arXiv subjects

Gilles Gasso

Publications and source records attributed to Gilles Gasso.

34 records · Page 2Linked to original sources

arXiv2021

Theoretical Guarantees for Bridging Metric Measure Embedding and Optimal Transport

We propose a novel approach for comparing distributions whose supports do not necessarily lie on the same metric space. Unlike Gromov-Wasserstein (GW) distance which compares pairwise distances of elements from each distribution, we consider a method allowing to embed the metric measure spaces in a common Euclidean space and compute an optimal transport (OT) on the embedded distributions. This leads to what we call a sub-embedding robust Wasserstein (SERW) distance. Under some conditions, SERW is a distance that considers an OT distance of the (low-distorted) embedded distributions using a common metric. In addition to this novel proposal that generalizes several recent OT works, our contributions stand on several theoretical analyses: (i) we characterize the embedding spaces to define SERW distance for distribution alignment; (ii) we prove that SERW mimics almost the same properties of GW distance, and we give a cost relation between GW and SERW. The paper also provides some numerical illustrations of how SERW behaves on matching problems.

stat.ML↗

arXiv2020

Open Set Domain Adaptation using Optimal Transport

We present a 2-step optimal transport approach that performs a mapping from a source distribution to a target distribution. Here, the target has the particularity to present new classes not present in the source domain. The first step of the approach aims at rejecting the samples issued from these new classes using an optimal transport plan. The second step solves the target (class ratio) shift still as an optimal transport problem. We develop a dual approach to solve the optimization problem involved at each step and we prove that our results outperform recent state-of-the-art performances. We further apply the approach to the setting where the source and target distributions present both a label-shift and an increasing covariate (features) shift to show its robustness.

cs.LG↗

arXiv2020

Foreground-Background Ambient Sound Scene Separation

Ambient sound scenes typically comprise multiple short events occurring on top of a somewhat stationary background. We consider the task of separating these events from the background, which we call foreground-background ambient sound scene separation. We propose a deep learning-based separation framework with a suitable feature normaliza-tion scheme and an optional auxiliary network capturing the background statistics, and we investigate its ability to handle the great variety of sound classes encountered in ambient sound scenes, which have often not been seen in training. To do so, we create single-channel foreground-background mixtures using isolated sounds from the DESED and Audioset datasets, and we conduct extensive experiments with mixtures of seen or unseen sound classes at various signal-to-noise ratios. Our experimental findings demonstrate the generalization ability of the proposed approach.

eess.AS↗

arXiv2020

Partial Optimal Transport with Applications on Positive-Unlabeled Learning

Classical optimal transport problem seeks a transportation map that preserves the total mass betwenn two probability distributions, requiring their mass to be the same. This may be too restrictive in certain applications such as color or shape matching, since the distributions may have arbitrary masses and/or that only a fraction of the total mass has to be transported. Several algorithms have been devised for computing partial Wasserstein metrics that rely on an entropic regularization, but when it comes with exact solutions, almost no partial formulation of neither Wasserstein nor Gromov-Wasserstein are available yet. This precludes from working with distributions that do not lie in the same metric space or when invariance to rotation or translation is needed. In this paper, we address the partial Wasserstein and Gromov-Wasserstein problems and propose exact algorithms to solve them. We showcase the new formulation in a positive-unlabeled (PU) learning application. To the best of our knowledge, this is the first application of optimal transport in this context and we first highlight that partial Wasserstein-based metrics prove effective in usual PU learning settings. We then demonstrate that partial Gromov-Wasserstein metrics is efficient in scenario where point clouds come from different domains or have different features.

stat.ML↗

arXiv2020

Pixel-wise Conditioned Generative Adversarial Networks for Image Synthesis and Completion

Generative Adversarial Networks (GANs) have proven successful for unsupervised image generation. Several works have extended GANs to image inpainting by conditioning the generation with parts of the image to be reconstructed. Despite their success, these methods have limitations in settings where only a small subset of the image pixels is known beforehand. In this paper we investigate the effectiveness of conditioning GANs when very few pixel values are provided. We propose a modelling framework which results in adding an explicit cost term to the GAN objective function to enforce pixel-wise conditioning. We investigate the influence of this regularization term on the quality of the generated images and the fulfillment of the given pixel constraints. Using the recent PacGAN technique, we ensure that we keep diversity in the generated samples. Conducted experiments on FashionMNIST show that the regularization term effectively controls the trade-off between quality of the generated images and the conditioning. Experimental evaluation on the CIFAR-10 and CelebA datasets evidences that our method achieves accurate results both visually and quantitatively in term of Fréchet Inception Distance, while still enforcing the pixel conditioning. We also evaluate our method on a texture image generation task using fully-convolutional networks. As a final contribution, we apply the method to a classical geological simulation application.

eess.IV↗

arXiv2020

Screening Sinkhorn Algorithm for Regularized Optimal Transport

We introduce in this paper a novel strategy for efficiently approximating the Sinkhorn distance between two discrete measures. After identifying neglectable components of the dual solution of the regularized Sinkhorn problem, we propose to screen those components by directly setting them at that value before entering the Sinkhorn problem. This allows us to solve a smaller Sinkhorn problem while ensuring approximation with provable guarantees. More formally, the approach is based on a new formulation of dual of Sinkhorn divergence problem and on the KKT optimality conditions of this problem, which enable identification of dual components to be screened. This new analysis leads to the Screenkhorn algorithm. We illustrate the efficiency of Screenkhorn on complex tasks such as dimensionality reduction and domain adaptation involving regularized optimal transport.

stat.ML↗

arXiv2019

Pixel-wise Conditioning of Generative Adversarial Networks

Generative Adversarial Networks (GANs) have proven successful for unsupervised image generation. Several works extended GANs to image inpainting by conditioning the generation with parts of the image one wants to reconstruct. However, these methods have limitations in settings where only a small subset of the image pixels is known beforehand. In this paper, we study the effectiveness of conditioning GANs by adding an explicit regularization term to enforce pixel-wise conditions when very few pixel values are provided. In addition, we also investigate the influence of this regularization term on the quality of the generated images and the satisfaction of the conditions. Conducted experiments on MNIST and FashionMNIST show evidence that this regularization term allows for controlling the trade-off between quality of the generated images and constraint satisfaction.

cs.CV↗

arXiv2019

Gradient-based deterministic inversion of geophysical data with Generative Adversarial Networks: is it feasible?

Global probabilistic inversion within the latent space learned by a Generative Adversarial Network (GAN) has been recently demonstrated. Compared to inversion on the original model space, using the latent space of a trained GAN can offer the following benefits: (1) the generated model proposals are geostatistically consistent with the prescribed prior training image (TI), and (2) the parameter space is reduced by orders of magnitude compared to the original model space. Nevertheless, exploring the learned latent space by state-of-the-art Markov chain Monte Carlo (MCMC) methods may still require a large computational effort. As an alternative, parameters in this latent space could possibly be optimized with much less computationally expensive gradient-based methods. We show that due to the typically highly nonlinear relationship between the latent space and the associated output space of a GAN, gradient-based deterministic inversion may fail even when considering a linear forward physical model. We tested two deterministic inversion approaches: a quasi-Newton gradient descent using the Adam algorithm and a Gauss-Newton (GN) method that makes use of the Jacobian matrix calculated by finite-differencing. For a channelized binary TI and a synthetic linear crosshole ground penetrating radar (GPR) tomography problem involving 576 measurements with low noise, we observe that when allowing for a total of 10,000 iterations only 13% of the gradient descent trials locate a solution that has the required data misfit. The tested GN inversion was unable to recover a solution with the appropriate data misfit. Our results suggest that deterministic inversion performance strongly depends on the inversion approach, starting model, true reference model, number of iterations and noise realization. In contrast, computationally-expensive probabilistic global optimization always finds an appropriate solution.

physics.geo-ph↗

arXiv2019

Dilated Spatial Generative Adversarial Networks for Ergodic Image Generation

Generative models have recently received renewed attention as a result of adversarial learning. Generative adversarial networks consist of samples generation model and a discrimination model able to distinguish between genuine and synthetic samples. In combination with convolutional (for the discriminator) and de-convolutional (for the generator) layers, they are particularly suitable for image generation, especially of natural scenes. However, the presence of fully connected layers adds global dependencies in the generated images. This may lead to high and global variations in the generated sample for small local variations in the input noise. In this work we propose to use architec-tures based on fully convolutional networks (including among others dilated layers), architectures specifically designed to generate globally ergodic images, that is images without global dependencies. Conducted experiments reveal that these architectures are well suited for generating natural textures such as geologic structures .

cs.CV↗

arXiv2019

Fast object detection in compressed JPEG Images

Object detection in still images has drawn a lot of attention over past few years, and with the advent of Deep Learning impressive performances have been achieved with numerous industrial applications. Most of these deep learning models rely on RGB images to localize and identify objects in the image. However in some application scenarii, images are compressed either for storage savings or fast transmission. Therefore a time consuming image decompression step is compulsory in order to apply the aforementioned deep models. To alleviate this drawback, we propose a fast deep architecture for object detection in JPEG images, one of the most widespread compression format. We train a neural network to detect objects based on the blockwise DCT (discrete cosine transform) coefficients {issued from} the JPEG compression algorithm. We modify the well-known Single Shot multibox Detector (SSD) by replacing its first layers with one convolutional layer dedicated to process the DCT inputs. Experimental evaluations on PASCAL VOC and industrial dataset comprising images of road traffic surveillance show that the model is about $2\times$ faster than regular SSD with promising detection performances. To the best of our knowledge, this paper is the first to address detection in compressed JPEG images.

cs.CV↗

arXiv2019

Screening Rules for Lasso with Non-Convex Sparse Regularizers

Leveraging on the convexity of the Lasso problem , screening rules help in accelerating solvers by discarding irrelevant variables, during the optimization process. However, because they provide better theoretical guarantees in identifying relevant variables, several non-convex regularizers for the Lasso have been proposed in the literature. This work is the first that introduces a screening rule strategy into a non-convex Lasso solver. The approach we propose is based on a iterative majorization-minimization (MM) strategy that includes a screening rule in the inner solver and a condition for propagating screened variables between iterations of MM. In addition to improve efficiency of solvers, we also provide guarantees that the inner solver is able to identify the zeros components of its critical point in finite time. Our experimental analysis illustrates the significant computational gain brought by the new screening rule compared to classical coordinate-descent or proximal gradient descent methods.

cs.LG↗

arXiv2018

An efficient supervised dictionary learning method for audio signal recognition

Machine hearing or listening represents an emerging area. Conventional approaches rely on the design of handcrafted features specialized to a specific audio task and that can hardly generalized to other audio fields. For example, Mel-Frequency Cepstral Coefficients (MFCCs) and its variants were successfully applied to computational auditory scene recognition while Chroma vectors are good at music chord recognition. Unfortunately, these predefined features may be of variable discrimination power while extended to other tasks or even within the same task due to different nature of clips. Motivated by this need of a principled framework across domain applications for machine listening, we propose a generic and data-driven representation learning approach. For this sake, a novel and efficient supervised dictionary learning method is presented. The method learns dissimilar dictionaries, one per each class, in order to extract heterogeneous information for classification. In other words, we are seeking to minimize the intra-class homogeneity and maximize class separability. This is made possible by promoting pairwise orthogonality between class specific dictionaries and controlling the sparsity structure of the audio clip's decomposition over these dictionaries. The resulting optimization problem is non-convex and solved using a proximal gradient descent method. Experiments are performed on both computational auditory scene (East Anglia and Rouen) and synthetic music chord recognition datasets. Obtained results show that our method is capable to reach state-of-the-art hand-crafted features for both applications.

cs.CV↗

arXiv2016

Importance sampling strategy for non-convex randomized block-coordinate descent

As the number of samples and dimensionality of optimization problems related to statistics an machine learning explode, block coordinate descent algorithms have gained popularity since they reduce the original problem to several smaller ones. Coordinates to be optimized are usually selected randomly according to a given probability distribution. We introduce an importance sampling strategy that helps randomized coordinate descent algorithms to focus on blocks that are still far from convergence. The framework applies to problems composed of the sum of two possibly non-convex terms, one being separable and non-smooth. We have compared our algorithm to a full gradient proximal approach as well as to a randomized block coordinate algorithm that considers uniform sampling and cyclic block coordinate descent. Experimental evidences show the clear benefit of using an importance sampling strategy.

cs.LG↗

arXiv2015

Histogram of gradients of Time-Frequency Representations for Audio scene detection

This paper addresses the problem of audio scenes classification and contributes to the state of the art by proposing a novel feature. We build this feature by considering histogram of gradients (HOG) of time-frequency representation of an audio scene. Contrarily to classical audio features like MFCC, we make the hypothesis that histogram of gradients are able to encode some relevant informations in a time-frequency {representation:} namely, the local direction of variation (in time and frequency) of the signal spectral power. In addition, in order to gain more invariance and robustness, histogram of gradients are locally pooled. We have evaluated the relevance of {the novel feature} by comparing its performances with state-of-the-art competitors, on several datasets, including a novel one that we provide, as part of our contribution. This dataset, that we make publicly available, involves $19$ classes and contains about $900$ minutes of audio scene recording. We thus believe that it may be the next standard dataset for evaluating audio scene classification algorithms. Our comparison results clearly show that our HOG-based features outperform its competitors

cs.SD↗

arXiv2015

DC Proximal Newton for Non-Convex Optimization Problems

We introduce a novel algorithm for solving learning problems where both the loss function and the regularizer are non-convex but belong to the class of difference of convex (DC) functions. Our contribution is a new general purpose proximal Newton algorithm that is able to deal with such a situation. The algorithm consists in obtaining a descent direction from an approximation of the loss function and then in performing a line search to ensure sufficient descent. A theoretical analysis is provided showing that the iterates of the proposed algorithm {admit} as limit points stationary points of the DC objective function. Numerical experiments show that our approach is more efficient than current state of the art for a problem with a convex loss functions and non-convex regularizer. We have also illustrated the benefit of our algorithm in high-dimensional transductive learning problem where both loss function and regularizers are non-convex.

cs.LG↗

arXiv2012

Adaptive Canonical Correlation Analysis Based On Matrix Manifolds

In this paper, we formulate the Canonical Correlation Analysis (CCA) problem on matrix manifolds. This framework provides a natural way for dealing with matrix constraints and tools for building efficient algorithms even in an adaptive setting. Finally, an adaptive CCA algorithm is proposed and applied to a change detection problem in EEG signals.

cs.LG↗