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Lifelong graph learning deals with the problem of continually adapting graph neural network (GNN) models to changes in evolving graphs. We address two critical challenges of lifelong graph learning in this work: dealing with new classes and tackling imbalanced class distributions. The combination of these two challenges is particularly relevant since newly emerging classes typically resemble only a tiny fraction of the data, adding to the already skewed class distribution. We make several contributions: First, we show that the amount of unlabeled data does not influence the results, which is an essential prerequisite for lifelong learning on a sequence of tasks. Second, we experiment with different label rates and show that our methods can perform well with only a tiny fraction of annotated nodes. Third, we propose the gDOC method to detect new classes under the constraint of having an imbalanced class distribution. The critical ingredient is a weighted binary cross-entropy loss function to account for the class imbalance. Moreover, we demonstrate combinations of gDOC with various base GNN models such as GraphSAGE, Simplified Graph Convolution, and Graph Attention Networks. Lastly, our k-neighborhood time difference measure provably normalizes the temporal changes across different graph datasets. With extensive experimentation, we find that the proposed gDOC method is consistently better than a naive adaption of DOC to graphs. Specifically, in experiments using the smallest history size, the out-of-distribution detection score of gDOC is 0.09 compared to 0.01 for DOC. Furthermore, gDOC achieves an Open-F1 score, a combined measure of in-distribution classification and out-of-distribution detection, of 0.33 compared to 0.25 of DOC (32% increase).

We propose FedGT, a novel framework for identifying malicious clients in federated learning with secure aggregation. Inspired by group testing, the framework leverages overlapping groups of clients to detect the presence of malicious clients in the groups and to identify them via a decoding operation. The identified clients are then removed from the training of the model, which is performed over the remaining clients. FedGT strikes a balance between privacy and security, allowing for improved identification capabilities while still preserving data privacy. Specifically, the server learns the aggregated model of the clients in each group. The effectiveness of FedGT is demonstrated through extensive experiments on the MNIST and CIFAR-10 datasets, showing its ability to identify malicious clients with low misdetection and false alarm probabilities, resulting in high model utility.

Stochastic dual dynamic programming is a cutting plane type algorithm for multi-stage stochastic optimization originated about 30 years ago. In spite of its popularity in practice, there does not exist any analysis on the convergence rates of this method. In this paper, we first establish the number of iterations, i.e., iteration complexity, required by a basic dynamic cutting plane method for solving relatively simple multi-stage optimization problems, by introducing novel mathematical tools including the saturation of search points. We then refine these basic tools and establish the iteration complexity for both deterministic and stochastic dual dynamic programming methods for solving more general multi-stage stochastic optimization problems under the standard stage-wise independence assumption. Our results indicate that the complexity of some deterministic variants of these methods mildly increases with the number of stages $T$, in fact linearly dependent on $T$ for discounted problems. Therefore, they are efficient for strategic decision making which involves a large number of stages, but with a relatively small number of decision variables in each stage. Without explicitly discretizing the state and action spaces, these methods might also be pertinent to the related reinforcement learning and stochastic control areas.

Discovering causal relations from observational data is important. The existence of unobserved variables (e.g. latent confounding or mediation) can mislead the causal identification. To overcome this problem, proximal causal discovery methods attempted to adjust for the bias via the proxy of the unobserved variable. Particularly, hypothesis test-based methods proposed to identify the causal edge by testing the induced violation of linearity. However, these methods only apply to discrete data with strict level constraints, which limits their practice in the real world. In this paper, we fix this problem by extending the proximal hypothesis test to cases where the system consists of continuous variables. Our strategy is to present regularity conditions on the conditional distributions of the observed variables given the hidden factor, such that if we discretize its observed proxy with sufficiently fine, finite bins, the involved discretization error can be effectively controlled. Based on this, we can convert the problem of testing continuous causal relations to that of testing discrete causal relations in each bin, which can be effectively solved with existing methods. These non-parametric regularities we present are mild and can be satisfied by a wide range of structural causal models. Using both simulated and real-world data, we show the effectiveness of our method in recovering causal relations when unobserved variables exist.

Proof Blocks is a software tool that allows students to practice writing mathematical proofs by dragging and dropping lines instead of writing proofs from scratch. Proof Blocks offers the capability of assigning partial credit and providing solution quality feedback to students. This is done by computing the edit distance from a student's submission to some predefined set of solutions. In this work, we propose an algorithm for the edit distance problem that significantly outperforms the baseline procedure of exhaustively enumerating over the entire search space. Our algorithm relies on a reduction to the minimum vertex cover problem. We benchmark our algorithm on thousands of student submissions from multiple courses, showing that the baseline algorithm is intractable, and that our proposed algorithm is critical to enable classroom deployment. Our new algorithm has also been used for problems in many other domains where the solution space can be modeled as a DAG, including but not limited to Parsons Problems for writing code, helping students understand packet ordering in networking protocols, and helping students sketch solution steps for physics problems. Integrated into multiple learning management systems, the algorithm serves thousands of students each year.

Performative prediction, as introduced by Perdomo et al. (2020), is a framework for studying social prediction in which the data distribution itself changes in response to the deployment of a model. Existing work on optimizing accuracy in this setting hinges on two assumptions that are easily violated in practice: that the performative risk is convex over the deployed model, and that the mapping from the model to the data distribution is known to the model designer in advance. In this paper, we initiate the study of tractable performative prediction problems that do not require these assumptions. To tackle this more challenging setting, we develop a two-level zeroth-order optimization algorithm, where one level aims to compute the distribution map, and the other level reparameterizes the performative prediction objective as a function of the induced data distribution. Under mild conditions, this reparameterization allows us to transform the non-convex objective into a convex one and achieve provable regret guarantees. In particular, we provide a regret bound that is sublinear in the total number of performative samples taken and only polynomial in the dimension of the model parameter.

We propose a new auto-regressive model for the statistical analysis of multivariate distributional time series. The data of interest consist of a collection of multiple series of probability measures supported over a bounded interval of the real line, and that are indexed by distinct time instants. The probability measures are modelled as random objects in the Wasserstein space. We establish the auto-regressive model in the tangent space at the Lebesgue measure by first centering all the raw measures so that their Fr\'echet means turn to be the Lebesgue measure. Using the theory of iterated random function systems, results on the existence, uniqueness and stationarity of the solution of such a model are provided. We also propose a consistent estimator for the model coefficient. In addition to the analysis of simulated data, the proposed model is illustrated with two real data sets made of observations from age distribution in different countries and bike sharing network in Paris. Finally, due to the positive and boundedness constraints that we impose on the model coefficients, the proposed estimator that is learned under these constraints, naturally has a sparse structure. The sparsity allows furthermore the application of the proposed model in learning a graph of temporal dependency from the multivariate distributional time series.

For clinical studies with continuous outcomes, when the data are potentially skewed, researchers may choose to report the whole or part of the five-number summary (the sample median, the first and third quartiles, and the minimum and maximum values) rather than the sample mean and standard deviation. In the recent literature, it is often suggested to transform the five-number summary back to the sample mean and standard deviation, which can be subsequently used in a meta-analysis. However, if a study contains skewed data, this transformation and hence the conclusions from the meta-analysis are unreliable. Therefore, we introduce a novel method for detecting the skewness of data using only the five-number summary and the sample size, and meanwhile propose a new flow chart to handle the skewed studies in a different manner. We further show by simulations that our skewness tests are able to control the type I error rates and provide good statistical power, followed by a simulated meta-analysis and a real data example that illustrate the usefulness of our new method in meta-analysis and evidence-based medicine.

We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.

The demand for artificial intelligence has grown significantly over the last decade and this growth has been fueled by advances in machine learning techniques and the ability to leverage hardware acceleration. However, in order to increase the quality of predictions and render machine learning solutions feasible for more complex applications, a substantial amount of training data is required. Although small machine learning models can be trained with modest amounts of data, the input for training larger models such as neural networks grows exponentially with the number of parameters. Since the demand for processing training data has outpaced the increase in computation power of computing machinery, there is a need for distributing the machine learning workload across multiple machines, and turning the centralized into a distributed system. These distributed systems present new challenges, first and foremost the efficient parallelization of the training process and the creation of a coherent model. This article provides an extensive overview of the current state-of-the-art in the field by outlining the challenges and opportunities of distributed machine learning over conventional (centralized) machine learning, discussing the techniques used for distributed machine learning, and providing an overview of the systems that are available.