The graph Laplacian is a standard tool in data science, machine learning, and image processing. The corresponding matrix inherits the complex structure of the underlying network and is in certain applications densely populated. This makes computations, in particular matrix-vector products, with the graph Laplacian a hard task. A typical application is the computation of a number of its eigenvalues and eigenvectors. Standard methods become infeasible as the number of nodes in the graph is too large. We propose the use of the fast summation based on the nonequispaced fast Fourier transform (NFFT) to perform the dense matrix-vector product with the graph Laplacian fast without ever forming the whole matrix. The enormous flexibility of the NFFT algorithm allows us to embed the accelerated multiplication into Lanczos-based eigenvalues routines or iterative linear system solvers. We illustrate the feasibility of our approach on a number of test problems from image segmentation to semi-supervised learning based on graph-based PDEs. In particular, we compare our approach with the Nystr\"om method. Moreover, we present and test an enhanced, hybrid version of the Nystr\"om method, which internally uses the NFFT.

Collaborative filtering is an important technique for recommendation. Whereas it has been repeatedly shown to be effective in previous work, its performance remains unsatisfactory in many real-world applications, especially those where the items or users are highly diverse. In this paper, we explore an ensemble-based framework to enhance the capability of a recommender in handling diverse data. Specifically, we formulate a probabilistic model which integrates the items, the users, as well as the associations between them into a generative process. On top of this formulation, we further derive a progressive algorithm to construct an ensemble of collaborative filters. In each iteration, a new filter is derived from re-weighted entries and incorporated into the ensemble. It is noteworthy that while the algorithmic procedure of our algorithm is apparently similar to boosting, it is derived from an essentially different formulation and thus differs in several key technical aspects. We tested the proposed method on three large datasets, and observed substantial improvement over the state of the art, including L2Boost, an effective method based on boosting.

Neural networks with ReLU activations have achieved great empirical success in various domains. However, existing results for learning ReLU networks either pose assumptions on the underlying data distribution being e.g. Gaussian, or require the network size and/or training size to be sufficiently large. In this context, the problem of learning a two-layer ReLU network is approached in a binary classification setting, where the data are linearly separable and a hinge loss criterion is adopted. Leveraging the power of random noise, this contribution presents a novel stochastic gradient descent (SGD) algorithm, which can provably train any single-hidden-layer ReLU network to attain global optimality, despite the presence of infinitely many bad local minima and saddle points in general. This result is the first of its kind, requiring no assumptions on the data distribution, training/network size, or initialization. Convergence of the resultant iterative algorithm to a global minimum is analyzed by establishing both an upper bound and a lower bound on the number of effective (non-zero) updates to be performed. Furthermore, generalization guarantees are developed for ReLU networks trained with the novel SGD. These guarantees highlight a fundamental difference (at least in the worst case) between learning a ReLU network as well as a leaky ReLU network in terms of sample complexity. Numerical tests using synthetic data and real images validate the effectiveness of the algorithm and the practical merits of the theory.

Long-term human motion can be represented as a series of motion modes---motion sequences that capture short-term temporal dynamics---with transitions between them. We leverage this structure and present a novel Motion Transformation Variational Auto-Encoders (MT-VAE) for learning motion sequence generation. Our model jointly learns a feature embedding for motion modes (that the motion sequence can be reconstructed from) and a feature transformation that represents the transition of one motion mode to the next motion mode. Our model is able to generate multiple diverse and plausible motion sequences in the future from the same input. We apply our approach to both facial and full body motion, and demonstrate applications like analogy-based motion transfer and video synthesis.

Several statistical and machine learning methods are proposed to estimate the type and intensity of physical load and accumulated fatigue . They are based on the statistical analysis of accumulated and moving window data subsets with construction of a kurtosis-skewness diagram. This approach was applied to the data gathered by the wearable heart monitor for various types and levels of physical activities, and for people with various physical conditions. The different levels of physical activities, loads, and fitness can be distinguished from the kurtosis-skewness diagram, and their evolution can be monitored. Several metrics for estimation of the instant effect and accumulated effect (physical fatigue) of physical loads were proposed. The data and results presented allow to extend application of these methods for modeling and characterization of complex human activity patterns, for example, to estimate the actual and accumulated physical load and fatigue, model the potential dangerous development, and give cautions and advice in real time.

As a promising area in artificial intelligence, a new learning paradigm, called Small Sample Learning (SSL), has been attracting prominent research attention in the recent years. In this paper, we aim to present a survey to comprehensively introduce the current techniques proposed on this topic. Specifically, current SSL techniques can be mainly divided into two categories. The first category of SSL approaches can be called "concept learning", which emphasizes learning new concepts from only few related observations. The purpose is mainly to simulate human learning behaviors like recognition, generation, imagination, synthesis and analysis. The second category is called "experience learning", which usually co-exists with the large sample learning manner of conventional machine learning. This category mainly focuses on learning with insufficient samples, and can also be called small data learning in some literatures. More extensive surveys on both categories of SSL techniques are introduced and some neuroscience evidences are provided to clarify the rationality of the entire SSL regime, and the relationship with human learning process. Some discussions on the main challenges and possible future research directions along this line are also presented.

We consider the problem in precision health of grouping people into subpopulations based on their degree of vulnerability to a risk factor. These subpopulations cannot be discovered with traditional clustering techniques because their quality is evaluated with a supervised metric: the ease of modeling a response variable over observations within them. Instead, we apply the supervised cadre model (SCM), which does use this metric. We extend the SCM formalism so that it may be applied to multivariate regression and binary classification problems. We also develop a way to use conditional entropy to assess the confidence in the process by which a subject is assigned their cadre. Using the SCM, we generalize the environment-wide association study (EWAS) workflow to be able to model heterogeneity in population risk. In our EWAS, we consider more than two hundred environmental exposure factors and find their association with diastolic blood pressure, systolic blood pressure, and hypertension. This requires adapting the SCM to be applicable to data generated by a complex survey design. After correcting for false positives, we found 25 exposure variables that had a significant association with at least one of our response variables. Eight of these were significant for a discovered subpopulation but not for the overall population. Some of these associations have been identified by previous researchers, while others appear to be novel associations. We examine several learned subpopulations in detail, and we find that they are interpretable and that they suggest further research questions.

Recent theoretical work has demonstrated that deep neural networks have superior performance over shallow networks, but their training is more difficult, e.g., they suffer from the vanishing gradient problem. This problem can be typically resolved by the rectified linear unit (ReLU) activation. However, here we show that even for such activation, deep and narrow neural networks will converge to erroneous mean or median states of the target function depending on the loss with high probability. We demonstrate this collapse of deep and narrow neural networks both numerically and theoretically, and provide estimates of the probability of collapse. We also construct a diagram of a safe region of designing neural networks that avoid the collapse to erroneous states. Finally, we examine different ways of initialization and normalization that may avoid the collapse problem.

Early detection of preventable diseases is important for better disease management, improved inter-ventions, and more efficient health-care resource allocation. Various machine learning approacheshave been developed to utilize information in Electronic Health Record (EHR) for this task. Majorityof previous attempts, however, focus on structured fields and lose the vast amount of information inthe unstructured notes. In this work we propose a general multi-task framework for disease onsetprediction that combines both free-text medical notes and structured information. We compareperformance of different deep learning architectures including CNN, LSTM and hierarchical models.In contrast to traditional text-based prediction models, our approach does not require disease specificfeature engineering, and can handle negations and numerical values that exist in the text. Ourresults on a cohort of about 1 million patients show that models using text outperform modelsusing just structured data, and that models capable of using numerical values and negations in thetext, in addition to the raw text, further improve performance. Additionally, we compare differentvisualization methods for medical professionals to interpret model predictions.

Optical coherence tomography (OCT) based measurements of retinal layer thickness, such as the retinal nerve fibre layer (RNFL) and the ganglion cell with inner plexiform layer (GCIPL) are commonly used for the diagnosis and monitoring of glaucoma. Previously, machine learning techniques have relied on segmentation-based imaging features such as the peripapillary RNFL thickness and the cup-to-disc ratio. Here, we propose a deep learning technique that classifies eyes as healthy or glaucomatous directly from raw, unsegmented OCT volumes of the optic nerve head (ONH) using a 3D Convolutional Neural Network (CNN). We compared the accuracy of this technique with various feature-based machine learning algorithms and demonstrated the superiority of the proposed deep learning based method. Logistic regression was found to be the best performing classical machine learning technique with an AUC of 0.89. In direct comparison, the deep learning approach achieved a substantially higher AUC of 0.94 with the additional advantage of providing insight into which regions of an OCT volume are important for glaucoma detection. Computing Class Activation Maps (CAM), we found that the CNN identified neuroretinal rim and optic disc cupping as well as the lamina cribrosa (LC) and its surrounding areas as the regions significantly associated with the glaucoma classification. These regions anatomically correspond to the well established and commonly used clinical markers for glaucoma diagnosis such as increased cup volume, cup diameter, and neuroretinal rim thinning at the superior and inferior segments.