Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph kernels, based on return probabilities of random walks. The advantages of our proposed kernels are that they can effectively exploit various node attributes, while being scalable to large datasets. We conduct extensive graph classification experiments to evaluate our graph kernels. The experimental results show that our graph kernels significantly outperform other state-of-the-art approaches in both accuracy and computational efficiency.

We study the query complexity of Bayesian Private Learning: a learner wishes to locate a random target within an interval by submitting queries, in the presence of an adversary who observes all of her queries but not the responses. How many queries are necessary and sufficient in order for the learner to accurately estimate the target, while simultaneously concealing the target from the adversary? Our main result is a query complexity lower bound that is tight up to the first order. We show that if the learner wants to estimate the target within an error of $\epsilon$, while ensuring that no adversary estimator can achieve a constant additive error with probability greater than $1/L$, then the query complexity is on the order of $L\log(1/\epsilon)$ as $\epsilon \to 0$. Our result demonstrates that increased privacy, as captured by $L$, comes at the expense of a \emph{multiplicative} increase in query complexity. The proof builds on Fano's inequality and properties of certain proportional-sampling estimators.

We review the current state of automatic differentiation (AD) for array programming in machine learning (ML), including the different approaches such as operator overloading (OO) and source transformation (ST) used for AD, graph-based intermediate representations for programs, and source languages. Based on these insights, we introduce a new graph-based intermediate representation (IR) which specifically aims to efficiently support fully-general AD for array programming. Unlike existing dataflow programming representations in ML frameworks, our IR naturally supports function calls, higher-order functions and recursion, making ML models easier to implement. The ability to represent closures allows us to perform AD using ST without a tape, making the resulting derivative (adjoint) program amenable to ahead-of-time optimization using tools from functional language compilers, and enabling higher-order derivatives. Lastly, we introduce a proof of concept compiler toolchain called Myia which uses a subset of Python as a front end.

Time series are widely used as signals in many classification/regression tasks. It is ubiquitous that time series contains many missing values. Given multiple correlated time series data, how to fill in missing values and to predict their class labels? Existing imputation methods often impose strong assumptions of the underlying data generating process, such as linear dynamics in the state space. In this paper, we propose BRITS, a novel method based on recurrent neural networks for missing value imputation in time series data.

Inferring intent from observed behavior has been studied extensively within the frameworks of Bayesian inverse planning and inverse reinforcement learning. These methods infer a goal or reward function that best explains the actions of the observed agent, typically a human demonstrator. Another agent can use this inferred intent to predict, imitate, or assist the human user. However, a central assumption in inverse reinforcement learning is that the demonstrator is close to optimal. While models of suboptimal behavior exist, they typically assume that suboptimal actions are the result of some type of random noise or a known cognitive bias, like temporal inconsistency. In this paper, we take an alternative approach, and model suboptimal behavior as the result of internal model misspecification: the reason that user actions might deviate from near-optimal actions is that the user has an incorrect set of beliefs about the rules -- the dynamics -- governing how actions affect the environment. Our insight is that while demonstrated actions may be suboptimal in the real world, they may actually be near-optimal with respect to the user's internal model of the dynamics. By estimating these internal beliefs from observed behavior, we arrive at a new method for inferring intent. We demonstrate in simulation and in a user study with 12 participants that this approach enables us to more accurately model human intent, and can be used in a variety of applications, including offering assistance in a shared autonomy framework and inferring human preferences.

Coresets are one of the central methods to facilitate the analysis of large data. We continue a recent line of research applying the theory of coresets to logistic regression. First, we show the negative result that no strongly sublinear sized coresets exist for logistic regression. To deal with intractable worst-case instances we introduce a complexity measure $\mu(X)$, which quantifies the hardness of compressing a data set for logistic regression.

We introduce two novel tree search algorithms that use a policy to guide search. The first algorithm is a best-first enumeration that uses a cost function that allows us to provide an upper bound on the number of nodes to be expanded before reaching a goal state. We show that this best-first algorithm is particularly well suited for ``needle-in-a-haystack'' problems. The second algorithm, which is based on sampling, provides an upper bound on the expected number of nodes to be expanded before reaching a set of goal states. We show that this algorithm is better suited for problems where many paths lead to a goal. We validate these tree search algorithms on 1,000 computer-generated levels of Sokoban, where the policy used to guide search comes from a neural network trained using A3C. Our results show that the policy tree search algorithms we introduce are competitive with a state-of-the-art domain-independent planner that uses heuristic search.

In many sequential decision making tasks, it is challenging to design reward functions that help an RL agent efficiently learn behavior that is considered good by the agent designer. A number of different formulations of the reward-design problem, or close variants thereof, have been proposed in the literature. In this paper we build on the Optimal Rewards Framework of Singh et al. that defines the optimal intrinsic reward function as one that when used by an RL agent achieves behavior that optimizes the task-specifying or extrinsic reward function. Previous work in this framework has shown how good intrinsic reward functions can be learned for lookahead search based planning agents. Whether it is possible to learn intrinsic reward functions for learning agents remains an open problem. In this paper we derive a novel algorithm for learning intrinsic rewards for policy-gradient based learning agents. We compare the performance of an augmented agent that uses our algorithm to provide additive intrinsic rewards to an A2C-based policy learner (for Atari games) and a PPO-based policy learner (for Mujoco domains) with a baseline agent that uses the same policy learners but with only extrinsic rewards. Our results show improved performance on most but not all of the domains.

Despite their impressive performance, Deep Neural Networks (DNNs) typically underperform Gradient Boosting Trees (GBTs) on many tabular-dataset learning tasks. We propose that applying a different regularization coefficient to each weight might boost the performance of DNNs by allowing them to make more use of the more relevant inputs. However, this will lead to an intractable number of hyperparameters. Here, we introduce Regularization Learning Networks (RLNs), which overcome this challenge by introducing an efficient hyperparameter tuning scheme which minimizes a new Counterfactual Loss. Our results show that RLNs significantly improve DNNs on tabular datasets, and achieve comparable results to GBTs, with the best performance achieved with an ensemble that combines GBTs and RLNs. RLNs produce extremely sparse networks, eliminating up to 99.8% of the network edges and 82% of the input features, thus providing more interpretable models and reveal the importance that the network assigns to different inputs. RLNs could efficiently learn a single network in datasets that comprise both tabular and unstructured data, such as in the setting of medical imaging accompanied by electronic health records.

By converting dense models into sparse ones, pruning appears to be a promising solution to reducing the computation/memory cost. This paper studies classification models, especially DNN-based ones, to demonstrate that there exists intrinsic relationships between their sparsity and adversarial robustness. Our analyses reveal, both theoretically and empirically, that nonlinear DNN-based classifiers behave differently under $l_2$ attacks from some linear ones. We further demonstrate that an appropriately higher model sparsity implies better robustness of nonlinear DNNs, whereas over-sparsified models can be more difficult to resist adversarial examples.