This work proposes a novel approach for multiple time series forecasting. At first, multi-way delay embedding transform (MDT) is employed to represent time series as low-rank block Hankel tensors (BHT). Then, the higher-order tensors are projected to compressed core tensors by applying Tucker decomposition. At the same time, the generalized tensor Autoregressive Integrated Moving Average (ARIMA) is explicitly used on consecutive core tensors to predict future samples. In this manner, the proposed approach tactically incorporates the unique advantages of MDT tensorization (to exploit mutual correlations) and tensor ARIMA coupled with low-rank Tucker decomposition into a unified framework. This framework exploits the low-rank structure of block Hankel tensors in the embedded space and captures the intrinsic correlations among multiple TS, which thus can improve the forecasting results, especially for multiple short time series. Experiments conducted on three public datasets and two industrial datasets verify that the proposed BHT-ARIMA effectively improves forecasting accuracy and reduces computational cost compared with the state-of-the-art methods.

In this game, Nature selects a prior over distributions that generate labeled data consisting of features and an associated outcome, and the Predictor observes data sampled from a distribution drawn from this prior. The Predictor's objective is to learn a function that maps from a new feature to an estimate of the associated outcome. We establish that, under reasonable conditions, the Predictor has an optimal strategy that is equivariant to shifts and rescalings of the outcome and is invariant to permutations of the observations and to shifts, rescalings, and permutations of the features. We introduce a neural network architecture that satisfies these properties. The proposed strategy performs favorably compared to standard practice in both parametric and nonparametric experiments.

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator consists of finding a low-rank tensor fit to the data under generalized parametric models. To overcome the difficulty of non-convexity in these problems, we introduce a unified approach of projected gradient descent that adapts to the underlying low-rank structure. Under mild conditions on the loss function, we establish both an upper bound on statistical error and the linear rate of computational convergence through a general deterministic analysis. Then we further consider a suite of generalized tensor estimation problems, including sub-Gaussian tensor denoising, tensor regression, and Poisson and binomial tensor PCA. We prove that the proposed algorithm achieves the minimax optimal rate of convergence in estimation error. Finally, we demonstrate the superiority of the proposed framework via extensive experiments on both simulated and real data.

Metric learning has been successful in learning new metrics adapted to numerical datasets. However, its development on categorical data still needs further exploration. In this paper, we propose a method, called CPML for \emph{categorical projected metric learning}, that tries to efficiently~(i.e. less computational time and better prediction accuracy) address the problem of metric learning in categorical data. We make use of the Value Distance Metric to represent our data and propose new distances based on this representation. We then show how to efficiently learn new metrics. We also generalize several previous regularizers through the Schatten $p$-norm and provides a generalization bound for it that complements the standard generalization bound for metric learning. Experimental results show that our method provides

Adversarial training based on the minimax formulation is necessary for obtaining adversarial robustness of trained models. However, it is conservative or even pessimistic so that it sometimes hurts the natural generalization. In this paper, we raise a fundamental question---do we have to trade off natural generalization for adversarial robustness? We argue that adversarial training is to employ confident adversarial data for updating the current model. We propose a novel approach of friendly adversarial training (FAT): rather than employing most adversarial data maximizing the loss, we search for least adversarial (i.e., friendly adversarial) data minimizing the loss, among the adversarial data that are confidently misclassified. Our novel formulation is easy to implement by just stopping the most adversarial data searching algorithms such as PGD (projected gradient descent) early, which we call early-stopped PGD. Theoretically, FAT is justified by an upper bound of the adversarial risk. Empirically, early-stopped PGD allows us to answer the earlier question negatively---adversarial robustness can indeed be achieved without compromising the natural generalization.

The proliferation of mobile phones, wearables and edge devices has led to an unprecedented growth in the generation of user interaction data. Systems which tap into the power of this rich data while respecting the privacy of users are geared to lead the next generation of intelligent applications and devices. The leading distributed learning framework in this setting is federated learning [30]. In federated learning, a number of client devices with privacy-sensitive data collaboratively learn a machine learning model under the orchestration of a central server, while keeping their data decentralized. This is achieved by pushing the actual computation to the devices while the server coordinates with the devices for aggregation of model updates.

Diabetes is a disease-causing high level of blood sugar. In type 1 Diabetes, body doesn't produce insulin, but if injected from external sources, will use it and in type 2, the body doesn't produce as well as use insulin. It is estimated that 30.3 million people of all ages in the US are suffering from Diabetes as of 2015, out of which 7.2 million are unaware[1]. As of 2016, it is ranked seventh in the list of global causes of mortality. Diabetes can be an underlying cause for many cardiovascular diseases, retinopathy, and nephropathy leading to frequent readmission in the hospital. The Centers for Medicare and Medicaid Services(CMS) labeled a 30-day readmission rate as a measure of healthcare quality offered by the hospital in order to provide the best inpatient care and improve the healthcare quality. Hospitals with high readmission rates will be penalized as per the Patient Protection and Affordable Care Act(ACA) of 2010[2]. During the recent studies[19], it was observed that a 30-day readmission rate for patients with Diabetes ranges between 14.4%-22.7%,

We consider the problem of meta-learning, or learning-to-learn [Thrun and Pratt, 1998], in which the goal is to use the data from numerous training tasks to reduce the sample complexity of an unseen but related test task. Although there is a long history of successful methods in meta-learning and the related areas of multi-task and lifelong learning [Evgeniou and Pontil, 2004, Ruvolo and Eaton, 2013], recent approaches have been developed with the diversity and scale of modern applications in mind. This has given rise to simple, model-agnostic methods that focus on learning a good initialization for some gradient-based method such as stochastic gradient descent (SGD), to be run on samples from a new task [Finn et al., 2017, Nichol et al., 2018]. These methods have found widespread applications in a variety of areas such as computer vision [Nichol et al., 2018], reinforcement learning [Finn et al., 2017], and federated learning [McMahan et al., 2017]. Inspired by their popularity, several recent learning-theoretic analyses of meta-learning have followed suit, eschewing customization to specific hypothesis classes such as halfspaces [Maurer and Pontil, 2013, Balcan et al., 2015] and instead favoring the convex-case study of gradient-based algorithms that could potentially be applied to deep neural networks [Denevi et al., 2019, Khodak et al., 2019].

Motivated by pricing in ad exchange markets, we consider the problem of robust learning of reserve prices against strategic buyers in repeated contextual second-price auctions. Buyers' valuations for an item depend on the context that describes the item. However, the seller is not aware of the relationship between the context and buyers' valuations, i.e., buyers' preferences. The seller's goal is to design a learning policy to set reserve prices via observing the past sales data, and her objective is to minimize her regret for revenue, where the regret is computed against a clairvoyant policy that knows buyers' heterogeneous preferences. Given the seller's goal, utility-maximizing buyers have the incentive to bid untruthfully in order to manipulate the seller's learning policy. We propose learning policies that are robust to such strategic behavior. These policies use the outcomes of the auctions, rather than the submitted bids, to estimate the preferences while controlling the long-term effect of the outcome of each auction on the future reserve prices. When the market noise distribution is known to the seller, we propose a policy called Contextual Robust Pricing (CORP) that achieves a T-period regret of $O(d\log(Td) \log (T))$, where $d$ is the dimension of {the} contextual information. When the market noise distribution is unknown to the seller, we propose two policies whose regrets are sublinear in $T$.

We consider the setting where a master wants to run a distributed stochastic gradient descent (SGD) algorithm on $n$ workers each having a subset of the data. Distributed SGD may suffer from the effect of stragglers, i.e., slow or unresponsive workers who cause delays. One solution studied in the literature is to wait at each iteration for the responses of the fastest $k