In the superset label learning problem (SLL), each training instance provides a set of candidate labels of which one is the true label of the instance. As in ordinary regression, the candidate label set is a noisy version of the true label. In this work, we solve the problem by maximizing the likelihood of the candidate label sets of training instances. We propose a probabilistic model, the Logistic Stick-Breaking Conditional Multinomial Model (LSB-CMM), to do the job. The LSB-CMM is derived from the logistic stick-breaking process. It first maps data points to mixture components and then assigns to each mixture component a label drawn from a component-specific multinomial distribution.

A gaze concurrence is a point in 3D where the gaze directions of two or more people intersect. It is a strong indicator of social saliency because the attention of the participating group is focused on that point. In scenes occupied by large groups of people, multiple concurrences may occur and transition over time. In this paper, we present a method to construct a 3D social saliency field and locate multiple gaze concurrences that occur in a social scene from videos taken by head-mounted cameras. We model the gaze as a cone-shaped distribution emanating from the center of the eyes, capturing the variation of eye-in-head motion. We calibrate the parameters of this distribution by exploiting the fixed relationship between the primary gaze ray and the head-mounted camera pose. The resulting gaze model enables us to build a social saliency field in 3D. We estimate the number and 3D locations of the gaze concurrences via provably convergent modeseeking in the social saliency field. Our algorithm is applied to reconstruct multiple gaze concurrences in several real world scenes and evaluated quantitatively against motion-captured ground truth.

While long term human visual memory can store a remarkable amount of visual information, it tends to degrade over time. Recent works have shown that image memorability is an intrinsic property of an image that can be reliably estimated using state-of-the-art image features and machine learning algorithms. However, the class of features and image information that is forgotten has not been explored yet. In this work, we propose a probabilistic framework that models how and which local regions from an image may be forgotten using a data-driven approach that combines local and global images features. The model automatically discovers memorability maps of individual images without any human annotation. We incorporate multiple image region attributes in our algorithm, leading to improved memorability prediction of images as compared to previous works.

We study surrogate losses for learning to rank, in a framework where the rankings are induced by scores and the task is to learn the scoring function. We focus on the calibration of surrogate losses with respect to a ranking evaluation metric, where the calibration is equivalent to the guarantee that near-optimal values of the surrogate risk imply near-optimal values of the risk defined by the evaluation metric. We prove that if a surrogate loss is a convex function of the scores, then it is not calibrated with respect to two evaluation metrics widely used for search engine evaluation, namely the Average Precision and the Expected Reciprocal Rank. We also show that such convex surrogate losses cannot be calibrated with respect to the Pairwise Disagreement, an evaluation metric used when learning from pairwise preferences. Our results cast lights on the intrinsic difficulty of some ranking problems, as well as on the limitations of learning-to-rank algorithms based on the minimization of a convex surrogate risk.

We introduce a new learning algorithm, named smooth-projected neighborhood pursuit, for estimating high dimensional undirected graphs. In particularly, we focus on the nonparanormal graphical model and provide theoretical guarantees for graph estimation consistency. In addition to new computational and theoretical analysis, we also provide an alternative view to analyze the tradeoff between computational efficiency and statistical error under a smoothing optimization framework. Numerical results on both synthetic and real datasets are provided to support our theory.

In the superset label learning problem (SLL), each training instance provides a set of candidate labels of which one is the true label of the instance. As in ordinary regression, the candidate label set is a noisy version of the true label. In this work, we solve the problem by maximizing the likelihood of the candidate label sets of training instances. We propose a probabilistic model, the Logistic Stick-Breaking Conditional Multinomial Model (LSB-CMM), to do the job. The LSB-CMM is derived from the logistic stick-breaking process. It first maps data points to mixture components and then assigns to each mixture component a label drawn from a component-specific multinomial distribution.

The minimax KL-divergence of any distribution from all distributions in a collection P has several practical implications. In compression, it is called redundancy and represents the least additional number of bits over the entropy needed to encode the output of any distribution in P. In online estimation and learning, it is the lowest expected log-loss regret when guessing a sequence of random values generated by a distribution in P. In hypothesis testing, it upper bounds the largest number of distinguishable distributions in P. Motivated by problems ranging from population estimation to text classification and speech recognition, several machine-learning and information-theory researchers have recently considered label-invariant observations and properties induced by i.i.d.

Sum-product networks are a new deep architecture that can perform fast, exact inference on high-treewidth models. Only generative methods for training SPNs have been proposed to date. In this paper, we present the first discriminative training algorithms for SPNs, combining the high accuracy of the former with the representational power and tractability of the latter. We show that the class of tractable discriminative SPNs is broader than the class of tractable generative ones, and propose an efficient backpropagation-style algorithm for computing the gradient of the conditional log likelihood. Standard gradient descent suffers from the diffusion problem, but networks with many layers can be learned reliably using "hard" gradient descent, where marginal inference is replaced by MPE inference (i.e., inferring the most probable state of the non-evidence variables). The resulting updates have a simple and intuitive form. We test discriminative SPNs on standard image classification tasks. We obtain the best results to date on the CIFAR-10 dataset, using fewer features than prior methods with an SPN architecture that learns local image structure discriminatively. We also report the highest published test accuracy on STL-10 even though we only use the labeled portion of the dataset.

The expected return is a widely used objective in decision making under uncertainty. Many algorithms, such as value iteration, have been proposed to optimize it. In risk-aware settings, however, the expected return is often not an appropriate objective to optimize. We propose a new optimization objective for risk-aware planning and show that it has desirable theoretical properties. We also draw connections to previously proposed objectives for risk-aware planing: minmax, exponential utility, percentile and mean minus variance. Our method applies to an extended class of Markov decision processes: we allow costs to be stochastic as long as they are bounded. Additionally, we present an efficient algorithm for optimizing the proposed objective. Synthetic and real-world experiments illustrate the effectiveness of our method, at scale.

We introduce a class of discrete divergences on sets (equivalently binary vectors) that we call the submodular-Bregman divergences. We consider two kinds, defined either from tight modular upper or tight modular lower bounds of a submodular function. We show that the properties of these divergences are analogous to the (standard continuous) Bregman divergence. We demonstrate how they generalize many useful divergences, including the weighted Hamming distance, squared weighted Hamming, weighted precision, recall, conditional mutual information, and a generalized KL-divergence on sets. We also show that the generalized Bregman divergence on the Lovász extension of a submodular function, which we call the Lovász-Bregman divergence, is a continuous extension of a submodular Bregman divergence. We point out a number of applications, and in particular show that a proximal algorithm defined through the submodular Bregman divergence provides a framework for many mirror-descent style algorithms related to submodular function optimization. We also show that a generalization of the k-means algorithm using the Lovász Bregman divergence is natural in clustering scenarios where ordering is important. A unique property of this algorithm is that computing the mean ordering is extremely efficient unlike other order based distance measures.