Optimization-based meta-learning typically assumes tasks are sampled from a single distribution - an assumption oversimplifies and limits the diversity of tasks that meta-learning can model. Handling tasks from multiple different distributions is challenging for meta-learning due to a so-called task ambiguity issue. This paper proposes a novel method, ST-MAML, that empowers model-agnostic meta-learning (MAML) to learn from multiple task distributions. ST-MAML encodes tasks using a stochastic neural network module, that summarizes every task with a stochastic representation. The proposed Stochastic Task (ST) strategy allows a meta-model to get tailored for the current task and enables us to learn a distribution of solutions for an ambiguous task. ST-MAML also propagates the task representation to revise the encoding of input variables. Empirically, we demonstrate that ST-MAML matches or outperforms the state-of-the-art on two few-shot image classification tasks, one curve regression benchmark, one image completion problem, and a real-world temperature prediction application. To the best of authors' knowledge, this is the first time optimization-based meta-learning method being applied on a large-scale real-world task.

While much of the causal inference literature has focused on addressing internal validity biases, both internal and external validity are necessary for unbiased estimates in a target population of interest. However, few generalizability approaches exist for estimating causal quantities in a target population when the target population is not well-represented by a randomized study but is reflected when additionally incorporating observational data. To generalize to a target population represented by a union of these data, we propose a class of novel conditional cross-design synthesis estimators that combine randomized and observational data, while addressing their respective biases. The estimators include outcome regression, propensity weighting, and double robust approaches. All use the covariate overlap between the randomized and observational data to remove potential unmeasured confounding bias. We apply these methods to estimate the causal effect of managed care plans on health care spending among Medicaid beneficiaries in New York City.

State-of-the-art deep learning classifiers are heavily overparameterized with respect to the amount of training examples and observed to generalize well on "clean" data, but be highly susceptible to infinitesmal adversarial perturbations. In this paper, we identify an overparameterized linear ensemble, that uses the "lifted" Fourier feature map, that demonstrates both of these behaviors. The input is one-dimensional, and the adversary is only allowed to perturb these inputs and not the non-linear features directly. We find that the learned model is susceptible to adversaries in an intermediate regime where classification generalizes but regression does not. Notably, the susceptibility arises despite the absence of model mis-specification or label noise, which are commonly cited reasons for adversarial-susceptibility. These results are extended theoretically to a random-Fourier-sum setup that exhibits double-descent behavior. In both feature-setups, the adversarial vulnerability arises because of a phenomenon we term spatial localization: the predictions of the learned model are markedly more sensitive in the vicinity of training points than elsewhere. This sensitivity is a consequence of feature lifting and is reminiscent of Gibb's and Runge's phenomena from signal processing and functional analysis. Despite the adversarial susceptibility, we find that classification with these features can be easier than the more commonly studied "independent feature" models.

Heterogeneous multi-typed, multimodal relational data is increasingly available in many domains and their exploratory analysis poses several challenges. We advance the state-of-the-art in neural unsupervised learning to analyze such data. We design the first neural method for collective matrix tri-factorization of arbitrary collections of matrices to perform spectral clustering of all constituent entities and learn cluster associations. Experiments on benchmark datasets demonstrate its efficacy over previous non-neural approaches. Leveraging signals from multi-way clustering and collective matrix completion we design a unique technique, called Discordance Analysis, to reveal information discrepancies across subsets of matrices in a collection with respect to two entities. We illustrate its utility in quality assessment of knowledge bases and in improving representation learning.

In this paper we propose a lightning fast graph embedding method called graph encoder embedding. The proposed method has a linear computational complexity and the capacity to process billions of edges within minutes on standard PC -- an unattainable feat for any existing graph embedding method. The speedup is achieved without sacrificing embedding performance: the encoder embedding performs as good as, and can be viewed as a transformation of the more costly spectral embedding. The encoder embedding is applicable to either adjacency matrix or graph Laplacian, and is theoretically sound, i.e., under stochastic block model or random dot product graph, the graph encoder embedding asymptotically converges to the block probability or latent positions, and is approximately normally distributed. We showcase three important applications: vertex classification, vertex clustering, and graph bootstrap; and the embedding performance is evaluated via a comprehensive set of synthetic and real data. In every case, the graph encoder embedding exhibits unrivalled computational advantages while delivering excellent numerical performance.

We study the mixing time of the Metropolis-adjusted Langevin algorithm (MALA) for sampling from a log-smooth and strongly log-concave distribution. We establish its optimal minimax mixing time under a warm start. Our main contribution is two-fold. First, for a $d$-dimensional log-concave density with condition number $\kappa$, we show that MALA with a warm start mixes in $\tilde O(\kappa \sqrt{d})$ iterations up to logarithmic factors. This improves upon the previous work on the dependency of either the condition number $\kappa$ or the dimension $d$. Our proof relies on comparing the leapfrog integrator with the continuous Hamiltonian dynamics, where we establish a new concentration bound for the acceptance rate. Second, we prove a spectral gap based mixing time lower bound for reversible MCMC algorithms on general state spaces. We apply this lower bound result to construct a hard distribution for which MALA requires at least $\tilde \Omega (\kappa \sqrt{d})$ steps to mix. The lower bound for MALA matches our upper bound in terms of condition number and dimension. Finally, numerical experiments are included to validate our theoretical results.

Systems that rely on forecasts to make decisions, e.g. control or energy trading systems, require frequent updates of the forecasts. Usually, the forecasts are updated whenever new observations become available, hence in an online setting. We present the R package onlineforecast that provides a generalized setup of data and models for online forecasting. It has functionality for time-adaptive fitting of linear regression-based models. Furthermore, dynamical and non-linear effects can be easily included in the models. The setup is tailored to enable effective use of forecasts as model inputs, e.g. numerical weather forecast. Users can create new models for their particular system applications and run models in an operational online setting. The package also allows users to easily replace parts of the setup, e.g. use kernel or neural network methods for estimation. The package comes with comprehensive vignettes and examples of online forecasting applications in energy systems, but can easily be applied in all fields where online forecasting is used.

Dimension reduction plays a pivotal role in analysing high-dimensional data. However, observations with missing values present serious difficulties in directly applying standard dimension reduction techniques. As a large number of dimension reduction approaches are based on the Gram matrix, we first investigate the effects of missingness on dimension reduction by studying the statistical properties of the Gram matrix with or without missingness, and then we present a bias-corrected Gram matrix with nice statistical properties under heterogeneous missingness. Extensive empirical results, on both simulated and publicly available real datasets, show that the proposed unbiased Gram matrix can significantly improve a broad spectrum of representative dimension reduction approaches.

Knowledge graphs have emerged as a widely adopted medium for storing relational data, making methods for automatically reasoning with them highly desirable. In this paper, we present a novel approach for inducing a hierarchy of subject clusters, building upon our earlier work done in taxonomy induction. Our method first constructs a tag hierarchy before assigning subjects to clusters on this hierarchy. We quantitatively demonstrate our method's ability to induce a coherent cluster hierarchy on three real-world datasets.

While deep neural networks have achieved great success on the graph analysis, recent works have shown that they are also vulnerable to adversarial attacks where fraudulent users can fool the model with a limited number of queries. Compared with adversarial attacks on image classification, performing adversarial attack on graphs is challenging because of the discrete and non-differential nature of a graph. To address these issues, we proposed Cluster Attack, a novel adversarial attack by introducing a set of fake nodes to the original graph which can mislead the classification on certain victim nodes. Specifically, we query the victim model for each victim node to acquire their most adversarial feature, which is related to how the fake node's feature will affect the victim nodes. We further cluster the victim nodes into several subgroups according to their most adversarial features such that we can reduce the searching space. Moreover, our attack is performed in a practical and unnoticeable manner: (1) We protect the predicted labels of nodes which we are not aimed for from being changed during attack. (2) We attack by introducing fake nodes into the original graph without changing existing links and features. (3) We attack with only partial information about the attacked graph, i.e., by leveraging the information of victim nodes along with their neighbors within $k$-hop instead of the whole graph. (4) We perform attack with a limited number of queries about the predicted scores of the model in a black-box manner, i.e., without model architecture and parameters. Extensive experiments demonstrate the effectiveness of our method in terms of the success rate of attack.