V-Monotone Independence google
We introduce and study a new notion of non-commutative independence, called V-monotone independence, which can be viewed as an extension of the monotone independence of Muraki. We investigate the combinatorics of mixed moments of V-monotone random variables and prove the central limit theorem. We obtain a combinatorial formula for the limit moments and we find the solution of the differential equation for the moment generating function in the implicit form. …

Feature Pyramid Hashing google
In recent years, deep-networks-based hashing has become a leading approach for large-scale image retrieval. Most deep hashing approaches use the high layer to extract the powerful semantic representations. However, these methods have limited ability for fine-grained image retrieval because the semantic features extracted from the high layer are difficult in capturing the subtle differences. To this end, we propose a novel two-pyramid hashing architecture to learn both the semantic information and the subtle appearance details for fine-grained image search. Inspired by the feature pyramids of convolutional neural network, a vertical pyramid is proposed to capture the high-layer features and a horizontal pyramid combines multiple low-layer features with structural information to capture the subtle differences. To fuse the low-level features, a novel combination strategy, called consensus fusion, is proposed to capture all subtle information from several low-layers for finer retrieval. Extensive evaluation on two fine-grained datasets CUB-200-2011 and Stanford Dogs demonstrate that the proposed method achieves significant performance compared with the state-of-art baselines. …

Empirical Bayes Method google
Empirical Bayes methods are procedures for statistical inference in which the prior distribution is estimated from the data. This approach stands in contrast to standard Bayesian methods, for which the prior distribution is fixed before any data are observed. Despite this difference in perspective, empirical Bayes may be viewed as an approximation to a fully Bayesian treatment of a hierarchical model wherein the parameters at the highest level of the hierarchy are set to their most likely values, instead of being integrated out. Empirical Bayes, also known as maximum marginal likelihood, represents one approach for setting hyperparameters. …

Deep Abstract Q-Network google
We examine the problem of learning and planning on high-dimensional domains with long horizons and sparse rewards. Recent approaches have shown great successes in many Atari 2600 domains. However, domains with long horizons and sparse rewards, such as Montezuma’s Revenge and Venture, remain challenging for existing methods. Methods using abstraction (Dietterich 2000; Sutton, Precup, and Singh 1999) have shown to be useful in tackling long-horizon problems. We combine recent techniques of deep reinforcement learning with existing model-based approaches using an expert-provided state abstraction. We construct toy domains that elucidate the problem of long horizons, sparse rewards and high-dimensional inputs, and show that our algorithm significantly outperforms previous methods on these domains. Our abstraction-based approach outperforms Deep Q-Networks (Mnih et al. 2015) on Montezuma’s Revenge and Venture, and exhibits backtracking behavior that is absent from previous methods. …

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