We introduce the Adaptive Skills, Adaptive Partitions (ASAP) framework that (1) learns skills (i.e., temporally extended actions or options) as well as (2) where to apply them. We believe that both (1) and (2) are necessary for a truly general skill learning framework, which is a key building block needed to scale up to lifelong learning agents. The ASAP framework is also able to solve related new tasks simply by adapting where it applies its existing learned skills. We prove that ASAP converges to a local optimum under natural conditions. Finally, our experimental results, which include a RoboCup domain, demonstrate the ability of ASAP to learn where to reuse skills as well as solve multiple tasks with considerably less experience than solving each task from scratch.

Despite having high accuracy, neural nets have been shown to be susceptible to adversarial examples, where a small perturbation to an input can cause it to become mislabeled. We propose metrics for measuring the robustness of a neural net and devise a novel algorithm for approximating these metrics based on an encoding of robustness as a linear program. We show how our metrics can be used to evaluate the robustness of deep neural nets with experiments on the MNIST and CIFAR-10 datasets. Our algorithm generates more informative estimates of robustness metrics compared to estimates based on existing algorithms. Furthermore, we show how existing approaches to improving robustness "overfit" to adversarial examples generated using a specific algorithm. Finally, we show that our techniques can be used to additionally improve neural net robustness both according to the metrics that we propose, but also according to previously proposed metrics.

We propose Confusions over Time (CoT), a novel generative framework which facilitates a multi-granular analysis of the decision making process. The CoT not only models the confusions or error properties of individual decision makers and their evolution over time, but also allows us to obtain diagnostic insights into the collective decision making process in an interpretable manner.

We consider the problem of jointly inferring the $M$-best diverse labelings for a binary (high-order) submodular energy of a graphical model. Recently, it was shown that this problem can be solved to a global optimum, for many practically interesting diversity measures. It was noted that the labelings are, so-called, nested. This nestedness property also holds for labelings of a class of parametric submodular minimization problems, where different values of the global parameter $\gamma$ give rise to different solutions. The popular example of the parametric submodular minimization is the monotonic parametric max-flow problem, which is also widely used for computing multiple labelings.

Decision making under uncertainty is commonly modelled as a process of competitive stochastic evidence accumulation to threshold (the drift-diffusion model). However, it is unknown how animals learn these decision thresholds. We examine threshold learning by constructing a reward function that averages over many trials to Wald's cost function that defines decision optimality. These rewards are highly stochastic and hence challenging to optimize, which we address in two ways: first, a simple two-factor reward-modulated learning rule derived from Williams' REINFORCE method for neural networks; and second, Bayesian optimization of the reward function with a Gaussian process. Bayesian optimization converges in fewer trials than REINFORCE but is slower computationally with greater variance. The REINFORCE method is also a better model of acquisition behaviour in animals and a similar learning rule has been proposed for modelling basal ganglia function.

Non-negative matrix factorization is a popular tool for decomposing data into feature and weight matrices under non-negativity constraints. It enjoys practical success but is poorly understood theoretically. This paper proposes an algorithm that alternates between decoding the weights and updating the features, and shows that assuming a generative model of the data, it provably recovers the ground-truth under fairly mild conditions. In particular, its only essential requirement on features is linear independence. Furthermore, the algorithm uses ReLU to exploit the non-negativity for decoding the weights, and thus can tolerate adversarial noise that can potentially be as large as the signal, and can tolerate unbiased noise much larger than the signal. The analysis relies on a carefully designed coupling between two potential functions, which we believe is of independent interest.

Collaborative filtering is a popular technique to infer users' preferences on new content based on the collective information of all users preferences. Recommender systems then use this information to make personalized suggestions to users. When users accept these recommendations it creates a feedback loop in the recommender system, and these loops iteratively influence the collaborative filtering algorithm's predictions over time. We investigate whether it is possible to identify items affected by these feedback loops. We state sufficient assumptions to deconvolve the feedback loops while keeping the inverse solution tractable. We furthermore develop a metric to unravel the recommender system's influence on the entire user-item rating matrix. We use this metric on synthetic and real-world datasets to (1) identify the extent to which the recommender system affects the final rating matrix, (2) rank frequently recommended items, and (3) distinguish whether a user's rated item was recommended or an intrinsic preference. Our results indicate that it is possible to recover the ratings matrix of intrinsic user preferences using a single snapshot of the ratings matrix without any temporal information.

We propose a framework for Semi-Supervised Active Clustering framework (SSAC), where the learner is allowed to interact with a domain expert, asking whether two given instances belong to the same cluster or not. We study the query and computational complexity of clustering in this framework. We consider a setting where the expert conforms to a center-based clustering with a notion of margin. We show that there is a trade off between computational complexity and query complexity; We prove that for the case of $k$-means clustering (i.e., when the expert conforms to a solution of $k$-means), having access to relatively few such queries allows efficient solutions to otherwise NP hard problems. In particular, we provide a probabilistic polynomial-time (BPP) algorithm for clustering in this setting that asks $O\big(k^2\log k + k\log n)$ same-cluster queries and runs with time complexity $O\big(kn\log n)$ (where $k$ is the number of clusters and $n$ is the number of instances). The success of the algorithm is guaranteed for data satisfying the margin condition under which, without queries, we show that the problem is NP hard. We also prove a lower bound on the number of queries needed to have a computationally efficient clustering algorithm in this setting.

We study regression and classification in a setting where the learning algorithm is allowed to access only a limited number of attributes per example, known as the limited attribute observation model. In this well-studied model, we provide the first lower bounds giving a limit on the precision attainable by any algorithm for several variants of regression, notably linear regression with the absolute loss and the squared loss, as well as for classification with the hinge loss. We complement these lower bounds with a general purpose algorithm that gives an upper bound on the achievable precision limit in the setting of learning with missing data.

We consider the problem of variational inference in probabilistic models with both log-submodular and log-supermodular higher-order potentials. These models can represent arbitrary distributions over binary variables, and thus generalize the commonly used pairwise Markov random fields and models with log-supermodular potentials only, for which efficient approximate inference algorithms are known. While inference in the considered models is #P-hard in general, we present efficient approximate algorithms exploiting recent advances in the field of discrete optimization. We demonstrate the effectiveness of our approach in a large set of experiments, where our model allows reasoning about preferences over sets of items with complements and substitutes.