Graph embedding methods produce unsupervised node features from graphs that can then be used for a variety of machine learning tasks. Modern graphs, particularly in industrial applications, contain billions of nodes and trillions of edges, which exceeds the capability of existing embedding systems. We present PyTorch-BigGraph (PBG), an embedding system that incorporates several modifications to traditional multi-relation embedding systems that allow it to scale to graphs with billions of nodes and trillions of edges. PBG uses graph partitioning to train arbitrarily large embeddings on either a single machine or in a distributed environment. We demonstrate comparable performance with existing embedding systems on common benchmarks, while allowing for scaling to arbitrarily large graphs and parallelization on multiple machines. We train and evaluate embeddings on several large social network graphs as well as the full Freebase dataset, which contains over 100 million nodes and 2 billion edges. Second, a model with two billion nodes and 100 embedding Graph structured data is a common input to a variety of parameters per node (expressed as floats) would require machine learning tasks (Wu et al., 2018; Cook & Holder, 800GB of memory just to store its parameters, thus many 2006; Nickel et al., 2016a; Hamilton et al., 2017b).

How is popularity gained online? Is being successful strictly related to rapidly becoming viral in an online platform or is it possible to acquire popularity in a steady and disciplined fashion? What are other temporal characteristics that can unveil the popularity of online content? To answer these questions, we leverage a multi-faceted temporal analysis of the evolution of popular online contents. Here, we present dipm-SC: a multi-dimensional shape-based time-series clustering algorithm with a heuristic to find the optimal number of clusters. First, we validate the accuracy of our algorithm on synthetic datasets generated from benchmark time series models. Second, we show that dipm-SC can uncover meaningful clusters of popularity behaviors in a real-world Twitter dataset. By clustering the multidimensional time-series of the popularity of contents coupled with other domain-specific dimensions, we uncover two main patterns of popularity: bursty and steady temporal behaviors. Moreover, we find that the way popularity is gained over time has no significant impact on the final cumulative popularity.

Acute Kidney Injury (AKI) is a common clinical syndrome characterized by the rapid loss of kidney excretory function, which aggravates the clinical severity of other diseases in a large number of hospitalized patients. Accurate early prediction of AKI can enable in-time interventions and treatments. However, AKI is highly heterogeneous, thus identification of AKI sub-phenotypes can lead to an improved understanding of the disease pathophysiology and development of more targeted clinical interventions. This study used a memory network-based deep learning approach to discover predictive AKI sub-phenotypes using structured and unstructured electronic health record (EHR) data of patients before AKI diagnosis. We leveraged a real world critical care EHR corpus including 37,486 ICU stays. Our approach identified three distinct sub-phenotypes: sub-phenotype I is with an average age of 63.03$ \pm 17.25 $ years, and is characterized by mild loss of kidney excretory function (Serum Creatinne (SCr) $1.55\pm 0.34$ mg/dL, estimated Glomerular Filtration Rate Test (eGFR) $107.65\pm 54.98$ mL/min/1.73$m^2$). These patients are more likely to develop stage I AKI. Sub-phenotype II is with average age 66.81$ \pm 10.43 $ years, and was characterized by severe loss of kidney excretory function (SCr $1.96\pm 0.49$ mg/dL, eGFR $82.19\pm 55.92$ mL/min/1.73$m^2$). These patients are more likely to develop stage III AKI. Sub-phenotype III is with average age 65.07$ \pm 11.32 $ years, and was characterized moderate loss of kidney excretory function and thus more likely to develop stage II AKI (SCr $1.69\pm 0.32$ mg/dL, eGFR $93.97\pm 56.53$ mL/min/1.73$m^2$). Both SCr and eGFR are significantly different across the three sub-phenotypes with statistical testing plus postdoc analysis, and the conclusion still holds after age adjustment.

We propose a nonparametric model for time series with missing data based on low-rank matrix factorization. The model expresses each instance in a set of time series as a linear combination of a small number of shared basis functions. Constraining the functions and the corresponding coefficients to be nonnegative yields an interpretable low-dimensional representation of the data. A time-smoothing regularization term ensures that the model captures meaningful trends in the data, instead of overfitting short-term fluctuations. The low-dimensional representation makes it possible to detect outliers and cluster the time series according to the interpretable features extracted by the model, and also to perform forecasting via kernel regression. We apply our methodology to a large real-world dataset of infant-sleep data gathered by caregivers with a mobile-phone app. Our analysis automatically extracts daily-sleep patterns consistent with the existing literature. This allows us to compute sleep-development trends for the cohort, which characterize the emergence of circadian sleep and different napping habits. We apply our methodology to detect anomalous individuals, to cluster the cohort into groups with different sleeping tendencies, and to obtain improved predictions of future sleep behavior.

Dynamic regressor selection (DRS) systems work by selecting the most competent regressors from an ensemble to estimate the target value of a given test pattern. This competence is usually quantified using the performance of the regressors in local regions of the feature space around the test pattern. However, choosing the best measure to calculate the level of competence correctly is not straightforward. The literature of dynamic classifier selection presents a wide variety of competence measures, which cannot be used or adapted for DRS. In this paper, we review eight measures used with regression problems, and adapt them to test the performance of the DRS algorithms found in the literature. Such measures are extracted from a local region of the feature space around the test pattern, called region of competence, therefore competence measures.To better compare the competence measures, we perform a set of comprehensive experiments of 15 regression datasets. Three DRS systems were compared against individual regressor and static systems that use the Mean and the Median to combine the outputs of the regressors from the ensemble. The DRS systems were assessed varying the competence measures. Our results show that DRS systems outperform individual regressors and static systems but the choice of the competence measure is problem-dependent.

The statistical analysis of such massive data of functional nature raises many challenging methodological questions. The primary goal of this paper is to extend the popular Isolation Forest (IF) approach to Anomaly Detection, originally dedicated to finite dimensional observations, to functional data. The major difficulty lies in the wide variety of topological structures that may equip a space of functions and the great variety of patterns that may characterize abnormal curves. We address the issue of (randomly) splitting the functional space in a flexible manner in order to isolate progressively any trajectory from the others, a key ingredient to the efficiency of the algorithm. Beyond a detailed description of the algorithm, computational complexity and stability issues are investigated at length. From the scoring function measuring the degree of abnormality of an observation provided by the proposed variant of the IF algorithm, a Functional Statistical Depth function is defined and discussed as well as a multivariate functional extension. Numerical experiments provide strong empirical evidence of the accuracy of the extension proposed.

Explanations for deep neural network predictions in terms of domain-related concepts can be valuable in medical applications, where justifications are important for confidence in the decision-making. In this work, we propose a methodology to exploit continuous concept measures as Regression Concept Vectors (RCVs) in the activation space of a layer. The directional derivative of the decision function along the RCVs represents the network sensitivity to increasing values of a given concept measure. When applied to breast cancer grading, nuclei texture emerges as a relevant concept in the detection of tumor tissue in breast lymph node samples. We evaluate score robustness and consistency by statistical analysis.

Stochastic-gradient-based optimization has been a core enabling methodology in applications to large-scale problems in machine learning and related areas. Despite the progress, the gap between theory and practice remains significant, with theoreticians pursuing mathematical optimality at a cost of obtaining specialized procedures in different regimes (e.g., modulus of strong convexity, magnitude of target accuracy, signal-to-noise ratio), and with practitioners not readily able to know which regime is appropriate to their problem, and seeking broadly applicable algorithms that are reasonably close to optimality. To bridge these perspectives it is necessary to study algorithms that are adaptive to different regimes. We present the stochastically controlled stochastic gradient (SCSG) method for composite convex finite-sum optimization problems and show that SCSG is adaptive to both strong convexity and target accuracy. The adaptivity is achieved by batch variance reduction with adaptive batch sizes and a novel technique, which we referred to as \emph{geometrization}, which sets the length of each epoch as a geometric random variable. The algorithm achieves strictly better theoretical complexity than other existing adaptive algorithms, while the tuning parameters of the algorithm only depend on the smoothness parameter of the objective.

Transfer learning aims at transferring knowledge from a well-labeled domain to a similar but different domain with limited or no labels. Unfortunately, existing learning-based methods often involve intensive model selection and hyperparameter tuning to obtain good results. Moreover, cross-validation is not possible for tuning hyperparameters since there are often no labels in the target domain. This would restrict wide applicability of transfer learning especially in computationally-constraint devices such as wearables. In this paper, we propose a practically Easy Transfer Learning (EasyTL) approach which requires no model selection and hyperparameter tuning, while achieving competitive performance. By exploiting intra-domain structures, EasyTL is able to learn both non-parametric transfer features and classifiers. Extensive experiments demonstrate that, compared to state-of-the-art traditional and deep methods, EasyTL satisfies the Occam's Razor principle: it is extremely easy to implement and use while achieving comparable or better performance in classification accuracy and much better computational efficiency. Additionally, it is shown that EasyTL can increase the performance of existing transfer feature learning methods.

In this paper, we study distributed stochastic optimization to minimize a sum of smooth and strongly-convex local cost functions over a network of agents, communicating over a strongly-connected graph. Assuming that each agent has access to a stochastic first-order oracle ($\mathcal{SFO}$), we propose a novel distributed method, called $\mathcal{S}$-$\mathcal{AB}$, where each agent uses an auxiliary variable to asymptotically track the gradient of the global cost in expectation. The $\mathcal{S}$-$\mathcal{AB}$ algorithm employs row- and column-stochastic weights simultaneously to ensure both consensus and optimality. Since doubly-stochastic weights are not used, $\mathcal{S}$-$\mathcal{AB}$ is applicable to arbitrary strongly-connected graphs. We show that under a sufficiently small constant step-size, $\mathcal{S}$-$\mathcal{AB}$ converges linearly (in expected mean-square sense) to a neighborhood of the global minimizer. We present numerical simulations based on real-world data sets to illustrate the theoretical results.