Methods incorporating momentum and acceleration play an important role in the current practice of machine learning Sutskever et al. (2013); Bottou et al. (2018), where they are commonly used in conjunction with stochastic gradients. However, the theoretical understanding of accelerated methods remains limited when used with stochastic gradients. This paper studies the accelerated gradient (ag) method of Nesterov (1983). Given an initial point x 0, and with x 1 x 0, the ag method repeats, for k 0, y k 1 x k β(x k x k 1) (2) x k 1 y k 1 αg k 1, (3) where α and β are the step-size and momentum parameters, 1 respectively, and in the deterministic setting, g k 1 f(y k 1). When the momentum parameter β is 0, ag simplifies to standard gradient descent (gd). When β 0 it is possible to achieve accelerated rates of convergence for certain combinations of α and β in the deterministic setting.

In the last few years, various communication compression techniques have emerged as an indispensable tool helping to alleviate the communication bottleneck in distributed learning. However, despite the fact {\em biased} compressors often show superior performance in practice when compared to the much more studied and understood {\em unbiased} compressors, very little is known about them. In this work we study three classes of biased compression operators, two of which are new, and their performance when applied to (stochastic) gradient descent and distributed (stochastic) gradient descent. We show for the first time that biased compressors can lead to linear convergence rates both in the single node and distributed settings. Our {\em distributed} SGD method enjoys the ergodic rate $\mathcal{O}\left(\frac{\delta L \exp(-K) }{\mu} + \frac{(C + D)}{K\mu}\right)$, where $\delta$ is a compression parameter which grows when more compression is applied, $L$ and $\mu$ are the smoothness and strong convexity constants, $C$ captures stochastic gradient noise ($C=0$ if full gradients are computed on each node) and $D$ captures the variance of the gradients at the optimum ($D=0$ for over-parameterized models). Further, via a theoretical study of several synthetic and empirical distributions of communicated gradients, we shed light on why and by how much biased compressors outperform their unbiased variants. Finally, we propose a new highly performing biased compressor---combination of Top-$k$ and natural dithering---which in our experiments outperforms all other compression techniques.

Fuzzy c-means based clustering algorithms are frequently used for Takagi-Sugeno-Kang (TSK) fuzzy classifier antecedent parameter estimation. One rule is initialized from each cluster. However, most of these clustering algorithms are unsupervised, which waste valuable label information in the training data. This paper proposes a supervised enhanced soft subspace clustering (SESSC) algorithm, which considers simultaneously the within-cluster compactness, between-cluster separation, and label information in clustering. It can effectively deal with high-dimensional data, be used as a classifier alone, or be integrated into a TSK fuzzy classifier to further improve its performance. Experiments on nine UCI datasets from various application domains demonstrated that SESSC based initialization outperformed other clustering approaches, especially when the number of rules is small.

Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance are automated approaches to theory building that scale efficiently for complex systems with many degrees of freedom. To date, available scalable methods aim at a data-driven interpolation, without exploiting or offering insight into fundamental underlying physical principles, such as locality of interactions. In this work, we show that various physical constraints can be captured via tensor network based parameterizations for the governing equation, which naturally ensures scalability. In addition to providing analytic results motivating the use of such models for realistic physical systems, we demonstrate that efficient rank-adaptive optimization algorithms can be used to learn optimal tensor network models without requiring a~priori knowledge of the exact tensor ranks. As such, we provide a physics-informed approach to recovering structured dynamical laws from data, which adaptively balances the need for expressivity and scalability.

A Machine can only learn if it is biased in some way. Typically the bias is supplied by hand, for example through the choice of an appropriate set of features. However, if the learning machine is embedded within an {\em environment} of related tasks, then it can {\em learn} its own bias by learning sufficiently many tasks from the environment. In this paper two models of bias learning (or equivalently, learning to learn) are introduced and the main theoretical results presented. The first model is a PAC-type model based on empirical process theory, while the second is a hierarchical Bayes model.

Shapley value is a classic notion from game theory, historically used to quantify the contributions of individuals within groups, and more recently applied to assign values to data points when training machine learning models. Despite its foundational role, a key limitation of the data Shapley framework is that it only provides valuations for points within a fixed data set. It does not account for statistical aspects of the data and does not give a way to reason about points outside the data set. To address these limitations, we propose a novel framework -- distributional Shapley -- where the value of a point is defined in the context of an underlying data distribution. We prove that distributional Shapley has several desirable statistical properties; for example, the values are stable under perturbations to the data points themselves and to the underlying data distribution. We leverage these properties to develop a new algorithm for estimating values from data, which comes with formal guarantees and runs two orders of magnitude faster than state-of-the-art algorithms for computing the (non-distributional) data Shapley values. We apply distributional Shapley to diverse data sets and demonstrate its utility in a data market setting.

We present, GEM, the first heterogeneous graph neural network approach for detecting malicious accounts at Alipay, one of the world's leading mobile cashless payment platform. Our approach, inspired from a connected subgraph approach, adaptively learns discriminative embeddings from heterogeneous account-device graphs based on two fundamental weaknesses of attackers, i.e. device aggregation and activity aggregation. For the heterogeneous graph consists of various types of nodes, we propose an attention mechanism to learn the importance of different types of nodes, while using the sum operator for modeling the aggregation patterns of nodes in each type. Experiments show that our approaches consistently perform promising results compared with competitive methods over time.

The aim of this study was to approach a difficult regression task on highly unbalanced data regarding active theater of war in Afghanistan. Our focus was set on predicting the negative events number without distinguishing precise nature of the events given historical data on investment and negative events per each of predefined 400 Afghanistan districts. In contrast with previous research on the matter, we propose an approach to analysis of time series data that benefits from non-conventional aggregation of these territorial entities. By carrying out initial exploratory data analysis we demonstrate that dividing data according to our proposal allows to identify strong trend and seasonal components in the selected target variable. Utilizing this approach we also tried to estimate which data regarding investments is most important for prediction performance. Based on our exploratory analysis and previous research we prepared 5 sets of independent variables that were fed to 3 machine learning regression models. The results expressed by mean absolute and mean square errors indicate that leveraging historical data regarding target variable allows for reasonable performance, however unfortunately other proposed independent variables does not seem to improve prediction quality.

Machine learning involves expensive data collection and training procedures. Model owners may be concerned that valuable intellectual property can be leaked if adversaries mount model extraction attacks. Because it is difficult to defend against model extraction without sacrificing significant prediction accuracy, watermarking leverages unused model capacity to have the model overfit to outlier input-output pairs, which are not sampled from the task distribution and are only known to the defender. The defender then demonstrates knowledge of the input-output pairs to claim ownership of the model at inference. The effectiveness of watermarks remains limited because they are distinct from the task distribution and can thus be easily removed through compression or other forms of knowledge transfer. We introduce Entangled Watermarking Embeddings (EWE). Our approach encourages the model to learn common features for classifying data that is sampled from the task distribution, but also data that encodes watermarks. An adversary attempting to remove watermarks that are entangled with legitimate data is also forced to sacrifice performance on legitimate data. Experiments on MNIST, Fashion-MNIST, and Google Speech Commands validate that the defender can claim model ownership with 95% confidence after less than 10 queries to the stolen copy, at a modest cost of 1% accuracy in the defended model's performance.

In the presence of large dimensional datasets that contain many irrelevant features (variables), dimensionality reduction algorithms have proven to be useful in removing features with low variance and combine features with high correlation. In this paper, we propose a new feature selection method which uses singular value decomposition of a matrix and the method of least squares to remove the irrelevant features and detect correlations between the remaining features. The effectiveness of our method has been verified by performing a series of comparisons with state-of-the-art feature selection methods over ten genetic datasets ranging up from 9,117 to 267,604 features. The results show that our method is favorable in various aspects compared to state-of-the-art feature selection methods.