In this paper, we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [4], which aimed at introducing the conceptual basis for new notions of traditional and accelerated gradient descent algorithms for the optimization of a function on a semi-discrete space using ideas from optimal transport theory. Our methods, which use the network morphism framework introduced in [3] as a baseline, can analyze forty times as many architectures as the hill climbing methods [3, 11] while using the same computational resources and time and achieving comparable levels of accuracy.

Gradient boosting is a powerful machine learning technique that is particularly successful for tasks containing heterogeneous features and noisy data. While gradient boosting classification models return a distribution over class labels, regressions models typically yield only point predictions. However, for many practical, high-risk applications, it is also important to be able to quantify uncertainty in the predictions to avoid costly mistakes. In this work, we examine a probabilistic ensemble-based framework for deriving uncertainty estimates in the predictions of gradient boosting classification and regression models. Crucially, the proposed approach allows the total uncertainty to be decomposed into \textit{data uncertainty}, which comes from the complexity and noise in data distribution, and \textit{knowledge uncertainty}, coming from the lack of information about a given region of the feature space. Two approaches for generating ensembles are considered: Stochastic Gradient Boosting (SGB) and Stochastic Gradient Langevin Boosting (SGLB). Notably, SGLB also enables the generation of a \emph{virtual} ensemble via only one gradient boosting model, which significantly reduces complexity. Experiments on a range of regression and classification datasets show that ensembles of gradient boosting models yield improved predictive performance, and measures of uncertainty successfully enable detection of out-of-domain inputs.

Dynamic and temporal graphs are rich data structures that are used to model complex relationships between entities over time. In particular, anomaly detection in temporal graphs is crucial for many real world applications such as intrusion identification in network systems, detection of ecosystem disturbances and detection of epidemic outbreaks. In this paper, we focus on change point detection in dynamic graphs and address two main challenges associated with this problem: I) how to compare graph snapshots across time, II) how to capture temporal dependencies. To solve the above challenges, we propose Laplacian Anomaly Detection (LAD) which uses the spectrum of the Laplacian matrix of the graph structure at each snapshot to obtain low dimensional embeddings. LAD explicitly models short term and long term dependencies by applying two sliding windows. In synthetic experiments, LAD outperforms the state-of-the-art method. We also evaluate our method on three real dynamic networks: UCI message network, US senate co-sponsorship network and Canadian bill voting network. In all three datasets, we demonstrate that our method can more effectively identify anomalous time points according to significant real world events.

In this paper, we propose and analyze a model selection method for tree tensor networks in an empirical risk minimization framework. Tree tensor networks, or tree-based tensor formats, are prominent model classes for the approximation of high-dimensional functions in numerical analysis and data science. They correspond to sum-product neural networks with a sparse connectivity associated with a dimension partition tree $T$, widths given by a tuple $r$ of tensor ranks, and multilinear activation functions (or units). The approximation power of these model classes has been proved to be near-optimal for classical smoothness classes. However, in an empirical risk minimization framework with a limited number of observations, the dimension tree $T$ and ranks $r$ should be selected carefully to balance estimation and approximation errors. In this paper, we propose a complexity-based model selection strategy \`a la Barron, Birg\'e, Massart. Given a family of model classes, with different trees, ranks and tensor product feature spaces, a model is selected by minimizing a penalized empirical risk, with a penalty depending on the complexity of the model class. After deriving bounds of the metric entropy of tree tensor networks with bounded parameters, we deduce a form of the penalty from bounds on suprema of empirical processes. This choice of penalty yields a risk bound for the predictor associated with the selected model. For classical smoothness spaces, we show that the proposed strategy is minimax optimal in a least-squares setting. In practice, the amplitude of the penalty is calibrated with a slope heuristics method. Numerical experiments in a least-squares regression setting illustrate the performance of the strategy for the approximation of multivariate functions and univariate functions identified with tensors by tensorization (quantization).

Empirical risk minimization (ERM) is typically designed to perform well on the average loss, which can result in estimators that are sensitive to outliers, generalize poorly, or treat subgroups unfairly. While many methods aim to address these problems individually, in this work, we explore them through a unified framework---tilted empirical risk minimization (TERM). In particular, we show that it is possible to flexibly tune the impact of individual losses through a straightforward extension to ERM using a hyperparameter called the tilt. We provide several interpretations of the resulting framework: We show that TERM can increase or decrease the influence of outliers, respectively, to enable fairness or robustness; has variance-reduction properties that can benefit generalization; and can be viewed as a smooth approximation to a superquantile method. We develop batch and stochastic first-order optimization methods for solving TERM, and show that the problem can be efficiently solved relative to common alternatives. Finally, we demonstrate that TERM can be used for a multitude of applications, such as enforcing fairness between subgroups, mitigating the effect of outliers, and handling class imbalance. TERM is not only competitive with existing solutions tailored to these individual problems, but can also enable entirely new applications, such as simultaneously addressing outliers and promoting fairness.

In federated learning, communication cost is often a critical bottleneck to scale up distributed optimization algorithms to collaboratively learn a model from millions of devices with potentially unreliable or limited communication and heterogeneous data distributions. Two notable trends to deal with the communication overhead of federated algorithms are \emph{gradient compression} and \emph{local computation with periodic communication}. Despite many attempts, characterizing the relationship between these two approaches has proven elusive. We address this by proposing a set of algorithms with periodical compressed (quantized or sparsified) communication and analyze their convergence properties in both homogeneous and heterogeneous local data distributions settings. For the homogeneous setting, our analysis improves existing bounds by providing tighter convergence rates for both \emph{strongly convex} and \emph{non-convex} objective functions. To mitigate data heterogeneity, we introduce a \emph{local gradient tracking} scheme and obtain sharp convergence rates that match the best-known communication complexities without compression for convex, strongly convex, and nonconvex settings. We complement our theoretical results and demonstrate the effectiveness of our proposed methods by several experiments on real-world datasets.

Randomized controlled trials typically analyze the effectiveness of treatments with the goal of making treatment recommendations for patient subgroups. With the advance of electronic health records, a great variety of data has been collected in clinical practice, enabling the evaluation of treatments and treatment policies based on observational data. In this paper, we focus on learning individualized treatment rules (ITRs) to derive a treatment policy that is expected to generate a better outcome for an individual patient. In our framework, we cast ITRs learning as a contextual bandit problem and minimize the expected risk of the treatment policy. We conduct experiments with the proposed framework both in a simulation study and based on a real-world dataset. In the latter case, we apply our proposed method to learn the optimal ITRs for the administration of intravenous (IV) fluids and vasopressors (VP). Based on various offline evaluation methods, we could show that the policy derived in our framework demonstrates better performance compared to both the physicians and other baselines, including a simple treatment prediction approach. As a long-term goal, our derived policy might eventually lead to better clinical guidelines for the administration of IV and VP.

It is becoming increasingly important to explain complex, black-box machine learning models. Although there is an expanding literature on this topic, Shapley values stand out as a sound method to explain predictions from any type of machine learning model. The original development of Shapley values for prediction explanation relied on the assumption that the features being described were independent. This methodology was then extended to explain dependent features with an underlying continuous distribution. In this paper, we propose a method to explain mixed (i.e. continuous, discrete, ordinal, and categorical) dependent features by modeling the dependence structure of the features using conditional inference trees. We demonstrate our proposed method against the current industry standards in various simulation studies and find that our method often outperforms the other approaches. Finally, we apply our method to a real financial data set used in the 2018 FICO Explainable Machine Learning Challenge and show how our explanations compare to the FICO challenge Recognition Award winning team.

Of these two modalities, the world's public transit systems where no official real-time real-time state is disproportionately important for the bus tracking is provided. We demonstrate that our neural routine trips that dominate most people's transportation sequence model improves over DeepTTE, the state-ofthe-art needs. Most transit users know by heart the routes connecting baseline, both in performance ( 30% MAPE) and their home, work, and other frequent destinations, training stability. We also demonstrate significant generalization but they have a well-established need for information gains over simpler models, evaluated on longitudinal about real-time changes. Transit variability is a data to cope with a constantly evolving world.

We study a family of algorithms, which we refer to as local update methods, that generalize many federated learning and meta-learning algorithms. We prove that for quadratic objectives, local update methods perform stochastic gradient descent on a surrogate loss function which we exactly characterize. We show that the choice of client learning rate controls the condition number of that surrogate loss, as well as the distance between the minimizers of the surrogate and true loss functions. We use this theory to derive novel convergence rates for federated averaging that showcase this trade-off between the condition number of the surrogate loss and its alignment with the true loss function. We validate our results empirically, showing that in communication-limited settings, proper learning rate tuning is often sufficient to reach near-optimal behavior. We also present a practical method for automatic learning rate decay in local update methods that helps reduce the need for learning rate tuning, and highlight its empirical performance on a variety of tasks and datasets.