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.

We propose a structure-adaptive variant of a state-of-the-art stochastic variancereduced gradient algorithm Katyusha for regularized empirical risk minimization. The proposed method is able to exploit the intrinsic low-dimensional structure of the solution, such as sparsity or low rank which is enforced by a non-smooth regularization, to achieve even faster convergence rate. This provable algorithmic improvement is done by restarting the Katyusha algorithm according to restricted strong-convexity (RSC) constants. We also propose an adaptive-restart variant which is able to estimate the RSC on the fly and adjust the restart period automatically. We demonstrate the effectiveness of our approach via numerical experiments.

Existing methods for interactive image retrieval have demonstrated the merit of integrating user feedback, improving retrieval results. However, most current systems rely on restricted forms of user feedback, such as binary relevance responses, or feedback based on a fixed set of relative attributes, which limits their impact. In this paper, we introduce a new approach to interactive image search that enables users to provide feedback via natural language, allowing for more natural and effective interaction. We formulate the task of dialog-based interactive image retrieval as a reinforcement learning problem, and reward the dialog system for improving the rank of the target image during each dialog turn. To mitigate the cumbersome and costly process of collecting human-machine conversations as the dialog system learns, we train our system with a user simulator, which is itself trained to describe the differences between target and candidate images. The efficacy of our approach is demonstrated in a footwear retrieval application. Experiments on both simulated and real-world data show that 1) our proposed learning framework achieves better accuracy than other supervised and reinforcement learning baselines and 2) user feedback based on natural language rather than pre-specified attributes leads to more effective retrieval results, and a more natural and expressive communication interface.

Non-local methods exploiting the self-similarity of natural signals have been well studied, for example in image analysis and restoration. Existing approaches, however, rely on k-nearest neighbors (KNN) matching in a fixed feature space. The main hurdle in optimizing this feature space w.r.t. application performance is the non-differentiability of the KNN selection rule. To overcome this, we propose a continuous deterministic relaxation of KNN selection that maintains differentiability w.r.t. pairwise distances, but retains the original KNN as the limit of a temperature parameter approaching zero. To exploit our relaxation, we propose the neural nearest neighbors block (N3 block), a novel non-local processing layer that leverages the principle of self-similarity and can be used as building block in modern neural network architectures. We show its effectiveness for the set reasoning task of correspondence classification as well as for image restoration, including image denoising and single image super-resolution, where we outperform strong convolutional neural network (CNN) baselines and recent non-local models that rely on KNN selection in hand-chosen features spaces.

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.

We describe a new software framework for fast training of generalized linear models. The framework, named Snap Machine Learning (Snap ML), combines recent advances in machine learning systems and algorithms in a nested manner to reflect the hierarchical architecture of modern computing systems. We prove theoretically that such a hierarchical system can accelerate training in distributed environments where intra-node communication is cheaper than inter-node communication. Additionally, we provide a review of the implementation of Snap ML in terms of GPU acceleration, pipelining, communication patterns and software architecture, highlighting aspects that were critical for achieving high performance. We evaluate the performance of Snap ML in both single-node and multi-node environments, quantifying the benefit of the hierarchical scheme and the data streaming functionality, and comparing with other widely-used machine learning software frameworks. Finally, we present a logistic regression benchmark on the Criteo Terabyte Click Logs dataset and show that Snap ML achieves the same test loss an order of magnitude faster than any of the previously reported results, including those obtained using TensorFlow and scikit-learn.

We present a formulation of deep learning that aims at producing a large margin classifier. The notion of \emc{margin}, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically successful results for both classification and regression tasks. However, most large margin algorithms are applicable only to shallow models with a preset feature representation; and conventional margin methods for neural networks only enforce margin at the output layer. Such methods are therefore not well suited for deep networks. In this work, we propose a novel loss function to impose a margin on any chosen set of layers of a deep network (including input and hidden layers). Our formulation allows choosing any $l_p$ norm ($p \geq 1$) on the metric measuring the margin. We demonstrate that the decision boundary obtained by our loss has nice properties compared to standard classification loss functions. Specifically, we show improved empirical results on the MNIST, CIFAR-10 and ImageNet datasets on multiple tasks: generalization from small training sets, corrupted labels, and robustness against adversarial perturbations. The resulting loss is general and complementary to existing data augmentation (such as random/adversarial input transform) and regularization techniques such as weight decay, dropout, and batch norm. \footnote{Code for the large margin loss function is released at \url{https://github.com/google-research/google-research/tree/master/large_margin}}

We propose a sparse and low-rank tensor regression model to relate a univariate outcome to a feature tensor, in which each unit-rank tensor from the CP decomposition of the coefficient tensor is assumed to be sparse. This structure is both parsimonious and highly interpretable, as it implies that the outcome is related to the features through a few distinct pathways, each of which may only involve subsets of feature dimensions. We take a divide-and-conquer strategy to simplify the task into a set of sparse unit-rank tensor regression problems. To make the computation efficient and scalable, for the unit-rank tensor regression, we propose a stagewise estimation procedure to efficiently trace out its entire solution path. We show that as the step size goes to zero, the stagewise solution paths converge exactly to those of the corresponding regularized regression. The superior performance of our approach is demonstrated on various real-world and synthetic examples.

In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating the conditional median. To address the challenge that both the input and output could be heavy-tailed, we propose a truncated minimization problem, and demonstrate that it enjoys an $O(\sqrt{d/n})$ excess risk, where $d$ is the dimensionality and $n$ is the number of samples. Compared with traditional work on $\ell_1$-regression, the main advantage of our result is that we achieve a high-probability risk bound without exponential moment conditions on the input and output. Furthermore, if the input is bounded, we show that the classical empirical risk minimization is competent for $\ell_1$-regression even when the output is heavy-tailed.