We present a nonparametric Bayesian approach to inverse reinforcement learning (IRL) for multiple reward functions. Most previous IRL algorithms assume that the behaviour data is obtained from an agent who is optimizing a single reward function, but this assumption is hard to be met in practice. Our approach is based on integrating the Dirichlet process mixture model into Bayesian IRL. We provide an efficient Metropolis-Hastings sampling algorithm utilizing the gradient of the posterior to estimate the underlying reward functions, and demonstrate that our approach outperforms the previous ones via experiments on a number of problem domains.

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 memorabilitymaps 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.

Multi-task learning (MTL) aims to improve generalization performance by learning multiple related tasks simultaneously and identifying the shared information among tasks. Most of existing MTL methods focus on learning linear models under the supervised setting. We propose a novel semi-supervised and nonlinear approach for MTL using vector fields. A vector field is a smooth mapping from the manifold to the tangent spaces which can be viewed as a directional derivative of functions on the manifold. We argue that vector fields provide a natural way to exploit the geometric structure of data as well as the shared differential structure of tasks, both are crucial for semi-supervised multi-task learning. In this paper, we develop multi-task vector field learning (MTVFL) which learns the prediction functions and the vector fields simultaneously. MTVFL has the following key properties: (1) the vector fields we learned are close to the gradient fields of the prediction functions; (2) within each task, the vector field is required to be as parallel as possible which is expected to span a low dimensional subspace; (3) the vector fields from all tasks share a low dimensional subspace. We formalize our idea in a regularization framework and also provide a convex relaxation method to solve the original non-convex problem. The experimental results on synthetic and real data demonstrate the effectiveness of our proposed approach.

In this paper, a novel, computationally fast, and alternative algorithm for com- puting weighted v-statistics in resampling both univariate and multivariate data is proposed. To avoid any real resampling, we have linked this problem with finite group action and converted it into a problem of orbit enumeration. For further computational cost reduction, an efficient method is developed to list all orbits by their symmetry order and calculate all index function orbit sums and data function orbit sums recursively. The computational complexity analysis shows reduction in the computational cost from n! or nn level to low-order polynomial level.

In this paper we apply boosting to learn complex non-linear local visual feature representations, drawing inspiration from its successful application to visual object detection. The main goal of local feature descriptors is to distinctively represent a salient image region while remaining invariant to viewpoint and illumination changes. This representation can be improved using machine learning, however, past approaches have been mostly limited to learning linear feature mappings in either the original input or a kernelized input feature space. While kernelized methods have proven somewhat effective for learning non-linear local feature descriptors, they rely heavily on the choice of an appropriate kernel function whose selection is often difficult and non-intuitive. We propose to use the boosting-trick to obtain a non-linear mapping of the input to a high-dimensional feature space. The non-linear feature mapping obtained with the boosting-trick is highly intuitive. We employ gradient-based weak learners resulting in a learned descriptor that closely resembles the well-known SIFT. As demonstrated in our experiments, the resulting descriptor can be learned directly from intensity patches achieving state-of-the-art performance.

We consider the online distributed non-stochastic experts problem, where the distributed system consists of one coordinator node that is connected to k sites, and the sites are required to communicate with each other via the coordinator. At each time-step t, one of the k site nodes has to pick an expert from the set {1, . . . , n}, and the same site receives information about payoffs of all experts for that round. The goal of the distributed system is to minimize regret at time horizon T, while simultaneously keeping communication to a minimum. The two extreme solutions to this problem are: (i) Full communication: This essentially simulates the non-distributed setting to obtain the optimal O(\sqrt{log(n)T}) regret bound at the cost of T communication. (ii) No communication: Each site runs an independent copy – the regret is O(\sqrt{log(n)kT}) and the communication is 0. This paper shows the difficulty of simultaneously achieving regret asymptotically better than \sqrt{kT} and communication better than T. We give a novel algorithm that for an oblivious adversary achieves a non-trivial trade-off: regret O(\sqrt{k^{5(1+\epsilon)/6} T}) and communication O(T/k^\epsilon), for any value of \epsilon in (0, 1/5). We also consider a variant of the model, where the coordinator picks the expert. In this model, we show that the label-efficient forecaster of Cesa-Bianchi et al. (2005) already gives us strategy that is near optimal in regret vs communication trade-off.

We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where the function oscillates more, while allocating the samples such that they are well spread on the domain (this notion shares similitude with low discrepancy). We prove that the estimate returned by the algorithm is almost as accurate as the estimate that an optimal oracle strategy (that would know the variations of the function everywhere) would return, and we provide a finite-sample analysis.

We uncover relations between robust MDPs and risk-sensitive MDPs. The objective of a robust MDP is to minimize a function, such as the expectation of cumulative cost, for the worst case when the parameters have uncertainties. The objective of a risk-sensitive MDP is to minimize a risk measure of the cumulative cost when the parameters are known. We show that a risk-sensitive MDP of minimizing the expected exponential utility is equivalent to a robust MDP of minimizing the worst-case expectation with a penalty for the deviation of the uncertain parameters from their nominal values, which is measured with the Kullback-Leibler divergence. We also show that a risk-sensitive MDP of minimizing an iterated risk measure that is composed of certain coherent risk measures is equivalent to a robust MDP of minimizing the worst-case expectation when the possible deviations of uncertain parameters from their nominal values are characterized with a concave function.

While human listeners excel at selectively attending to a conversation in a cocktail party, machine performance is still far inferior by comparison. We show that the cocktail party problem, or the speech separation problem, can be effectively approached via structured prediction. To account for temporal dynamics in speech, we employ conditional random fields (CRFs) to classify speech dominance within each time-frequency unit for a sound mixture. To capture complex, nonlinear relationship between input and output, both state and transition feature functions in CRFs are learned by deep neural networks. The formulation of the problem as classification allows us to directly optimize a measure that is well correlated with human speech intelligibility. The proposed system substantially outperforms existing ones in a variety of noises.

The representer theorem is a property that lies at the foundation of regularization theory and kernel methods. A class of regularization functionals is said to admit a linear representer theorem if every member of the class admits minimizers that lie in the finite dimensional subspace spanned by the representers of the data. A recent characterization states that certain classes of regularization functionals with differentiable regularization term admit a linear representer theorem for any choice of the data if and only if the regularization term is a radial nondecreasing function. In this paper, we extend such result by weakening the assumptions on the regularization term. In particular, the main result of this paper implies that, for a sufficiently large family of regularization functionals, radial nondecreasing functions are the only lower semicontinuous regularization terms that guarantee existence of a representer theorem for any choice of the data.