Stochastic gradient descent (SGD) gives an optimal convergence rate when minimizing convex stochastic objectives $f(x)$. However, in terms of making the gradients small, the original SGD does not give an optimal rate, even when $f(x)$ is convex. If $f(x)$ is convex, to find a point with gradient norm $\varepsilon$, we design an algorithm SGD3 with a near-optimal rate $\tilde{O}(\varepsilon^{-2})$, improving the best known rate $O(\varepsilon^{-8/3})$. If $f(x)$ is nonconvex, to find its $\varepsilon$-approximate local minimum, we design an algorithm SGD5 with rate $\tilde{O}(\varepsilon^{-3.5})$, where previously SGD variants only achieve $\tilde{O}(\varepsilon^{-4})$. This is no slower than the best known stochastic version of Newton's method in all parameter regimes.

We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and hypergraphs settings, such as graph-based semi-supervised learning and PageRank. We approach the problem via a new dual strategy and describe an objective that may be optimized via random coordinate descent (RCD) methods and projections onto cones. We also establish the linear convergence rate of the RCD algorithm and develop efficient projection algorithms with provable performance guarantees. Numerical experiments in semi-supervised learning on hypergraphs confirm the efficiency of the proposed algorithm and demonstrate the significant improvements in prediction accuracy with respect to state-of-the-art methods.

We study consistency properties of machine learning methods based on minimizing convex surrogates. We extend the recent framework of Osokin et al. (2017) for the quantitative analysis of consistency properties to the case of inconsistent surrogates. Our key technical contribution consists in a new lower bound on the calibration function for the quadratic surrogate, which is non-trivial (not always zero) for inconsistent cases. The new bound allows to quantify the level of inconsistency of the setting and shows how learning with inconsistent surrogates can have guarantees on sample complexity and optimization difficulty. We apply our theory to two concrete cases: multi-class classification with the tree-structured loss and ranking with the mean average precision loss. The results show the approximation-computation trade-offs caused by inconsistent surrogates and their potential benefits.

Asynchronous Gibbs sampling has been recently shown to be fast-mixing and an accurate method for estimating probabilities of events on a small number of variables of a graphical model satisfying Dobrushin's condition [DSOR16]. We investigate whether it can be used to accurately estimate expectations of functions of all the variables of the model. Under the same condition, we show that the synchronous (sequential) and asynchronous Gibbs samplers can be coupled so that the expected Hamming distance between their (multivariate) samples remains bounded by O(τ log n), where n is the number of variables in the graphical model, and τ is a measure of the asynchronicity. A similar bound holds for any constant power of the Hamming distance. Hence, the expectation of any function that is Lipschitz with respect to a power of the Hamming distance, can be estimated with a bias that grows logarithmically in n. Going beyond Lipschitz functions, we consider the bias arising from asynchronicity in estimating the expectation of polynomial functions of all variables in the model. Using recent concentration of measure results [DDK17, GLP17, GSS18], we show that the bias introduced by the asynchronicity is of smaller order than the standard deviation of the function value already present in the true model. We perform experiments on a multiprocessor machine to empirically illustrate our theoretical findings.

Objects and their relationships are critical contents for image understanding. A scene graph provides a structured description that captures these properties of an image. However, reasoning about the relationships between objects is very challenging and only a few recent works have attempted to solve the problem of generating a scene graph from an image. In this paper, we present a novel method that improves scene graph generation by explicitly modeling inter-dependency among the entire object instances. We design a simple and effective relational embedding module that enables our model to jointly represent connections among all related objects, rather than focus on an object in isolation. Our novel method significantly benefits two main parts of the scene graph generation task: object classification and relationship classification. Using it on top of a basic Faster R-CNN, our model achieves state-of-the-art results on the Visual Genome benchmark. We further push the performance by introducing global context encoding module and geometrical layout encoding module. We validate our final model, LinkNet, through extensive ablation studies, demonstrating its efficacy in scene graph generation.

In this paper, we present a deep convolutional neural network to capture the inherent properties of image degradation, which can handle different kernels and saturated pixels in a unified framework. The proposed neural network is motivated by the low-rank property of pseudo-inverse kernels. We first compute a generalized low-rank approximation for a large number of blur kernels, and then use separable filters to initialize the convolutional parameters in the network. Our analysis shows that the estimated decomposed matrices contain the most essential information of the input kernel, which ensures the proposed network to handle various blurs in a unified framework and generate high-quality deblurring results. Experimental results on benchmark datasets with noise and saturated pixels demonstrate that the proposed algorithm performs favorably against state-of-the-art methods.

We introduce a game-theoretic approach to the study of recommendation systems with strategic content providers. Such systems should be fair and stable. Showing that traditional approaches fail to satisfy these requirements, we propose the Shapley mediator. We show that the Shapley mediator satisfies the fairness and stability requirements, runs in linear time, and is the only economically efficient mechanism satisfying these properties.

In this work, we introduce interactive structure learning, a framework that unifies many different interactive learning tasks. We present a generalization of the query-by-committee active learning algorithm for this setting, and we study its consistency and rate of convergence, both theoretically and empirically, with and without noise.

Fine-Grained Visual Classification (FGVC) is an important computer vision problem that involves small diversity within the different classes, and often requires expert annotators to collect data. Utilizing this notion of small visual diversity, we revisit Maximum-Entropy learning in the context of fine-grained classification, and provide a training routine that maximizes the entropy of the output probability distribution for training convolutional neural networks on FGVC tasks. We provide a theoretical as well as empirical justification of our approach, and achieve state-of-the-art performance across a variety of classification tasks in FGVC, that can potentially be extended to any fine-tuning task. Our method is robust to different hyperparameter values, amount of training data and amount of training label noise and can hence be a valuable tool in many similar problems.

By providing a simple and efficient way of computing low-variance gradients of continuous random variables, the reparameterization trick has become the technique of choice for training a variety of latent variable models. However, it is not applicable to a number of important continuous distributions. We introduce an alternative approach to computing reparameterization gradients based on implicit differentiation and demonstrate its broader applicability by applying it to Gamma, Beta, Dirichlet, and von Mises distributions, which cannot be used with the classic reparameterization trick. Our experiments show that the proposed approach is faster and more accurate than the existing gradient estimators for these distributions.