1,721,103 research outputs found
Learning Mixed Membership Community Models in Social Tagging Networks through Tensor Methods
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Efficient approaches for escaping higher order saddle points in non-convex optimization
Full text linkLocal search heuristics for non-convex optimizations are popular in applied machine learning. However, in general it is hard to guarantee that such algorithms even converge to a local minimum, due to the existence of complicated saddle point structures in high dimensions. Many functions have degenerate saddle points such that the first and second order derivatives cannot distinguish them with local optima. In this paper we use higher order derivatives to escape these saddle points: we design the first efficient algorithm guaranteed to converge to a third order local optimum (while existing techniques are at most second order). We also show that it is NP-hard to extend this further to finding fourth order local optima
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Training Input-Output Recurrent Neural Networks through Spectral Methods
Full text linkWe consider the problem of training input-output recurrent neural networks (RNN) for sequence labeling tasks. We propose a novel spectral approach for learning the network parameters. It is based on decomposition of the cross-moment tensor between the output and a non-linear transformation of the input, based on score functions. We guarantee consistent learning with polynomial sample and computational complexity under transparent conditions such as non-degeneracy of model parameters, polynomial activations for the neurons, and a Markovian evolution of the input sequence. We also extend our results to Bidirectional RNN which uses both previous and future information to output the label at each time point, and is employed in many NLP tasks such as POS tagging
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Provable Methods for Training Neural Networks with Sparse Connectivity
Full text linkWe provide novel guaranteed approaches for training feedforward neural networks with sparse connectivity. We leverage on the techniques developed previously for learning linear networks and show that they can also be effectively adopted to learn non-linear networks. We operate on the moments involving label and the score function of the input, and show that their factorization provably yields the weight matrix of the first layer of a deep network under mild conditions. In practice, the output of our method can be employed as effective initializers for gradient descent
Competitive Gradient Descent
Full text linkWe introduce a new algorithm for the numerical computation of Nash equilibria of competitive two-player games. Our method is a natural generalization of gradient descent to the two-player setting where the update is given by the Nash equilibrium of a regularized bilinear local approximation of the underlying game. It avoids oscillatory and divergent behaviors seen in alternating gradient descent. Using numerical experiments and rigorous analysis, we provide a detailed comparison to methods based on optimism and consensus and show that our method avoids making any unnecessary changes to the gradient dynamics while achieving exponential (local) convergence for (locally) convex-concave zero sum games. Convergence and stability properties of our method are robust to strong interactions between the players, without adapting the stepsize, which is not the case with previous methods. In our numerical experiments on non-convex-concave problems, existing methods are prone to divergence and instability due to their sensitivity to interactions among the players, whereas we never observe divergence of our algorithm. The ability to choose larger stepsizes furthermore allows our algorithm to achieve faster convergence, as measured by the number of model evaluations
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Learning Mixed Membership Community Models in Social Tagging Networks through Tensor Methods
Full text linkCommunity detection in graphs has been extensively studied both in theory and in applications. However, detecting communities in hypergraphs is more challenging. In this paper, we propose a tensor decomposition approach for guaranteed learning of communities in a special class of hypergraphs modeling social tagging systems or folksonomies. A folksonomy is a tripartite 3-uniform hypergraph consisting of (user, tag, resource) hyperedges. We posit a probabilistic mixed membership community model, and prove that the tensor method consistently learns the communities under efficient sample complexity and separation requirements
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Multi-Object Classification and Unsupervised Scene Understanding Using Deep Learning Features and Latent Tree Probabilistic Models
Full text linkDeep learning has shown state-of-art classification performance on datasets such as ImageNet, which contain a single object in each image. However, multi-object classification is far more challenging. We present a unified framework which leverages the strengths of multiple machine learning methods, viz deep learning, probabilistic models and kernel methods to obtain state-of-art performance on Microsoft COCO, consisting of non-iconic images. We incorporate contextual information in natural images through a conditional latent tree probabilistic model (CLTM), where the object co-occurrences are conditioned on the extracted fc7 features from pre-trained Imagenet CNN as input. We learn the CLTM tree structure using conditional pairwise probabilities for object co-occurrences, estimated through kernel methods, and we learn its node and edge potentials by training a new 3-layer neural network, which takes fc7 features as input. Object classification is carried out via inference on the learnt conditional tree model, and we obtain significant gain in precision-recall and F-measures on MS-COCO, especially for difficult object categories. Moreover, the latent variables in the CLTM capture scene information: the images with top activations for a latent node have common themes such as being a grasslands or a food scene, and on on. In addition, we show that a simple k-means clustering of the inferred latent nodes alone significantly improves scene classification performance on the MIT-Indoor dataset, without the need for any retraining, and without using scene labels during training. Thus, we present a unified framework for multi-object classification and unsupervised scene understanding
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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