The use of distributions and high-level features from deep architecture has become commonplace in modern computer vision. Both of these methodologies have separately achieved a great deal of success in many computer vision tasks. However, there has been little work attempting to leverage the power of these to methodologies jointly. To this end, this paper presents the Deep Mean Maps (DMMs) framework, a novel family of methods to non-parametrically represent distributions of features in convolutional neural network models. DMMs are able to both classify images using the distribution of top-level features, and to tune the top-level features for performing this task. We show how to implement DMMs using a special mean map layer composed of typical CNN operations, making both forward and backward propagation simple. We illustrate the efficacy of DMMs at analyzing distributional patterns in image data in a synthetic data experiment. We also show that we extending existing deep architectures with DMMs improves the performance of existing CNNs on several challenging real-world datasets.
Mean map embeddings @cite_38 @cite_35 @cite_2 have served as a practical and flexible method to learn using datasets of sample sets drawn from distributions @cite_18 @cite_28 . Furthermore, the use of random features @cite_8 @cite_21 has allowed for scalable learning over distributions @cite_32 @cite_1 @cite_20 @cite_4 . Mean map embeddings have also been used extensively for the comparison and two-sample testing of distributions @cite_35 @cite_29 @cite_6 . Recent research has also explored the use of mean maps in deep architectures for building fast sampling mechanisms, by conducting two-sample tests between generated sample points and original data @cite_13 @cite_34 ; this work differs from ours in using mean maps in the loss function, rather than in the architecture itself.
@cite_38 @cite_18 @cite_35 @cite_4 @cite_8 @cite_28 @cite_29 @cite_21 @cite_1 @cite_32 @cite_6 @cite_2 @cite_34 @cite_13 @cite_20
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Mapping the Internet generally consists in sampling the network from a limited set of sources by using "traceroute"-like probes. This methodology, akin to the merging of different spanning trees to a set of destinations, has been argued to introduce uncontrolled sampling biases that might produce statistical properties of the sampled graph which sharply differ from the original ones. Here we explore these biases and provide a statistical analysis of their origin. We derive a mean-field analytical approximation for the probability of edge and vertex detection that exploits the role of the number of sources and targets and allows us to relate the global topological properties of the underlying network with the statistical accuracy of the sampled graph. In particular we find that the edge and vertex detection probability is depending on the betweenness centrality of each element. This allows us to show that shortest path routed sampling provides a better characterization of underlying graphs with scale-free topology. We complement the analytical discussion with a throughout numerical investigation of simulated mapping strategies in different network models. We show that sampled graphs provide a fair qualitative characterization of the statistical properties of the original networks in a fair range of different strategies and exploration parameters. The numerical study also allows the identification of intervals of the exploration parameters that optimize the fraction of nodes and edges discovered in the sampled graph. This finding might hint the steps toward more efficient mapping strategies. Continuous space word embeddings learned from large, unstructured corpora have been shown to be effective at capturing semantic regularities in language. In this paper we replace LDA’s parameterization of “topics” as categorical distributions over opaque word types with multivariate Gaussian distributions on the embedding space. This encourages the model to group words that are a priori known to be semantically related into topics. To perform inference, we introduce a fast collapsed Gibbs sampling algorithm based on Cholesky decompositions of covariance matrices of the posterior predictive distributions. We further derive a scalable algorithm that draws samples from stale posterior predictive distributions and corrects them with a Metropolis–Hastings step. Using vectors learned from a domain-general corpus (English Wikipedia), we report results on two document collections (20-newsgroups and NIPS). Qualitatively, Gaussian LDA infers different (but still very sensible) topics relative to standard LDA. Quantitatively, our technique outperforms existing models at dealing with OOV words in held-out documents. We suggest a new loss for learning deep embeddings. The key characteristics of the new loss is the absence of tunable parameters and very good results obtained across a range of datasets and problems. The loss is computed by estimating two distribution of similarities for positive (matching) and negative (non-matching) point pairs, and then computing the probability of a positive pair to have a lower similarity score than a negative pair based on these probability estimates. We show that these operations can be performed in a simple and piecewise-differentiable manner using 1D histograms with soft assignment operations. This makes the proposed loss suitable for learning deep embeddings using stochastic optimization. The experiments reveal favourable results compared to recently proposed loss functions. Instance embeddings are an efficient and versatile image representation that facilitates applications like recognition, verification, retrieval, and clustering. Many metric learning methods represent the input as a single point in the embedding space. Often the distance between points is used as a proxy for match confidence. However, this can fail to represent uncertainty arising when the input is ambiguous, e.g., due to occlusion or blurriness. This work addresses this issue and explicitly models the uncertainty by hedging the location of each input in the embedding space. We introduce the hedged instance embedding (HIB) in which embeddings are modeled as random variables and the model is trained under the variational information bottleneck principle. Empirical results on our new N-digit MNIST dataset show that our method leads to the desired behavior of hedging its bets across the embedding space upon encountering ambiguous inputs. This results in improved performance for image matching and classification tasks, more structure in the learned embedding space, and an ability to compute a per-exemplar uncertainty measure that is correlated with downstream performance.