Pierre Jacob

Kimia Nadjahi, Alain Durmus, Pierre E. Jacob et al.

The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits. Since it is defined as an expectation over random projections, SW is commonly approximated by Monte Carlo. We adopt a new perspective to approximate SW by making use of the concentration of measure phenomenon: under mild assumptions, one-dimensional projections of a high-dimensional random vector are approximately Gaussian. Based on this observation, we develop a simple deterministic approximation for SW. Our method does not require sampling a number of random projections, and is therefore both accurate and easy to use compared to the usual Monte Carlo approximation. We derive nonasymptotical guarantees for our approach, and show that the approximation error goes to zero as the dimension increases, under a weak dependence condition on the data distribution. We validate our theoretical findings on synthetic datasets, and illustrate the proposed approximation on a generative modeling problem.

Pierre Jacob, David Picard, Aymeric Histace et al.

In deep metric learning, the training procedure relies on sampling informative tuples. However, as the training procedure progresses, it becomes nearly impossible to sample relevant hard negative examples without proper mining strategies or generation-based methods. Recent work on hard negative generation have shown great promises to solve the mining problem. However, this generation process is difficult to tune and often leads to incorrectly labelled examples. To tackle this issue, we introduce MIRAGE, a generation-based method that relies on virtual classes entirely composed of generated examples that act as buffer areas between the training classes. We empirically show that virtual classes significantly improve the results on popular datasets (Cub-200-2011, Cars-196 and Stanford Online Products) compared to other generation methods.

Pierre Jacob, David Picard, Aymeric Histace et al.

Recent breakthroughs in representation learning of unseen classes and examples have been made in deep metric learning by training at the same time the image representations and a corresponding metric with deep networks. Recent contributions mostly address the training part (loss functions, sampling strategies, etc.), while a few works focus on improving the discriminative power of the image representation. In this paper, we propose DIABLO, a dictionary-based attention method for image embedding. DIABLO produces richer representations by aggregating only visually-related features together while being easier to train than other attention-based methods in deep metric learning. This is experimentally confirmed on four deep metric learning datasets (Cub-200-2011, Cars-196, Stanford Online Products, and In-Shop Clothes Retrieval) for which DIABLO shows state-of-the-art performances.

Espen Bernton, Jeremy Heng, Arnaud Doucet et al.

Consider a reference Markov process with initial distribution $π_{0}$ and transition kernels $\{M_{t}\}_{t\in[1:T]}$, for some $T\in\mathbb{N}$. Assume that you are given distribution $π_{T}$, which is not equal to the marginal distribution of the reference process at time $T$. In this scenario, Schrödinger addressed the problem of identifying the Markov process with initial distribution $π_{0}$ and terminal distribution equal to $π_{T}$ which is the closest to the reference process in terms of Kullback--Leibler divergence. This special case of the so-called Schrödinger bridge problem can be solved using iterative proportional fitting, also known as the Sinkhorn algorithm. We leverage these ideas to develop novel Monte Carlo schemes, termed Schrödinger bridge samplers, to approximate a target distribution $π$ on $\mathbb{R}^{d}$ and to estimate its normalizing constant. This is achieved by iteratively modifying the transition kernels of the reference Markov chain to obtain a process whose marginal distribution at time $T$ becomes closer to $π_T = π$, via regression-based approximations of the corresponding iterative proportional fitting recursion. We report preliminary experiments and make connections with other problems arising in the optimal transport, optimal control and physics literatures.

Pierre Jacob, David Picard, Aymeric Histace et al.

Learning an effective similarity measure between image representations is key to the success of recent advances in visual search tasks (e.g. verification or zero-shot learning). Although the metric learning part is well addressed, this metric is usually computed over the average of the extracted deep features. This representation is then trained to be discriminative. However, these deep features tend to be scattered across the feature space. Consequently, the representations are not robust to outliers, object occlusions, background variations, etc. In this paper, we tackle this scattering problem with a distribution-aware regularization named HORDE. This regularizer enforces visually-close images to have deep features with the same distribution which are well localized in the feature space. We provide a theoretical analysis supporting this regularization effect. We also show the effectiveness of our approach by obtaining state-of-the-art results on 4 well-known datasets (Cub-200-2011, Cars-196, Stanford Online Products and Inshop Clothes Retrieval).

Pierre Jacob, David Picard, Aymeric Histace et al.

Learning rich and compact representations is an open topic in many fields such as object recognition or image retrieval. Deep neural networks have made a major breakthrough during the last few years for these tasks but their representations are not necessary as rich as needed nor as compact as expected. To build richer representations, high order statistics have been exploited and have shown excellent performances, but they produce higher dimensional features. While this drawback has been partially addressed with factorization schemes, the original compactness of first order models has never been retrieved, or at the cost of a strong performance decrease. Our method, by jointly integrating codebook strategy to factorization scheme, is able to produce compact representations while keeping the second order performances with few additional parameters. This formulation leads to state-of-the-art results on three image retrieval datasets.

Lawrence Middleton, George Deligiannidis, Arnaud Doucet et al.

We consider the approximation of expectations with respect to the distribution of a latent Markov process given noisy measurements. This is known as the smoothing problem and is often approached with particle and Markov chain Monte Carlo (MCMC) methods. These methods provide consistent but biased estimators when run for a finite time. We propose a simple way of coupling two MCMC chains built using Particle Independent Metropolis-Hastings (PIMH) to produce unbiased smoothing estimators. Unbiased estimators are appealing in the context of parallel computing, and facilitate the construction of confidence intervals. The proposed scheme only requires access to off-the-shelf Particle Filters (PF) and is thus easier to implement than recently proposed unbiased smoothers. The approach is demonstrated on a Lévy-driven stochastic volatility model and a stochastic kinetic model.

Alexander Lin, Yingzhuo Zhang, Jeremy Heng et al.

We propose a general statistical framework for clustering multiple time series that exhibit nonlinear dynamics into an a-priori-unknown number of sub-groups. Our motivation comes from neuroscience, where an important problem is to identify, within a large assembly of neurons, subsets that respond similarly to a stimulus or contingency. Upon modeling the multiple time series as the output of a Dirichlet process mixture of nonlinear state-space models, we derive a Metropolis-within-Gibbs algorithm for full Bayesian inference that alternates between sampling cluster assignments and sampling parameter values that form the basis of the clustering. The Metropolis step employs recent innovations in particle-based methods. We apply the framework to clustering time series acquired from the prefrontal cortex of mice in an experiment designed to characterize the neural underpinnings of fear.

Pierre Jacob, David Picard, Aymeric Histace et al.

Most image retrieval methods use global features that aggregate local distinctive patterns into a single representation. However, the aggregation process destroys the relative spatial information by considering orderless sets of local descriptors. We propose to integrate relative spatial information into the aggregation process by taking into account co-occurrences of local patterns in a tensor framework. The resulting signature called Improved Spatial Tensor Aggregation (ISTA) is able to reach state of the art performances on well known datasets such as Holidays, Oxford5k and Paris6k.