Leonardo Rey Vega

Lautaro Estienne, Matias Vera, Leonardo Rey Vega

Sentiment Classification is a fundamental task in the field of Natural Language Processing, and has very important academic and commercial applications. It aims to automatically predict the degree of sentiment present in a text that contains opinions and subjectivity at some level, like product and movie reviews, or tweets. This can be really difficult to accomplish, in part, because different domains of text contains different words and expressions. In addition, this difficulty increases when text is written in a non-English language due to the lack of databases and resources. As a consequence, several cross-domain and cross-language techniques are often applied to this task in order to improve the results. In this work we perform a study on the ability of a classification system trained with a large database of product reviews to generalize to different Spanish domains. Reviews were collected from the MercadoLibre website from seven Latin American countries, allowing the creation of a large and balanced dataset. Results suggest that generalization across domains is feasible though very challenging when trained with these product reviews, and can be improved by pre-training and fine-tuning the classification model.

Georg Pichler, Marco Romanelli, Leonardo Rey Vega et al.

Federated Learning is expected to provide strong privacy guarantees, as only gradients or model parameters but no plain text training data is ever exchanged either between the clients or between the clients and the central server. In this paper, we challenge this claim by introducing a simple but still very effective membership inference attack algorithm, which relies only on a single training step. In contrast to the popular honest-but-curious model, we investigate a framework with a dishonest central server. Our strategy is applicable to models with ReLU activations and uses the properties of this activation function to achieve perfect accuracy. Empirical evaluation on visual classification tasks with MNIST, CIFAR10, CIFAR100 and CelebA datasets show that our method provides perfect accuracy in identifying one sample in a training set with thousands of samples. Occasional failures of our method lead us to discover duplicate images in the CIFAR100 and CelebA datasets.

Matias Vera, Leonardo Rey Vega, Pablo Piantanida

The ultimate performance of machine learning algorithms for classification tasks is usually measured in terms of the empirical error probability (or accuracy) based on a testing dataset. Whereas, these algorithms are optimized through the minimization of a typically different--more convenient--loss function based on a training set. For classification tasks, this loss function is often the negative log-loss that leads to the well-known cross-entropy risk which is typically better behaved (from a numerical perspective) than the error probability. Conventional studies on the generalization error do not usually take into account the underlying mismatch between losses at training and testing phases. In this work, we introduce an analysis based on point-wise PAC approach over the generalization gap considering the mismatch of testing based on the accuracy metric and training on the negative log-loss. We label this analysis PACMAN. Building on the fact that the mentioned mismatch can be written as a likelihood ratio, concentration inequalities can be used to provide some insights for the generalization problem in terms of some point-wise PAC bounds depending on some meaningful information-theoretic quantities. An analysis of the obtained bounds and a comparison with available results in the literature are also provided.

Matias Vera, Leonardo Rey Vega, Pablo Piantanida

Overfitting data is a well-known phenomenon related with the generation of a model that mimics too closely (or exactly) a particular instance of data, and may therefore fail to predict future observations reliably. In practice, this behaviour is controlled by various--sometimes heuristics--regularization techniques, which are motivated by developing upper bounds to the generalization error. In this work, we study the generalization error of classifiers relying on stochastic encodings trained on the cross-entropy loss, which is often used in deep learning for classification problems. We derive bounds to the generalization error showing that there exists a regime where the generalization error is bounded by the mutual information between input features and the corresponding representations in the latent space, which are randomly generated according to the encoding distribution. Our bounds provide an information-theoretic understanding of generalization in the so-called class of variational classifiers, which are regularized by a Kullback-Leibler (KL) divergence term. These results give theoretical grounds for the highly popular KL term in variational inference methods that was already recognized to act effectively as a regularization penalty. We further observe connections with well studied notions such as Variational Autoencoders, Information Dropout, Information Bottleneck and Boltzmann Machines. Finally, we perform numerical experiments on MNIST and CIFAR datasets and show that mutual information is indeed highly representative of the behaviour of the generalization error.

Matias Vera, Pablo Piantanida, Leonardo Rey Vega

Machine learning theory has mostly focused on generalization to samples from the same distribution as the training data. Whereas a better understanding of generalization beyond the training distribution where the observed distribution changes is also fundamentally important to achieve a more powerful form of generalization. In this paper, we attempt to study through the lens of information measures how a particular architecture behaves when the true probability law of the samples is potentially different at training and testing times. Our main result is that the testing gap between the empirical cross-entropy and its statistical expectation (measured with respect to the testing probability law) can be bounded with high probability by the mutual information between the input testing samples and the corresponding representations, generated by the encoder obtained at training time. These results of theoretical nature are supported by numerical simulations showing that the mentioned mutual information is representative of the testing gap, capturing qualitatively the dynamic in terms of the hyperparameters of the network.

Matías Vera, Pablo Piantanida, Leonardo Rey Vega

A grand challenge in representation learning is to learn the different explanatory factors of variation behind the high dimen- sional data. Encoder models are often determined to optimize performance on training data when the real objective is to generalize well to unseen data. Although there is enough numerical evidence suggesting that noise injection (during training) at the representation level might improve the generalization ability of encoders, an information-theoretic understanding of this principle remains elusive. This paper presents a sample-dependent bound on the generalization gap of the cross-entropy loss that scales with the information complexity (IC) of the representations, meaning the mutual information between inputs and their representations. The IC is empirically investigated for standard multi-layer neural networks with SGD on MNIST and CIFAR-10 datasets; the behaviour of the gap and the IC appear to be in direct correlation, suggesting that SGD selects encoders to implicitly minimize the IC. We specialize the IC to study the role of Dropout on the generalization capacity of deep encoders which is shown to be directly related to the encoder capacity, being a measure of the distinguishability among samples from their representations. Our results support some recent regularization methods.

Matías Vera, Leonardo Rey Vega, Pablo Piantanida

This paper investigates, from information theoretic grounds, a learning problem based on the principle that any regularity in a given dataset can be exploited to extract compact features from data, i.e., using fewer bits than needed to fully describe the data itself, in order to build meaningful representations of a relevant content (multiple labels). We begin by introducing the noisy lossy source coding paradigm with the log-loss fidelity criterion which provides the fundamental tradeoffs between the \emph{cross-entropy loss} (average risk) and the information rate of the features (model complexity). Our approach allows an information theoretic formulation of the \emph{multi-task learning} (MTL) problem which is a supervised learning framework in which the prediction models for several related tasks are learned jointly from common representations to achieve better generalization performance. Then, we present an iterative algorithm for computing the optimal tradeoffs and its global convergence is proven provided that some conditions hold. An important property of this algorithm is that it provides a natural safeguard against overfitting, because it minimizes the average risk taking into account a penalization induced by the model complexity. Remarkably, empirical results illustrate that there exists an optimal information rate minimizing the \emph{excess risk} which depends on the nature and the amount of available training data. An application to hierarchical text categorization is also investigated, extending previous works.

Matías Vera, Leonardo Rey Vega, Pablo Piantanida

This paper investigates a multi-terminal source coding problem under a logarithmic loss fidelity which does not necessarily lead to an additive distortion measure. The problem is motivated by an extension of the Information Bottleneck method to a multi-source scenario where several encoders have to build cooperatively rate-limited descriptions of their sources in order to maximize information with respect to other unobserved (hidden) sources. More precisely, we study fundamental information-theoretic limits of the so-called: (i) Two-way Collaborative Information Bottleneck (TW-CIB) and (ii) the Collaborative Distributed Information Bottleneck (CDIB) problems. The TW-CIB problem consists of two distant encoders that separately observe marginal (dependent) components $X_1$ and $X_2$ and can cooperate through multiple exchanges of limited information with the aim of extracting information about hidden variables $(Y_1,Y_2)$, which can be arbitrarily dependent on $(X_1,X_2)$. On the other hand, in CDIB there are two cooperating encoders which separately observe $X_1$ and $X_2$ and a third node which can listen to the exchanges between the two encoders in order to obtain information about a hidden variable $Y$. The relevance (figure-of-merit) is measured in terms of a normalized (per-sample) multi-letter mutual information metric (log-loss fidelity) and an interesting tradeoff arises by constraining the complexity of descriptions, measured in terms of the rates needed for the exchanges between the encoders and decoders involved. Inner and outer bounds to the complexity-relevance region of these problems are derived from which optimality is characterized for several cases of interest. Our resulting theoretical complexity-relevance regions are finally evaluated for binary symmetric and Gaussian statistical models.