This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated gradient methods in (wibisono, et. al. 2016) from vector valued variables to probability distributions. The variational problem is modeled as a mean-field optimal control problem. The maximum principle of optimal control theory is used to derive Hamilton's equations for the optimal gradient flow. The Hamilton's equation are shown to achieve the accelerated form of density transport from any initial probability distribution to a target probability distribution. A quantitative estimate on the asymptotic convergence rate is provided based on a Lyapunov function construction, when the objective functional is displacement convex. Two numerical approximations are presented to implement the Hamilton's equations as a system of $N$ interacting particles. The continuous limit of the Nesterov's algorithm is shown to be a special case with $N=1$. The algorithm is illustrated with numerical examples.

The event-driven and elastic nature of serverless runtimes makes them a very efficient and cost-effective alternative for scaling up computations. So far, they have mostly been used for stateless, data parallel and ephemeral computations. In this work, we propose using serverless runtimes to solve generic, large-scale optimization problems. Specifically, we build a master-worker setup using AWS Lambda as the source of our workers, implement a parallel optimization algorithm to solve a regularized logistic regression problem, and show that relative speedups up to 256 workers and efficiencies above 70% up to 64 workers can be expected. We also identify possible algorithmic and system-level bottlenecks, propose improvements, and discuss the limitations and challenges in realizing these improvements.

We introduce a principled method for the signed clustering problem, where the goal is to partition a graph whose edge weights take both positive and negative values, such that edges within the same cluster are mostly positive, while edges spanning across clusters are mostly negative. Our method relies on a graph-based diffuse interface model formulation utilizing the Ginzburg-Landau functional, based on an adaptation of the classic numerical Merriman-Bence-Osher (MBO) scheme for minimizing such graph-based functionals. The proposed objective function aims to minimize the total weight of inter-cluster positively-weighted edges, while maximizing the total weight of the inter-cluster negatively-weighted edges. Our method scales to large sparse networks, and can be easily adjusted to incorporate labelled data information, as is often the case in the context of semi-supervised learning. We tested our method on a number of both synthetic stochastic block models and real-world data sets (including financial correlation matrices), and obtained promising results that compare favourably against a number of state-of-the-art approaches from the recent literature.

Due to its efficiency and ease to implement, stochastic gradient descent (SGD) has been widely used in machine learning. In particular, SGD is one of the most popular optimization methods for distributed learning. Recently, quantized SGD (QSGD), which adopts quantization to reduce the communication cost in SGD-based distributed learning, has attracted much attention. Although several QSGD methods have been proposed, some of them are heuristic without theoretical guarantee, and others have high quantization variance which makes the convergence become slow. In this paper, we propose a new method, called Quantized Epoch-SGD (QESGD), for communication-efficient distributed learning. QESGD compresses (quantizes) the parameter with variance reduction, so that it can get almost the same performance as that of SGD with less communication cost. QESGD is implemented on the Parameter Server framework, and empirical results on distributed deep learning show that QESGD can outperform other state-of-the-art quantization methods to achieve the best performance.

Convex clustering is a promising new approach to the classical problem of clustering, combining strong performance in empirical studies with rigorous theoretical foundations. Despite these advantages, convex clustering has not been widely adopted, due to its computationally intensive nature and its lack of compelling visualizations. To address these impediments, we introduce Algorithmic Regularization, an innovative technique for obtaining high-quality estimates of regularization paths using an iterative one-step approximation scheme. We justify our approach with a novel theoretical result, guaranteeing global convergence of the approximate path to the exact solution under easily-checked non-data-dependent assumptions. The application of algorithmic regularization to convex clustering yields the Convex Clustering via Algorithmic Regularization Paths (CARP) algorithm for computing the clustering solution path. On example data sets from genomics and text analysis, CARP delivers over a 100-fold speed-up over existing methods, while attaining a finer approximation grid than standard methods. Furthermore, CARP enables improved visualization of clustering solutions: the fine solution grid returned by CARP can be used to construct a convex clustering-based dendrogram, as well as forming the basis of a dynamic path-wise visualization based on modern web technologies. Our methods are implemented in the open-source R package clustRviz, available at https://github.com/DataSlingers/clustRviz.

The parameter server architecture is prevalently used for distributed deep learning. Each worker machine in a parameter server system trains the complete model, which leads to a hefty amount of network data transfer between workers and servers. We empirically observe that the data transfer has a non-negligible impact on training time. To tackle the problem, we design a new distributed training system called Stanza. Stanza exploits the fact that in many models such as convolution neural networks, most data exchange is attributed to the fully connected layers, while most computation is carried out in convolutional layers. Thus, we propose layer separation in distributed training: the majority of the nodes just train the convolutional layers, and the rest train the fully connected layers only. Gradients and parameters of the fully connected layers no longer need to be exchanged across the cluster, thereby substantially reducing the data transfer volume. We implement Stanza on PyTorch and evaluate its performance on Azure and EC2. Results show that Stanza accelerates training significantly over current parameter server systems: on EC2 instances with Tesla V100 GPU and 10Gb bandwidth for example, Stanza is 1.34x--13.9x faster for common deep learning models.

Diabetes mellitus is a common disease of human body caused by a group of metabolic disorders where the sugar levels over a prolonged period is very high. It affects different organs of the human body which thus harm a large number of the body's system, in particular the blood veins and nerves. Early prediction in such disease can be controlled and save human life. To achieve the goal, this research work mainly explores various risk factors related to this disease using machine learning techniques. Machine learning techniques provide efficient result to extract knowledge by constructing predicting models from diagnostic medical datasets collected from the diabetic patients. Extracting knowledge from such data can be useful to predict diabetic patients. In this work, we employ four popular machine learning algorithms, namely Support Vector Machine (SVM), Naive Bayes (NB), K-Nearest Neighbor (KNN) and C4.5 Decision Tree, on adult population data to predict diabetic mellitus. Our experimental results show that C4.5 decision tree achieved higher accuracy compared to other machine learning techniques.

Transfer learning can address the learning tasks of unlabeled data in the target domain by leveraging plenty of labeled data from a different but related source domain. A core issue in transfer learning is to learn a shared feature space in where the distributions of the data from two domains are matched. This learning process can be named as transfer representation learning (TRL). The feature transformation methods are crucial to ensure the success of TRL. The most commonly used feature transformation method in TRL is kernel-based nonlinear mapping to the high-dimensional space followed by linear dimensionality reduction. But the kernel functions are lack of interpretability and are difficult to be selected. To this end, the TSK fuzzy system (TSK-FS) is combined with transfer learning and a more intuitive and interpretable modeling method, called transfer representation learning with TSK-FS (TRL-TSK-FS) is proposed in this paper. Specifically, TRL-TSK-FS realizes TRL from two aspects. On one hand, the data in the source and target domains are transformed into the fuzzy feature space in which the distribution distance of the data between two domains is min-imized. On the other hand, discriminant information and geo-metric properties of the data are preserved by linear discriminant analysis and principal component analysis. In addition, another advantage arises with the proposed method, that is, the nonlinear transformation is realized by constructing fuzzy mapping with the antecedent part of the TSK-FS instead of kernel functions which are difficult to be selected. Extensive experiments are conducted on the text and image datasets. The results obviously show the superiority of the proposed method.

Natural human-computer interaction and audio-visual human behaviour sensing systems, which would achieve robust performance in-the-wild are more needed than ever as digital devices are becoming indispensable part of our life more and more. Accurately annotated real-world data are the crux in devising such systems. However, existing databases usually consider controlled settings, low demographic variability, and a single task. In this paper, we introduce the SEWA database of more than 2000 minutes of audio-visual data of 398 people coming from six cultures, 50% female, and uniformly spanning the age range of 18 to 65 years old. Subjects were recorded in two different contexts: while watching adverts and while discussing adverts in a video chat. The database includes rich annotations of the recordings in terms of facial landmarks, facial action units (FAU), various vocalisations, mirroring, and continuously valued valence, arousal, liking, agreement, and prototypic examples of (dis)liking. This database aims to be an extremely valuable resource for researchers in affective computing and automatic human sensing and is expected to push forward the research in human behaviour analysis, including cultural studies. Along with the database, we provide extensive baseline experiments for automatic FAU detection and automatic valence, arousal and (dis)liking intensity estimation.

First-order methods play a fundamental role in large-scale machine learning and optimization tasks. In most scenarios, the performance of a first-order method is represented by its convergence rate: the relationship between ε (the optimization error) versus T (the number of gradient computations). This is meaningful because in most applications, the time complexities for evaluating gradients at different points are of the same magnitude. In other words, the worse-case time complexities of first-order methods are usually proportional to a fixed parameter times T . In large-scale settings, however, if we have already spent time computing the (full) gradient at x, perhaps we can use such information to reduce the time complexity to compute full gradients at other points near x. We call this the "lingering" of gradients, because the gradient at x may be partially reused for future consideration, but will eventually fade away once we are far from x. Formally, consider the (finite-sum) stochastic convex minimization problem: { min