We introduce a tensor-based model of shared representation for meta-learning from a diverse set of tasks. Prior works on learning linear representations for meta-learning assume that there is a common shared representation across different tasks, and do not consider the additional task-specific observable side information. In this work, we model the meta-parameter through an order-$3$ tensor, which can adapt to the observed task features of the task. We propose two methods to estimate the underlying tensor. The first method solves a tensor regression problem and works under natural assumptions on the data generating process. The second method uses the method of moments under additional distributional assumptions and has an improved sample complexity in terms of the number of tasks. We also focus on the meta-test phase, and consider estimating task-specific parameters on a new task. Substituting the estimated tensor from the first step allows us estimating the task-specific parameters with very few samples of the new task, thereby showing the benefits of learning tensor representations for meta-learning. Finally, through simulation and several real-world datasets, we evaluate our methods and show that it improves over previous linear models of shared representations for meta-learning.

The wisdom of the crowd has long become the de facto approach for eliciting information from individuals or experts in order to predict the ground truth. However, classical democratic approaches for aggregating individual \emph{votes} only work when the opinion of the majority of the crowd is relatively accurate. A clever recent approach, \emph{surprisingly popular voting}, elicits additional information from the individuals, namely their \emph{prediction} of other individuals' votes, and provably recovers the ground truth even when experts are in minority. This approach works well when the goal is to pick the correct option from a small list, but when the goal is to recover a true ranking of the alternatives, a direct application of the approach requires eliciting too much information. We explore practical techniques for extending the surprisingly popular algorithm to ranked voting by partial votes and predictions and designing robust aggregation rules. We experimentally demonstrate that even a little prediction information helps surprisingly popular voting outperform classical approaches.

Graph Neural Networks (GNNs), a generalization of deep neural networks on graph data have been widely used in various domains, ranging from drug discovery to recommender systems. However, GNNs on such applications are limited when there are few available samples. Meta-learning has been an important framework to address the lack of samples in machine learning, and in recent years, the researchers have started to apply meta-learning to GNNs. In this work, we provide a comprehensive survey of different meta-learning approaches involving GNNs on various graph problems showing the power of using these two approaches together. We categorize the literature based on proposed architectures, shared representations, and applications. Finally, we discuss several exciting future research directions and open problems.

We initiate the study of fair classifiers that are robust to perturbations in the training distribution. Despite recent progress, the literature on fairness has largely ignored the design of fair and robust classifiers. In this work, we develop classifiers that are fair not only with respect to the training distribution, but also for a class of distributions that are weighted perturbations of the training samples. We formulate a min-max objective function whose goal is to minimize a distributionally robust training loss, and at the same time, find a classifier that is fair with respect to a class of distributions. We first reduce this problem to finding a fair classifier that is robust with respect to the class of distributions. Based on online learning algorithm, we develop an iterative algorithm that provably converges to such a fair and robust solution. Experiments on standard machine learning fairness datasets suggest that, compared to the state-of-the-art fair classifiers, our classifier retains fairness guarantees and test accuracy for a large class of perturbations on the test set. Furthermore, our experiments show that there is an inherent trade-off between fairness robustness and accuracy of such classifiers.

Marginal Structural Models (MSM) {Robins, 2000} are the most popular models for causal inference from time-series observational data. However, they have two main drawbacks: (a) they do not capture subject heterogeneity, and (b) they only consider fixed time intervals and do not scale gracefully with longer intervals. In this work, we propose a new family of MSMs to address these two concerns. We model the potential outcomes as a three-dimensional tensor of low rank, where the three dimensions correspond to the agents, time periods and the set of possible histories. Unlike the traditional MSM, we allow the dimensions of the tensor to increase with the number of agents and time periods. We set up a weighted tensor completion problem as our estimation procedure, and show that the solution to this problem converges to the true model in an appropriate sense. Then we show how to solve the estimation problem, providing conditions under which we can approximately and efficiently solve the estimation problem. Finally, we propose an algorithm based on projected gradient descent, which is easy to implement and evaluate its performance on a simulated dataset.

Increased interest in web-based education has spurred the proliferation of online learning environments. However, these platforms suffer from high dropout rates due to lack of sustained motivation among the students taking the course. In an effort to address this problem, we propose an incentive-based, instructor-driven approach to orchestrate the interactions in online educational forums (OEFs). Our approach takes into account the heterogeneity in skills among the students as well as the limited budget available to the instructor. We first analytically model OEFs in a non-strategic setting using ideas from lumpable continuous time Markov chains and compute expected aggregate transient net-rewards for the instructor and the students. We next consider a strategic setting where we use the rewards computed above to set up a mixed-integer linear program which views an OEF as a single-leader-multiple-followers Stackelberg game and recommends an optimal plan to the instructor for maximizing student participation. Our experimental results reveal several interesting phenomena including a striking non-monotonicity in the level of participation of students vis-a-vis the instructor's arrival rate.

Motivated by current day crowdsourcing platforms and emergence of online labor markets, this work addresses the problem of task allocation and payment decisions when unreliable and strategic workers arrive over time to work on tasks which must be completed within a deadline. We consider the following scenario: a requester has a set of tasks that must be completed before a deadline; agents (aka crowd workers) arrive over time and it is required to make sequential decisions regarding task allocation and pricing. Agents may have different costs for providing service and these costs are private information of the agents. We assume that agents are not strategic about their arrival times but could be strategic about their costs of service. In addition, agents could be unreliable in the sense of not being able to complete the assigned tasks within the allocated time; these tasks must then be reallocated to other agents to ensure ontime completion of the set of tasks by the deadline. For this setting, we propose two mechanisms: a DPM (DynamicPrice Mechanism) and an ABM (Auction Based Mechanism). Both mechanisms are dominant strategy incentive compatible, budget feasible, and also satisfy ex-post individual rationality for agents who complete the allocated tasks. These mechanisms can be implemented in current day crowdsourcing platforms with minimal changes to the current interaction model.