In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Input: Consider Input: Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To address this problem, we propose Circulant Binary Embedding (CBE) which generates binary codes by projecting the data with a circulant matrix. The circulant structure enables the use of Fast Fourier Transformation to speed up the computation. Compared to methods that use unstructured matrices, the proposed method improves the time complexity from O(d2) to O(d log d), and the space complexity from O(d2) to O(d) where d is the input dimensionality. We also propose a novel time-frequency alternating optimization to learn data-dependent circulant projections, which alternatively minimizes the objective in original and Fourier domains. We show by extensive experiments that the proposed approach gives much better performance than the state-of-the-art approaches for fixed time, and provides much faster computation with no performance degradation for fixed number of bits.

Output: Circulant Binary Embedding


Input: Consider Input: Robust belief revision methods are crucial in streaming data situations for updating existing knowledge (or beliefs) with new incoming evidence. Bayes conditioning is the primary mechanism in use for belief revision in data fusion systems that use probabilistic inference. However, traditional conditioning methods face several challenges due to inherent data/source imperfections in big-data environments that harness soft (i.e., human or human-based) sources in addition to hard (i.e., physicsbased) sensors. The objective of this paper is to investigate the most natural extension of Bayes conditioning that is suitable for evidence updating in the presence of such uncertainties. By viewing the evidence updating process as a thought experiment, an elegant strategy is derived for robust evidence updating in the presence of extreme uncertainties that are characteristic of big-data environments. In particular, utilizing the Fagin-Halpern conditional notions, a natural extension to Bayes conditioning is derived for evidence that takes the form of a general belief function. The presented work differs fundamentally from the Conditional Update Equation (CUE) and authors own extensions of it. An overview of this development is provided via illustrative examples. Furthermore, insights into parameter selection under various fusion contexts are also provided.

Output: Evidence Updating for Stream-Processing in Big-Data: Robust Conditioning in Soft and Hard Data Fusion Environments


Input: Consider Input: Cumulative prospect theory (CPT) is known to model human decisions well, with substantial empirical evidence supporting this claim. CPT works by distorting probabilities and is more general than the classic expected utility and coherent risk measures. We bring this idea to a risk-sensitive reinforcement learning (RL) setting and design algorithms for both estimation and control. The estimation scheme that we propose uses the empirical distribution in order to estimate the CPT-value of a random variable. We then use this scheme in the inner loop of policy optimization procedures for a Markov decision process (MDP). We propose both gradient-based as well as gradient-free policy optimization algorithms. The former includes both first-order and second-order methods that are based on the well-known simulation optimization idea of simultaneous perturbation stochastic approximation (SPSA), while the latter is based on a reference distribution that concentrates on the global optima. Using an empirical distribution over the policy space in conjunction with Kullback-Leibler (KL) divergence to the reference distribution, we get a global policy optimization scheme. We provide theoretical convergence guarantees for all the proposed algorithms.


Output: Cumulative Prospect Theory Meets Reinforcement Learning: Estimation and Control