A survey of early work exploring how AI can be used in medicine, with somewhat more technical expositions than in the complementary volume Artificial Intelligence in Medicine."Each chapter is preceded by a brief introduction that outlines our view of its contribution to the field, the reason it was selected for inclusion in this volume, an overview of its content, and a discussion of how the work evolved after the article appeared and how it relates to other chapters in the book.

BACKGROUND AND PURPOSE: Alberta Stroke Program Early CT Score (ASPECTS) was devised as a systematic method to assess the extent of early ischemic change on noncontrast CT (NCCT) in patients with acute ischemic stroke (AIS). Our aim was to automate ASPECTS to objectively score NCCT of AIS patients. MATERIALS AND METHODS: We collected NCCT images with a 5-mm thickness of 257 patients with acute ischemic stroke ( 8 hours from onset to scans) followed by a diffusion-weighted imaging acquisition within 1 hour. Expert ASPECTS readings on DWI were used as ground truth. Texture features were extracted from each ASPECTS region of the 157 training patient images to train a random forest classifier. The unseen 100 testing patient images were used to evaluate the performance of the trained classifier.

We investigate the problem of classification in the presence of unknown class conditional label noise in which the labels observed by the learner have been corrupted with some unknown class dependent probability. In order to obtain finite sample rates, previous approaches to classification with unknown class conditional label noise have required that the regression function attains its extrema uniformly on sets of positive measure. We shall consider this problem in the setting of non-compact metric spaces, where the regression function need not attain its extrema. In this setting we determine the minimax optimal learning rates (up to logarithmic factors). The rate displays interesting threshold behaviour: When the regression function approaches its extrema at a sufficient rate, the optimal learning rates are of the same order as those obtained in the label-noise free setting. If the regression function approaches its extrema more gradually then classification performance necessarily degrades. In addition, we present an algorithm which attains these rates without prior knowledge of either the distributional parameters or the local density. This identifies for the first time a scenario in which finite sample rates are achievable in the label noise setting, but they differ from the optimal rates without label noise.

We propose a novel exponentially-modified Gaussian (EMG) mixture residual model. The EMG mixture is well suited to model residuals that are contaminated by a distribution with positive support. This is in contrast to commonly used robust residual models, like the Huber loss or $\ell_1$, which assume a symmetric contaminating distribution and are otherwise asymptotically biased. We propose an expectation-maximization algorithm to optimize an arbitrary model with respect to the EMG mixture. We apply the approach to linear regression and probabilistic matrix factorization (PMF). We compare against other residual models, including quantile regression. Our numerical experiments demonstrate the strengths of the EMG mixture on both tasks. The PMF model arises from considering spectroscopic data. In particular, we demonstrate the effectiveness of PMF in conjunction with the EMG mixture model on synthetic data and two real-world applications: X-ray diffraction and Raman spectroscopy. We show how our approach is effective in inferring background signals and systematic errors in data arising from these experimental settings, dramatically outperforming existing approaches and revealing the data's physically meaningful components.

Quantum Clustering is a powerful method to detect clusters in data with mixed density. However, it is very sensitive to a length parameter that is inherent to the Schr\"odinger equation. In addition, linking data points into clusters requires local estimates of covariance that are also controlled by length parameters. This raises the question of how to adjust the control parameters of the Schr\"odinger equation for optimal clustering. We propose a probabilistic framework that provides an objective function for the goodness-of-fit to the data, enabling the control parameters to be optimised within a Bayesian framework. This naturally yields probabilities of cluster membership and data partitions with specific numbers of clusters. The proposed framework is tested on real and synthetic data sets, assessing its validity by measuring concordance with known data structure by means of the Jaccard score (JS). This work also proposes an objective way to measure performance in unsupervised learning that correlates very well with JS.

In the context of individual-level causal inference, we study the problem of predicting whether someone will respond or not to a treatment based on their features and past examples of features, treatment indicator (e.g., drug/no drug), and a binary outcome (e.g., recovery from disease). As a classification task, the problem is made difficult by not knowing the example outcomes under the opposite treatment indicators. We assume the effect is monotonic, as in advertising's effect on a purchase or bail-setting's effect on reappearance in court: either it would have happened regardless of treatment, not happened regardless, or happened only depending on exposure to treatment. Predicting whether the latter is latently the case is our focus. While previous work focuses on conditional average treatment effect estimation, formulating the problem as a classification task rather than an estimation task allows us to develop new tools more suited to this problem. By leveraging monotonicity, we develop new discriminative and generative algorithms for the responder-classification problem. We explore and discuss connections to corrupted data and policy learning. We provide an empirical study with both synthetic and real datasets to compare these specialized algorithms to standard benchmarks.

In this paper we study the generalisation capabilities of fully-connected neural networks trained in the context of time series forecasting. Time series do not satisfy the typical assumption in statistical learning theory of the data being i.i.d. samples from some data-generating distribution. We use the input and weight Hessians, that is the smoothness of the learned function with respect to the input and the width of the minimum in weight space, to quantify a network's ability to generalise to unseen data. While such generalisation metrics have been studied extensively in the i.i.d. setting of for example image recognition, here we empirically validate their use in the task of time series forecasting. Furthermore we discuss how one can control the generalisation capability of the network by means of the training process using the learning rate, batch size and the number of training iterations as controls. Using these hyperparameters one can efficiently control the complexity of the output function without imposing explicit constraints.

We give nearly matching upper and lower bounds on the oracle complexity of finding $\epsilon$-stationary points ($\| \nabla F(x) \| \leq\epsilon$) in stochastic convex optimization. We jointly analyze the oracle complexity in both the local stochastic oracle model and the global oracle (or, statistical learning) model. This allows us to decompose the complexity of finding near-stationary points into optimization complexity and sample complexity, and reveals some surprising differences between the complexity of stochastic optimization versus learning. Notably, we show that in the global oracle/statistical learning model, only logarithmic dependence on smoothness is required to find a near-stationary point, whereas polynomial dependence on smoothness is necessary in the local stochastic oracle model. In other words, the separation in complexity between the two models can be exponential, and that the folklore understanding that smoothness is required to find stationary points is only weakly true for statistical learning. Our upper bounds are based on extensions of a recent "recursive regularization" technique proposed by Allen-Zhu (2018). We show how to extend the technique to achieve near-optimal rates, and in particular show how to leverage the extra information available in the global oracle model. Our algorithm for the global model can be implemented efficiently through finite sum methods, and suggests an interesting new computational-statistical tradeoff.

We design and study a Contextual Memory Tree (CMT), a learning memory controller that inserts new memories into an experience store of unbounded size. It is designed to efficiently query for memories from that store, supporting logarithmic time insertion and retrieval operations. Hence CMT can be integrated into existing statistical learning algorithms as an augmented memory unit without substantially increasing training and inference computation. Furthermore CMT operates as a reduction to classification, allowing it to benefit from advances in representation or architecture. We demonstrate the efficacy of CMT by augmenting existing multi-class and multi-label classification algorithms with CMT and observe statistical improvement. We also test CMT learning on several image-captioning tasks to demonstrate that it performs computationally better than a simple nearest neighbors memory system while benefitting from reward learning.

Distinguishing between classes of time series sampled from dynamic systems is a common challenge in systems and control engineering, for example in the context of health monitoring, fault detection, and quality control. The challenge is increased when no underlying model of a system is known, measurement noise is present, and long signals need to be interpreted. In this paper we address these issues with a new non parametric classifier based on topological signatures. Our model learns classes as weighted kernel density estimates (KDEs) over persistent homology diagrams and predicts new trajectory labels using Sinkhorn divergences on the space of diagram KDEs to quantify proximity. We show that this approach accurately discriminates between states of chaotic systems that are close in parameter space, and its performance is robust to noise.