Networks and graphs, which consist of objects of interest and a vast array of possible relationships between them, arise very naturally in fields as diverse as political science (party affiliations among voters); bioinformatics (gene interactions); physics (dimer systems); and sociology (social network analysis), to name but a few. As such, they are a useful data structure for modeling complex interactions between different experimental entities. Network data, however, is qualitatively distinct from more traditional Euclidean data, and statistical inference on networks is a comparatively new discipline, one that has seen explosive growth over the last two decades. While there is a significant literature devoted to the rigorous statistical study of single networks, multiple network inference-- the analogue of the classical problem of multiple-sample Euclidean inference--is still relatively nascent. Much recent progress in network inference has relied on extracting Euclidean representations of networks, and popular methods include spectral embeddings of network adjacency [3] or Laplacian [45] matrices, representation learning [20, 44], or Bayesian hierarchical methods [16].

We analyze the complexity of biased stochastic gradient methods (SGD), where individual updates are corrupted by deterministic, i.e. biased error terms. We derive convergence results for smooth (non-convex) functions and give improved rates under the Polyak-Lojasiewicz condition. We quantify how the magnitude of the bias impacts the attainable accuracy and convergence rates. Our framework covers many applications where either only biased gradient updates are available or preferred over unbiased ones for performance reasons. For instance, in the domain of distributed learning, biased gradient compression techniques such as top-k compression have been proposed as a tool to alleviate the communication bottleneck and in derivative-free optimization, only biased gradient estimators can be queried. We discuss a few guiding examples that show the broad applicability of our analysis.

Poisoning attacks on machine learning systems compromise the model performance by deliberately injecting malicious samples in the training dataset to influence the training process. Prior works focus on either availability attacks (i.e., lowering the overall model accuracy) or integrity attacks (i.e., enabling specific instance based backdoor). In this paper, we advance the adversarial objectives of the availability attacks to a per-class basis, which we refer to as class-oriented poisoning attacks. We demonstrate that the proposed attack is capable of forcing the corrupted model to predict in two specific ways: (i) classify unseen new images to a targeted "supplanter" class, and (ii) misclassify images from a "victim" class while maintaining the classification accuracy on other non-victim classes. To maximize the adversarial effect, we propose a gradient-based framework that manipulates the logits to retain/eliminate the desired/undesired feature information in the generated poisoning images. Using newly defined metrics at the class level, we illustrate the effectiveness of the proposed class-oriented poisoning attacks on various models (e.g., LeNet-5, Vgg-9, and ResNet-50) over a wide range of datasets (e.g., MNIST, CIFAR-10, and ImageNet-ILSVRC2012).

In this paper, we study a novel problem: "automatic prescription recommendation for PD patients." To realize this goal, we first build a dataset by collecting 1) symptoms of PD patients, and 2) their prescription drug provided by neurologists. Then, we build a novel computer-aided prescription model by learning the relation between observed symptoms and prescription drug. Finally, for the new coming patients, we could recommend (predict) suitable prescription drug on their observed symptoms by our prescription model. From the methodology part, our proposed model, namely Prescription viA Learning lAtent Symptoms (PALAS), could recommend prescription using the multi-modality representation of the data. In PALAS, a latent symptom space is learned to better model the relationship between symptoms and prescription drug, as there is a large semantic gap between them. Moreover, we present an efficient alternating optimization method for PALAS. We evaluated our method using the data collected from 136 PD patients at Nanjing Brain Hospital, which can be regarded as a large dataset in PD research community. The experimental results demonstrate the effectiveness and clinical potential of our method in this recommendation task, if compared with other competing methods.

In order to perform network analysis tasks, representations that capture the most relevant information in the graph structure are needed. However, existing methods do not learn representations that can be interpreted in a straightforward way and that are robust to perturbations to the graph structure. In this work, we address these two limitations by proposing node2coords, a representation learning algorithm for graphs, which learns simultaneously a low-dimensional space and coordinates for the nodes in that space. The patterns that span the low dimensional space reveal the graph's most important structural information. The coordinates of the nodes reveal the proximity of their local structure to the graph structural patterns. In order to measure this proximity by taking into account the underlying graph, we propose to use Wasserstein distances. We introduce an autoencoder that employs a linear layer in the encoder and a novel Wasserstein barycentric layer at the decoder. Node connectivity descriptors, that capture the local structure of the nodes, are passed through the encoder to learn the small set of graph structural patterns. In the decoder, the node connectivity descriptors are reconstructed as Wasserstein barycenters of the graph structural patterns. The optimal weights for the barycenter representation of a node's connectivity descriptor correspond to the coordinates of that node in the low-dimensional space. Experimental results demonstrate that the representations learned with node2coords are interpretable, lead to node embeddings that are stable to perturbations of the graph structure and achieve competitive or superior results compared to state-of-the-art methods in node classification.

In high-dimensions, the prior tails can have a significant effect on both posterior computation and asymptotic concentration rates. To achieve optimal rates while keeping the posterior computations relatively simple, an empirical Bayes approach has recently been proposed, featuring thin-tailed conjugate priors with data-driven centers. While conjugate priors ease some of the computational burden, Markov chain Monte Carlo methods are still needed, which can be expensive when dimension is high. In this paper, we develop a variational approximation to the empirical Bayes posterior that is fast to compute and retains the optimal concentration rate properties of the original. In simulations, our method is shown to have superior performance compared to existing variational approximations in the literature across a wide range of high-dimensional settings.

This paper proposes a new optimizer for deep learning, named d-AmsGrad. In the real-world data, noise and outliers cannot be excluded from dataset to be used for learning robot skills. This problem is especially striking for robots that learn by collecting data in real time, which cannot be sorted manually. Several noise-robust optimizers have therefore been developed to resolve this problem, and one of them, named AmsGrad, which is a variant of Adam optimizer, has a proof of its convergence. However, in practice, it does not improve learning performance in robotics scenarios. This reason is hypothesized that most of robot learning problems are non-stationary, but AmsGrad assumes the maximum second momentum during learning to be stationarily given. In order to adapt to the non-stationary problems, an improved version, which slowly decays the maximum second momentum, is proposed. The proposed optimizer has the same capability of reaching the global optimum as baselines, and its performance outperformed that of the baselines in robotics problems.

The quality of learned features by representation learning determines the performance of learning algorithms and the related application tasks (such as high-dimensional data clustering). As a relatively new paradigm for representation learning, Concept Factorization (CF) has attracted a great deal of interests in the areas of machine learning and data mining for over a decade. Lots of effective CF based methods have been proposed based on different perspectives and properties, but note that it still remains not easy to grasp the essential connections and figure out the underlying explanatory factors from exiting studies. In this paper, we therefore survey the recent advances on CF methodologies and the potential benchmarks by categorizing and summarizing the current methods. Specifically, we first re-view the root CF method, and then explore the advancement of CF-based representation learning ranging from shallow to deep/multilayer cases. We also introduce the potential application areas of CF-based methods. Finally, we point out some future directions for studying the CF-based representation learning. Overall, this survey provides an insightful overview of both theoretical basis and current developments in the field of CF, which can also help the interested researchers to understand the current trends of CF and find the most appropriate CF techniques to deal with particular applications.

We study the problem of estimating the mean of a distribution in high dimensions when either the samples are adversarially corrupted or the distribution is heavy-tailed. Recent developments in robust statistics have established efficient and (near) optimal procedures for both settings. However, the algorithms developed on each side tend to be sophisticated and do not directly transfer to the other, with many of them having ad-hoc or complicated analyses. In this paper, we provide a meta-problem and a duality theorem that lead to a new unified view on robust and heavy-tailed mean estimation in high dimensions. We show that the meta-problem can be solved either by a variant of the Filter algorithm from the recent literature on robust estimation or by the quantum entropy scoring scheme (QUE), due to Dong, Hopkins and Li (NeurIPS '19). By leveraging our duality theorem, these results translate into simple and efficient algorithms for both robust and heavy-tailed settings. Furthermore, the QUE-based procedure has run-time that matches the fastest known algorithms on both fronts. Our analysis of Filter is through the classic regret bound of the multiplicative weights update method. This connection allows us to avoid the technical complications in previous works and improve upon the run-time analysis of a gradient-descent-based algorithm for robust mean estimation by Cheng, Diakonikolas, Ge and Soltanolkotabi (ICML '20).

In this paper, we propose a novel multi-variate algorithm using a triple-regression methodology to predict the airborne-pollen allergy season that can be customized for each patient in the long term. To improve the prediction accuracy, we first perform a pre-processing to integrate the historical data of pollen concentration and various inferential signals from other covariates such as the meteorological data. We then propose a novel algorithm which encompasses three-stage regressions: in Stage 1, a regression model to predict the start/end date of a airborne-pollen allergy season is trained from a feature matrix extracted from 12 time series of the covariates with a rolling window; in Stage 2, a regression model to predict the corresponding uncertainty is trained based on the feature matrix and the prediction result from Stage 1; in Stage 3, a weighted linear regression model is built upon prediction results from Stage 1 and 2. It is observed and proved that Stage 3 contributes to the improved forecasting accuracy and the reduced uncertainty of the multi-variate triple-regression algorithm. Based on different allergy sensitivity level, the triggering concentration of the pollen - the definition of the allergy season can be customized individually. In our backtesting, a mean absolute error (MAE) of 4.7 days was achieved using the algorithm. We conclude that this algorithm could be applicable in both generic and long-term forecasting problems.