Federated learning provides a framework to address the challenges of distributed computing, data ownership and privacy over a large number of distributed clients with low computational and communication capabilities. In this paper, we study the problem of learning the exact support of sparse linear regression in the federated learning setup. We provide a simple communication efficient algorithm which only needs one-shot communication with the centralized server to compute the exact support. Our method does not require the clients to solve any optimization problem and thus, can be run on devices with low computational capabilities. Our method is naturally robust to the problems of client failure, model poisoning and straggling clients. We formally prove that our method requires a number of samples per client that is polynomial with respect to the support size, but independent of the dimension of the problem. We require the number of distributed clients to be logarithmic in the dimension of the problem. If the predictor variables are mutually independent then the overall sample complexity matches the optimal sample complexity of the non-federated centralized setting. Furthermore, our method is easy to implement and has an overall polynomial time complexity.

Hypergraphs provide a natural representation for many real world datasets. We propose a novel framework, HNHN, for hypergraph representation learning. HNHN is a hypergraph convolution network with nonlinear activation functions applied to both hypernodes and hyperedges, combined with a normalization scheme that can flexibly adjust the importance of high-cardinality hyperedges and high-degree vertices depending on the dataset. We demonstrate improved performance of HNHN in both classification accuracy and speed on real world datasets when compared to state of the art methods.

In this paper, we propose embedding sparsity into the structure of deep neural networks, where model parameters can be exactly zero during training with the stochastic gradient descent. Thus, it can learn the sparsified structure and the weights of networks simultaneously. The proposed approach can learn structured as well as unstructured sparsity.

Traffic forecasting has recently attracted increasing interest due to the popularity of online navigation services, ridesharing and smart city projects. Owing to the non-stationary nature of road traffic, forecasting accuracy is fundamentally limited by the lack of contextual information. To address this issue, we propose the Hybrid Spatio-Temporal Graph Convolutional Network (H-STGCN), which is able to "deduce" future travel time by exploiting the data of upcoming traffic volume. Specifically, we propose an algorithm to acquire the upcoming traffic volume from an online navigation engine. Taking advantage of the piecewise-linear flow-density relationship, a novel transformer structure converts the upcoming volume into its equivalent in travel time. We combine this signal with the commonly-utilized travel-time signal, and then apply graph convolution to capture the spatial dependency. Particularly, we construct a compound adjacency matrix which reflects the innate traffic proximity. We conduct extensive experiments on real-world datasets. The results show that H-STGCN remarkably outperforms state-of-the-art methods in various metrics, especially for the prediction of non-recurring congestion.

Finding methods for making generalizable predictions is a fundamental problem of machine learning. By looking into similarities between the prediction problem for unknown data and the lossless compression we have found an approach that gives a solution. In this paper we propose a compression principle that states that an optimal predictive model is the one that minimizes a total compressed message length of all data and model definition while guarantees decodability. Following the compression principle we use Bayesian approach to build probabilistic models of data and network definitions. A method to approximate Bayesian integrals using a sequence of variational approximations is implemented as an optimizer for hyper-parameters: Bayesian Stochastic Gradient Descent (BSGD). Training with BSGD is completely defined by setting only three parameters: number of epochs, the size of the dataset and the size of the minibatch, which define a learning rate and a number of iterations. We show that dropout can be used for a continuous dimensionality reduction that allows to find optimal network dimensions as required by the compression principle.

Out of the recent advances in systems and control (S\&C)-based analysis of optimization algorithms, not enough work has been specifically dedicated to machine learning (ML) algorithms and its applications. This paper addresses this gap by illustrating how (discrete-time) Lyapunov stability theory can serve as a powerful tool to aid, or even lead, in the analysis (and potential design) of optimization algorithms that are not necessarily gradient-based. The particular ML problem that this paper focuses on is that of parameter estimation in an incomplete-data Bayesian framework via the popular optimization algorithm known as maximum a posteriori expectation-maximization (MAP-EM). Following first principles from dynamical systems stability theory, conditions for convergence of MAP-EM are developed. Furthermore, if additional assumptions are met, we show that fast convergence (linear or quadratic) is achieved, which could have been difficult to unveil without our adopted S\&C approach. The convergence guarantees in this paper effectively expand the set of sufficient conditions for EM applications, thereby demonstrating the potential of similar S\&C-based convergence analysis of other ML algorithms.

Recent methods in the machine learning literature have proposed a Gaussian noise-based exogenous signal to learn the parameters of a dynamic system. In this paper, we propose the use of a spectral lines-based deterministic exogenous signal to solve the same problem. Our theoretical analysis consists of a new toolkit which employs the theory of spectral lines, retains the stochastic setting, and leads to non-asymptotic bounds on the parameter estimation error. The results are shown to lead to a tunable parameter identification error. In particular, it is shown that the identification error can be minimized through an an optimal choice of the spectrum of the exogenous signal.

Many modern data analyses benefit from explicitly modeling dependence structure in data - such as measurements across time or space, ordered words in a sentence, or genes in a genome. A gold standard evaluation technique is structured cross-validation (CV), which leaves out some data subset (such as data within a time interval or data in a geographic region) in each fold. But CV here can be prohibitively slow due to the need to rerun already-expensive learning algorithms many times. Previous work has shown approximate cross-validation (ACV) methods provide a fast and provably accurate alternative in the setting of empirical risk minimization. But this existing ACV work is restricted to simpler models by the assumptions that (i) data across CV folds are independent and (ii) an exact initial model fit is available. In structured data analyses, both these assumptions are often untrue. In the present work, we address (i) by extending ACV to CV schemes with dependence structure between the folds. To address (ii), we verify - both theoretically and empirically - that ACV quality deteriorates smoothly with noise in the initial fit. We demonstrate the accuracy and computational benefits of our proposed methods on a diverse set of real-world applications.

Within the machine learning community, the widely-used uniform convergence framework seeks to answer the question of how complex models such as modern neural networks can generalize well to new data. This approach bounds the test error of the \emph{worst-case} model one could have fit to the data, which presents fundamental limitations. In this paper, we revisit the statistical mechanics approach to learning, which instead attempts to understand the behavior of the \emph{typical} model. To quantify this typicality in the setting of over-parameterized linear classification, we develop a methodology to compute the full distribution of test errors among interpolating classifiers. We apply our method to compute this distribution for several real and synthetic datasets. We find that in many regimes of interest, an overwhelming proportion of interpolating classifiers have good test performance, even though---as we demonstrate---classifiers with very high test error do exist. This shows that the behavior of the worst-case model can deviate substantially from that of the usual model. Furthermore, we observe that for a given training set and testing distribution, there is a critical value $\varepsilon^* > 0$ which is \emph{typical}, in the sense that nearly all test errors eventually concentrate around it. Based on these empirical results, we study this phenomenon theoretically under simplifying assumptions on the data, and we derive simple asymptotic expressions for both the distribution of test errors as well as the critical value $\varepsilon^*$. Both of these results qualitatively reproduce our empirical findings. Our results show that the usual style of analysis in statistical learning theory may not be fine-grained enough to capture the good generalization performance observed in practice, and that approaches based on the statistical mechanics of learning offer a promising alternative.

In this paper we study Meta learning of Gaussian graphical models. In our setup, each task has a different true precision matrix, each with a possibly different support (i.e., set of edges in the graph). We assume that the union of the supports of all the true precision matrices (i.e., the true support union) is small in size, which relates to sparse graphs. We propose to pool all the samples from different tasks, and estimate a single precision matrix by $\ell_1$-regularized maximum likelihood estimation. We show that with high probability, the support of the estimated single precision matrix is equal to the true support union, provided a sufficient number of samples per task $n \in O((\log N)/K)$, for $N$ nodes and $K$ tasks. That is, one requires less samples per task when more tasks are available. We prove a matching information-theoretic lower bound for the necessary number of samples, which is $n \in \Omega((\log N)/K)$, and thus, our algorithm is minimax optimal. Synthetic experiments validate our theory.