arXiv subjects

Simon Lacoste-Julien

Publications and source records attributed to Simon Lacoste-Julien.

At least 91 records · Page 5Linked to original sources

arXiv2019

Quantifying Learning Guarantees for Convex but Inconsistent Surrogates

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.

cs.LG↗

arXiv2018

Scattering Networks for Hybrid Representation Learning

Scattering networks are a class of designed Convolutional Neural Networks (CNNs) with fixed weights. We argue they can serve as generic representations for modelling images. In particular, by working in scattering space, we achieve competitive results both for supervised and unsupervised learning tasks, while making progress towards constructing more interpretable CNNs. For supervised learning, we demonstrate that the early layers of CNNs do not necessarily need to be learned, and can be replaced with a scattering network instead. Indeed, using hybrid architectures, we achieve the best results with predefined representations to-date, while being competitive with end-to-end learned CNNs. Specifically, even applying a shallow cascade of small-windowed scattering coefficients followed by 1$\times$1-convolutions results in AlexNet accuracy on the ILSVRC2012 classification task. Moreover, by combining scattering networks with deep residual networks, we achieve a single-crop top-5 error of 11.4% on ILSVRC2012. Also, we show they can yield excellent performance in the small sample regime on CIFAR-10 and STL-10 datasets, exceeding their end-to-end counterparts, through their ability to incorporate geometrical priors. For unsupervised learning, scattering coefficients can be a competitive representation that permits image recovery. We use this fact to train hybrid GANs to generate images. Finally, we empirically analyze several properties related to stability and reconstruction of images from scattering coefficients.

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arXiv2018

Adaptive Stochastic Dual Coordinate Ascent for Conditional Random Fields

This work investigates the training of conditional random fields (CRFs) via the stochastic dual coordinate ascent (SDCA) algorithm of Shalev-Shwartz and Zhang (2016). SDCA enjoys a linear convergence rate and a strong empirical performance for binary classification problems. However, it has never been used to train CRFs. Yet it benefits from an `exact' line search with a single marginalization oracle call, unlike previous approaches. In this paper, we adapt SDCA to train CRFs, and we enhance it with an adaptive non-uniform sampling strategy based on block duality gaps. We perform experiments on four standard sequence prediction tasks. SDCA demonstrates performances on par with the state of the art, and improves over it on three of the four datasets, which have in common the use of sparse features.

stat.ML↗

arXiv2018

Frank-Wolfe Splitting via Augmented Lagrangian Method

Minimizing a function over an intersection of convex sets is an important task in optimization that is often much more challenging than minimizing it over each individual constraint set. While traditional methods such as Frank-Wolfe (FW) or proximal gradient descent assume access to a linear or quadratic oracle on the intersection, splitting techniques take advantage of the structure of each sets, and only require access to the oracle on the individual constraints. In this work, we develop and analyze the Frank-Wolfe Augmented Lagrangian (FW-AL) algorithm, a method for minimizing a smooth function over convex compact sets related by a "linear consistency" constraint that only requires access to a linear minimization oracle over the individual constraints. It is based on the Augmented Lagrangian Method (ALM), also known as Method of Multipliers, but unlike most existing splitting methods, it only requires access to linear (instead of quadratic) minimization oracles. We use recent advances in the analysis of Frank-Wolfe and the alternating direction method of multipliers algorithms to prove a sublinear convergence rate for FW-AL over general convex compact sets and a linear convergence rate for polytopes.

math.OC↗

arXiv2018

SEARNN: Training RNNs with Global-Local Losses

We propose SEARNN, a novel training algorithm for recurrent neural networks (RNNs) inspired by the "learning to search" (L2S) approach to structured prediction. RNNs have been widely successful in structured prediction applications such as machine translation or parsing, and are commonly trained using maximum likelihood estimation (MLE). Unfortunately, this training loss is not always an appropriate surrogate for the test error: by only maximizing the ground truth probability, it fails to exploit the wealth of information offered by structured losses. Further, it introduces discrepancies between training and predicting (such as exposure bias) that may hurt test performance. Instead, SEARNN leverages test-alike search space exploration to introduce global-local losses that are closer to the test error. We first demonstrate improved performance over MLE on two different tasks: OCR and spelling correction. Then, we propose a subsampling strategy to enable SEARNN to scale to large vocabulary sizes. This allows us to validate the benefits of our approach on a machine translation task.

cs.LG↗

arXiv2018

On Structured Prediction Theory with Calibrated Convex Surrogate Losses

We provide novel theoretical insights on structured prediction in the context of efficient convex surrogate loss minimization with consistency guarantees. For any task loss, we construct a convex surrogate that can be optimized via stochastic gradient descent and we prove tight bounds on the so-called "calibration function" relating the excess surrogate risk to the actual risk. In contrast to prior related work, we carefully monitor the effect of the exponential number of classes in the learning guarantees as well as on the optimization complexity. As an interesting consequence, we formalize the intuition that some task losses make learning harder than others, and that the classical 0-1 loss is ill-suited for general structured prediction.

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arXiv2018

A3T: Adversarially Augmented Adversarial Training

Recent research showed that deep neural networks are highly sensitive to so-called adversarial perturbations, which are tiny perturbations of the input data purposely designed to fool a machine learning classifier. Most classification models, including deep learning models, are highly vulnerable to adversarial attacks. In this work, we investigate a procedure to improve adversarial robustness of deep neural networks through enforcing representation invariance. The idea is to train the classifier jointly with a discriminator attached to one of its hidden layer and trained to filter the adversarial noise. We perform preliminary experiments to test the viability of the approach and to compare it to other standard adversarial training methods.

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arXiv2017

ASAGA: Asynchronous Parallel SAGA

We describe ASAGA, an asynchronous parallel version of the incremental gradient algorithm SAGA that enjoys fast linear convergence rates. Through a novel perspective, we revisit and clarify a subtle but important technical issue present in a large fraction of the recent convergence rate proofs for asynchronous parallel optimization algorithms, and propose a simplification of the recently introduced "perturbed iterate" framework that resolves it. We thereby prove that ASAGA can obtain a theoretical linear speedup on multi-core systems even without sparsity assumptions. We present results of an implementation on a 40-core architecture illustrating the practical speedup as well as the hardware overhead.

math.OC↗

arXiv2017

Breaking the Nonsmooth Barrier: A Scalable Parallel Method for Composite Optimization

Due to their simplicity and excellent performance, parallel asynchronous variants of stochastic gradient descent have become popular methods to solve a wide range of large-scale optimization problems on multi-core architectures. Yet, despite their practical success, support for nonsmooth objectives is still lacking, making them unsuitable for many problems of interest in machine learning, such as the Lasso, group Lasso or empirical risk minimization with convex constraints. In this work, we propose and analyze ProxASAGA, a fully asynchronous sparse method inspired by SAGA, a variance reduced incremental gradient algorithm. The proposed method is easy to implement and significantly outperforms the state of the art on several nonsmooth, large-scale problems. We prove that our method achieves a theoretical linear speedup with respect to the sequential version under assumptions on the sparsity of gradients and block-separability of the proximal term. Empirical benchmarks on a multi-core architecture illustrate practical speedups of up to 12x on a 20-core machine.

math.OC↗

arXiv2017

Joint Discovery of Object States and Manipulation Actions

Many human activities involve object manipulations aiming to modify the object state. Examples of common state changes include full/empty bottle, open/closed door, and attached/detached car wheel. In this work, we seek to automatically discover the states of objects and the associated manipulation actions. Given a set of videos for a particular task, we propose a joint model that learns to identify object states and to localize state-modifying actions. Our model is formulated as a discriminative clustering cost with constraints. We assume a consistent temporal order for the changes in object states and manipulation actions, and introduce new optimization techniques to learn model parameters without additional supervision. We demonstrate successful discovery of seven manipulation actions and corresponding object states on a new dataset of videos depicting real-life object manipulations. We show that our joint formulation results in an improvement of object state discovery by action recognition and vice versa.

cs.CV↗

arXiv2017

A Closer Look at Memorization in Deep Networks

We examine the role of memorization in deep learning, drawing connections to capacity, generalization, and adversarial robustness. While deep networks are capable of memorizing noise data, our results suggest that they tend to prioritize learning simple patterns first. In our experiments, we expose qualitative differences in gradient-based optimization of deep neural networks (DNNs) on noise vs. real data. We also demonstrate that for appropriately tuned explicit regularization (e.g., dropout) we can degrade DNN training performance on noise datasets without compromising generalization on real data. Our analysis suggests that the notions of effective capacity which are dataset independent are unlikely to explain the generalization performance of deep networks when trained with gradient based methods because training data itself plays an important role in determining the degree of memorization.

stat.ML↗

arXiv2017

Frank-Wolfe Algorithms for Saddle Point Problems

We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained smooth convex-concave saddle point (SP) problems. Remarkably, the method only requires access to linear minimization oracles. Leveraging recent advances in FW optimization, we provide the first proof of convergence of a FW-type saddle point solver over polytopes, thereby partially answering a 30 year-old conjecture. We also survey other convergence results and highlight gaps in the theoretical underpinnings of FW-style algorithms. Motivating applications without known efficient alternatives are explored through structured prediction with combinatorial penalties as well as games over matching polytopes involving an exponential number of constraints.

math.OC↗

arXiv2017

PAC-Bayesian Theory Meets Bayesian Inference

We exhibit a strong link between frequentist PAC-Bayesian risk bounds and the Bayesian marginal likelihood. That is, for the negative log-likelihood loss function, we show that the minimization of PAC-Bayesian generalization risk bounds maximizes the Bayesian marginal likelihood. This provides an alternative explanation to the Bayesian Occam's razor criteria, under the assumption that the data is generated by an i.i.d distribution. Moreover, as the negative log-likelihood is an unbounded loss function, we motivate and propose a PAC-Bayesian theorem tailored for the sub-gamma loss family, and we show that our approach is sound on classical Bayesian linear regression tasks.

stat.ML↗

arXiv2016

Convergence Rate of Frank-Wolfe for Non-Convex Objectives

We give a simple proof that the Frank-Wolfe algorithm obtains a stationary point at a rate of $O(1/\sqrt{t})$ on non-convex objectives with a Lipschitz continuous gradient. Our analysis is affine invariant and is the first, to the best of our knowledge, giving a similar rate to what was already proven for projected gradient methods (though on slightly different measures of stationarity).

math.OC↗

arXiv2016

Unsupervised Learning from Narrated Instruction Videos

We address the problem of automatically learning the main steps to complete a certain task, such as changing a car tire, from a set of narrated instruction videos. The contributions of this paper are three-fold. First, we develop a new unsupervised learning approach that takes advantage of the complementary nature of the input video and the associated narration. The method solves two clustering problems, one in text and one in video, applied one after each other and linked by joint constraints to obtain a single coherent sequence of steps in both modalities. Second, we collect and annotate a new challenging dataset of real-world instruction videos from the Internet. The dataset contains about 800,000 frames for five different tasks that include complex interactions between people and objects, and are captured in a variety of indoor and outdoor settings. Third, we experimentally demonstrate that the proposed method can automatically discover, in an unsupervised manner, the main steps to achieve the task and locate the steps in the input videos.

cs.CV↗

arXiv2016

Beyond CCA: Moment Matching for Multi-View Models

We introduce three novel semi-parametric extensions of probabilistic canonical correlation analysis with identifiability guarantees. We consider moment matching techniques for estimation in these models. For that, by drawing explicit links between the new models and a discrete version of independent component analysis (DICA), we first extend the DICA cumulant tensors to the new discrete version of CCA. By further using a close connection with independent component analysis, we introduce generalized covariance matrices, which can replace the cumulant tensors in the moment matching framework, and, therefore, improve sample complexity and simplify derivations and algorithms significantly. As the tensor power method or orthogonal joint diagonalization are not applicable in the new setting, we use non-orthogonal joint diagonalization techniques for matching the cumulants. We demonstrate performance of the proposed models and estimation techniques on experiments with both synthetic and real datasets.

stat.ML↗

arXiv2016

Minding the Gaps for Block Frank-Wolfe Optimization of Structured SVMs

In this paper, we propose several improvements on the block-coordinate Frank-Wolfe (BCFW) algorithm from Lacoste-Julien et al. (2013) recently used to optimize the structured support vector machine (SSVM) objective in the context of structured prediction, though it has wider applications. The key intuition behind our improvements is that the estimates of block gaps maintained by BCFW reveal the block suboptimality that can be used as an adaptive criterion. First, we sample objects at each iteration of BCFW in an adaptive non-uniform way via gapbased sampling. Second, we incorporate pairwise and away-step variants of Frank-Wolfe into the block-coordinate setting. Third, we cache oracle calls with a cache-hit criterion based on the block gaps. Fourth, we provide the first method to compute an approximate regularization path for SSVM. Finally, we provide an exhaustive empirical evaluation of all our methods on four structured prediction datasets.

cs.LG↗

arXiv2016

Variance Reduced Stochastic Gradient Descent with Neighbors

Stochastic Gradient Descent (SGD) is a workhorse in machine learning, yet its slow convergence can be a computational bottleneck. Variance reduction techniques such as SAG, SVRG and SAGA have been proposed to overcome this weakness, achieving linear convergence. However, these methods are either based on computations of full gradients at pivot points, or on keeping per data point corrections in memory. Therefore speed-ups relative to SGD may need a minimal number of epochs in order to materialize. This paper investigates algorithms that can exploit neighborhood structure in the training data to share and re-use information about past stochastic gradients across data points, which offers advantages in the transient optimization phase. As a side-product we provide a unified convergence analysis for a family of variance reduction algorithms, which we call memorization algorithms. We provide experimental results supporting our theory.

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