We propose combinatorial cascading bandits, a class of partial monitoring problems where at each step a learning agent chooses a tuple of ground items subject to constraints and receives a reward if and only if the weights of all chosen items are one. The weights of the items are binary, stochastic, and drawn independently of each other. The agent observes the index of the first chosen item whose weight is zero. This observation model arises in network routing, for instance, where the learning agent may only observe the first link in the routing path which is down, and blocks the path. We propose a UCB-like algorithm for solving our problems, CombCascade; and prove gap-dependent and gap-free upper bounds on its n-step regret. Our proofs build on recent work in stochastic combinatorial semi-bandits but also address two novel challenges of our setting, a non-linear reward function and partial observability. We evaluate CombCascade on two real-world problems and show that it performs well even when our modeling assumptions are violated. We also demonstrate that our setting requires a new learning algorithm.

Causal structure learning from time series data is a major scientific challenge. Existing algorithms assume that measurements occur sufficiently quickly; more precisely, they assume that the system and measurement timescales are approximately equal. In many scientific domains, however, measurements occur at a significantly slower rate than the underlying system changes. Moreover, the size of the mismatch between timescales is often unknown. This paper provides three distinct causal structure learning algorithms, all of which discover all dynamic graphs that could explain the observed measurement data as arising from undersampling at some rate. That is, these algorithms all learn causal structure without assuming any particular relation between the measurement and system timescales; they are thus rate-agnostic. We apply these algorithms to data from simulations. The results provide insight into the challenge of undersampling.

Some crowdsourcing platforms ask workers to express their opinions by approving a set of k good alternatives. It seems that the only reasonable way to aggregate these k-approval votes is the approval voting rule, which simply counts the number of times each alternative was approved. We challenge this assertion by proposing a probabilistic framework of noisy voting, and asking whether approval voting yields an alternative that is most likely to be the best alternative, given k-approval votes. While the answer is generally positive, our theoretical and empirical results call attention to situations where approval voting is suboptimal.

Linear regression studies the problem of estimating a model parameter $\beta^* \in \R^p$, from $n$ observations $\{(y_i,x_i)\}_{i=1}^n$ from linear model $y_i = \langle \x_i,\beta^* \rangle + \epsilon_i$. We consider a significant generalization in which the relationship between $\langle x_i,\beta^* \rangle$ and $y_i$ is noisy, quantized to a single bit, potentially nonlinear, noninvertible, as well as unknown. This model is known as the single-index model in statistics, and, among other things, it represents a significant generalization of one-bit compressed sensing. We propose a novel spectral-based estimation procedure and show that we can recover $\beta^*$ in settings (i.e., classes of link function $f$) where previous algorithms fail. In general, our algorithm requires only very mild restrictions on the (unknown) functional relationship between $y_i$ and $\langle x_i,\beta^* \rangle$. We also consider the high dimensional setting where $\beta^*$ is sparse, and introduce a two-stage nonconvex framework that addresses estimation challenges in high dimensional regimes where $p \gg n$. For a broad class of link functions between $\langle x_i,\beta^* \rangle$ and $y_i$, we establish minimax lower bounds that demonstrate the optimality of our estimators in both the classical and high dimensional regimes.

The goal of this paper is to generate high-quality 3D object proposals in the context of autonomous driving. Our method exploits stereo imagery to place proposals in the form of 3D bounding boxes. We formulate the problem as minimizing an energy function encoding object size priors, ground plane as well as several depth informed features that reason about free space, point cloud densities and distance to the ground. Our experiments show significant performance gains over existing RGB and RGB-D object proposal methods on the challenging KITTI benchmark. Combined with convolutional neural net (CNN) scoring, our approach outperforms all existing results on all three KITTI object classes.

Given a multi-armed bandit problem it may be desirable to achieve a smaller-than-usual worst-case regret for some special actions. I show that the price for such unbalanced worst-case regret guarantees is rather high. Specifically, if an algorithm enjoys a worst-case regret of B with respect to some action, then there must exist another action for which the worst-case regret is at least Ω(nK/B), where n is the horizon and K the number of actions. I also give upper bounds in both the stochastic and adversarial settings showing that this result cannot be improved. For the stochastic case the pareto regret frontier is characterised exactly up to constant factors.

Humans have the remarkable ability to follow the gaze of other people to identify what they are looking at. Following eye gaze, or gaze-following, is an important ability that allows us to understand what other people are thinking, the actions they are performing, and even predict what they might do next. Despite the importance of this topic, this problem has only been studied in limited scenarios within the computer vision community. In this paper, we propose a deep neural networkbased approachfor gaze-following and a new benchmark dataset, GazeFollow, for thorough evaluation. Given an image and the location of a head, our approach follows the gaze of the person and identifies the object being looked at. Our deep network is able to discover how to extract head pose and gaze orientation, and to select objects in the scene that are in the predicted line of sight and likely to be looked at (such as televisions, balls and food). The quantitative evaluation shows that our approach produces reliable results, even when viewing only the back of the head. While our method outperforms several baseline approaches, we are still far from reaching human performance on this task. Overall, we believe that gazefollowing isa challenging and important problem that deserves more attention from the community.

A key bottleneck in structured output prediction is the need for inference during training and testing, usually requiring some form of dynamic programming. Rather than using approximate inference or tailoring a specialized inference method for a particular structure---standard responses to the scaling challenge---we propose to embed prediction constraints directly into the learned representation. By eliminating the need for explicit inference a more scalable approach to structured output prediction can be achieved, particularly at test time. We demonstrate the idea for multi-label prediction under subsumption and mutual exclusion constraints, where a relationship to maximum margin structured output prediction can be established. Experiments demonstrate that the benefits of structured output training can still be realized even after inference has been eliminated.

Computing the MAP assignment in graphical models is generally intractable. As a result, for discrete graphical models, the MAP problem is often approximated using linear programming relaxations. Much research has focused on characterizing when these LP relaxations are tight, and while they are relatively well-understood in the discrete case, only a few results are known for their continuous analog. In this work, we use graph covers to provide necessary and sufficient conditions for continuous MAP relaxations to be tight. We use this characterization to give simple proofs that the relaxation is tight for log-concave decomposable and log-supermodular decomposable models. We conclude by exploring the relationship between these two seemingly distinct classes of functions and providing specific conditions under which the MAP relaxation can and cannot be tight.

Tractable learning aims to learn probabilistic models where inference is guaranteed to be efficient. However, the particular class of queries that is tractable depends on the model and underlying representation. Usually this class is MPE or conditional probabilities $\Pr(\xs|\ys)$ for joint assignments~$\xs,\ys$. We propose a tractable learner that guarantees efficient inference for a broader class of queries. It simultaneously learns a Markov network and its tractable circuit representation, in order to guarantee and measure tractability. Our approach differs from earlier work by using Sentential Decision Diagrams (SDD) as the tractable language instead of Arithmetic Circuits (AC). SDDs have desirable properties, which more general representations such as ACs lack, that enable basic primitives for Boolean circuit compilation. This allows us to support a broader class of complex probability queries, including counting, threshold, and parity, in polytime.