due to memory demands, local approaches have limitations when learning kernels from large datasets -- particularly with multi-layered structures, e.g., convolutional neural network (CNN) -- and/or applying the learned kernels to high-dimensional signal recovery problems. The so-called global approach has been studied within the "synthesis" signal model, e.g., convolutional dictionary learning, overcoming the memory problems by careful algorithmic designs. This paper proposes a new convolutional analysis operator learning (CAOL) framework in the global approach, and develops a new convergent Block Proximal Gradient method using a Majorizer (BPG-M) to solve the corresponding block multi-nonconvex problems. To learn diverse filters within the CAOL framework, this paper introduces an orthogonality constraint that enforces a tight-frame (TF) filter condition, and a regularizer that promotes diversity between filters. Numerical experiments show that, for tight majorizers, BPG-M significantly accelerates the CAOL convergence rate compared to the state-of-the-art method, BPG. Numerical experiments for sparse-view computational tomography show that CAOL using TF filters significantly improves reconstruction quality compared to a conventional edge-preserving regularizer. Finally, this paper shows that CAOL can be useful to mathematically model a CNN, and the corresponding updates obtained via BPG-M coincide with core modules of the CNN.

Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy; also called N-distance or energy distance), with numerous successful applications. The representation is constructed as the expectation of the feature map defined by a kernel. As a mean, its classical empirical estimator, however, can be arbitrary severely affected even by a single outlier in case of unbounded features. To the best of our knowledge, unfortunately even the consistency of the existing few techniques trying to alleviate this serious sensitivity bottleneck is unknown. In this paper, we show how the recently emerged principle of median-of-means can be used to design minimax-optimal estimators for kernel mean embedding and MMD, with finite-sample strong outlier-robustness guarantees.

We propose a new Bayesian model for flexible nonlinear regression and classification using tree ensembles. The model is based on the RuleFit approach in Friedman and Popescu (2008) where rules from decision trees and linear terms are used in a L1-regularized regression. We modify RuleFit by replacing the L1-regularization by a horseshoe prior, which is well known to give aggressive shrinkage of noise predictor while leaving the important signal essentially untouched. This is especially important when a large number of rules are used as predictors as many of them only contribute noise. Our horseshoe prior has an additional hierarchical layer that applies more shrinkage a priori to rules with a large number of splits, and to rules that are only satisfied by a few observations. The aggressive noise shrinkage of our prior also makes it possible to complement the rules from boosting in Friedman and Popescu (2008) with an additional set of trees from random forest, which brings a desirable diversity to the ensemble. We sample from the posterior distribution using a very efficient and easily implemented Gibbs sampler. The new model is shown to outperform state-of-the-art methods like RuleFit, BART and random forest on 16 datasets. The model and its interpretation is demonstrated on the well known Boston housing data, and on gene expression data for cancer classification. The posterior sampling, prediction and graphical tools for interpreting the model results are implemented in a publicly available R package.

Regularization has become a primary tool for developing reliable estimators of the covariance matrix in high-dimensional settings. To curb the curse of dimensionality, numerous methods assume that the population covariance (or inverse covariance) matrix is sparse, while making no particular structural assumptions on the desired pattern of sparsity. A highly-related, yet complementary, literature studies the specific setting in which the measured variables have a known ordering, in which case a banded population matrix is often assumed. While the banded approach is conceptually and computationally easier than asking for "patternless sparsity," it is only applicable in very specific situations (such as when data are measured over time or one-dimensional space). This work proposes a generalization of the notion of bandedness that greatly expands the range of problems in which banded estimators apply. We develop convex regularizers occupying the broad middle ground between the former approach of "patternless sparsity" and the latter reliance on having a known ordering. Our framework defines bandedness with respect to a known graph on the measured variables. Such a graph is available in diverse situations, and we provide a theoretical, computational, and applied treatment of two new estimators. An R package, called ggb, implements these new methods.

A reliable modeling of uncertain evidence in Bayesian networks based on a set-valued quantification is proposed. Both soft and virtual evidences are considered. We show that evidence propagation in this setup can be reduced to standard updating in an augmented credal network, equivalent to a set of consistent Bayesian networks. A characterization of the computational complexity for this task is derived together with an efficient exact procedure for a subclass of instances. In the case of multiple uncertain evidences over the same variable, the proposed procedure can provide a set-valued version of the geometric approach to opinion pooling.