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Register a new userStochastic Shared Embeddings: Data-driven Regularization of Embedding Layers
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In deep neural nets, lower level embedding layers account for a large portion of the total number of parameters. Tikhonov regularization, graph-based regularization, and hard parameter sharing are approaches that introduce explicit biases into training in a hope to reduce statistical complexity. Alternatively, we propose stochastically shared embeddings (SSE), a data-driven approach to regularizing embedding layers, which stochastically transitions between embeddings during stochastic gradient descent (SGD). Because SSE integrates seamlessly with existing SGD algorithms, it can be used with only minor modifications when training large scale neural networks. We develop tw
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The effectiveness and performance of artificial neural networks, particularly for visual tasks, depends in crucial ways on the receptive field of neurons. The receptive field itself depends on the interplay between several architectural aspects, including sparsity, pooling, and activation functions. In recent literature there are several ad hoc proposals trying to make receptive fields more flexible and adaptive to data. For instance, different parameterizations of convolutional and pooling layers have been proposed to increase their adaptivity. In this paper, we propose the novel theoretical framework of density-embedded layers, generalizing the transformation represented by a neuron. Specifically, the affine transformation applied on the input is replaced by a scalar product of the input, suitably represented as a piecewise constant function, with a density function associated with the neuron. This density is shown to describe directly the receptive field of the neuron. Crucially, by suitably representing such a density as a linear combination of a parametric family of functions, we can efficiently train the densities by means of any automatic differentiation system, making it adaptable to the problem at hand, and computationally efficient to evaluate. This framework captures and generalizes recent methods, allowing a fine tuning of the receptive field. In the paper, we define some novel layers and we experimentally validate them on the classic MNIST dataset.
We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic subgradients with efficient incremental SVD updates, made possible by highly optimized and parallelizable dense linear algebra operations on small matrices. Our practical algorithms always maintain a low-rank factorization of iterates that can be conveniently held in memory and efficiently multiplied to generate predictions in matrix completion settings. Empirical comparisons confirm that our approach is highly competitive with several recently proposed state-of-the-art solvers for such problems.
Metric learning methods for dimensionality reduction in combination with k-Nearest Neighbors (kNN) have been extensively deployed in many classification, data embedding, and information retrieval applications. However, most of these approaches involve pairwise training data comparisons, and thus have quadratic computational complexity with respect to the size of training set, preventing them from scaling to fairly big datasets. Moreover, during testing, comparing test data against all the training data points is also expensive in terms of both computational cost and resources required. Furthermore, previous metrics are either too constrained or too expressive to be well learned. To effectively solve these issues, we present an exemplar-centered supervised shallow parametric data embedding model, using a Maximally Collapsing Metric Learning (MCML) objective. Our strategy learns a shallow high-order parametric embedding function and compares training/test data only with learned or precomputed exemplars, resulting in a cost function with linear computational complexity for both training and testing. We also empirically demonstrate, using several benchmark datasets, that for classification in two-dimensional embedding space, our approach not only gains speedup of kNN by hundreds of times, but also outperforms state-of-the-art supervised embedding approaches.
The dynamic ensemble selection of classifiers is an effective approach for processing label-imbalanced data classifications. However, such a technique is prone to overfitting, owing to the lack of regularization methods and the dependence of the aforementioned technique on local geometry. In this study, focusing on binary imbalanced data classification, a novel dynamic ensemble method, namely adaptive ensemble of classifiers with regularization (AER), is proposed, to overcome the stated limitations. The method solves the overfitting problem through implicit regularization. Specifically, it leverages the properties of stochastic gradient descent to obtain the solution with the minimum norm, thereby achieving regularization; furthermore, it interpolates the ensemble weights by exploiting the global geometry of data to further prevent overfitting. According to our theoretical proofs, the seemingly complicated AER paradigm, in addition to its regularization capabilities, can actually reduce the asymptotic time and memory complexities of several other algorithms. We evaluate the proposed AER method on seven benchmark imbalanced datasets from the UCI machine learning repository and one artificially generated GMM-based dataset with five variations. The results show that the proposed algorithm outperforms the major existing algorithms based on multiple metrics in most cases, and two hypothesis tests (McNemars and Wilcoxon tests) verify the statistical significance further. In addition, the proposed method has other preferred properties such as special advantages in dealing with highly imbalanced data, and it pioneers the research on the regularization for dynamic ensemble methods.
We study data-driven assistants that provide congestion forecasts to users of shared facilities (roads, cafeterias, etc.), to support coordination between them, and increase efficiency of such collective systems. Key questions are: (1) when and how much can (accurate) predictions help for coordination, and (2) which assistant algorithms reach optimal predictions? First we lay conceptual ground for this setting where user preferences are a priori unknown and predictions influence outcomes. Addressing (1), we establish conditions under which self-fulfilling prophecies, i.e., perfect (probabilistic) predictions of what will happen, solve the coordination problem in the game-theoretic sense of selecting a Bayesian Nash equilibrium (BNE). Next we prove that such prophecies exist even in large-scale settings where only aggregated statistics about users are available. This entails a new (nonatomic) BNE existence result. Addressing (2), we propose two assistant algorithms that sequentially learn from users reactions, together with optimality/convergence guarantees. We validate one of them in a large real-world experiment.
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