Scientific Publications

Abstract: Equivariant neural networks have shown improved performance, expressiveness and sample complexity on symmetrical domains. But for some specific symmetries, representations, and choice of coordinates, the most common point-wise activations, such as ReLU, are not equivariant, hence they cannot be employed in the design of equivariant neural networks. The theorem we present in this paper describes all possibile combinations of representations, choice of coordinates and point-wise activations to obtain an equivariant layer, generalizing and strengthening existing characterizations. Notable cases of practical relevance are discussed as corollaries. Indeed, we prove that rotation-equivariant networks can only be invariant, as it happens for any network which is equivariant with respect to connected compact groups. Then, we discuss implications of our findings when applied to important instances of equivariant networks. First, we completely characterize permutation equivariant networks such as Invariant Graph Networks with point-wise nonlinearities and their geometric counterparts, highlighting a plethora of models whose expressive power and performance are still unknown. Second, we show that feature spaces of disentangled steerable convolutional neural networks are trivial representations.

Type of Publication: Conference Proceeding

Title of Conference: International Conference on Learning Representations 2024 (ICLR 2024)

Abstract: Social networks contribute to the distribution of social capital, defined as the relationships, norms of trust and reciprocity within a community or society that facilitate cooperation and collective action. Social capital exists in the relations among individuals, such that better positioned members in a social network benefit from faster access to diverse information and higher influence on information dissemination. A variety of methods have been proposed in the literature to measure social capital at an individual level. However, there is a lack of methods to quantify social capital at a group level, which is particularly important when the groups are defined on the grounds of protected attributes. Furthermore, state-of-the-art approaches fail to model the role of long-range interactions between nodes in the network and their contributions to social capital. To fill this gap, we propose to measure the social capital of a group of nodes by means of their information flow and emphasize the importance of considering the whole network topology. Grounded in spectral graph theory, we introduce three effective resistance-based measures of group social capital, namely group isolation, group diameter and group control. We denote the social capital disparity among different groups in a network as structural group unfairness, and propose to mitigate it by means of a budgeted edge augmentation heuristic that systematically increases the social capital of the most disadvantaged group. In experiments on real networks, we uncover significant levels of structural group unfairness when using gender as the protected attribute, with females being the most disadvantaged group in comparison to males. We also illustrate how our proposed edge augmentation approach is able to not only effectively mitigate the structural group unfairness but also increase the social capital of all groups in the network.

Type of Publication: Conference Proceeding

Title of Conference: WWW 2024 workshop on Trustworthy Learning on Graphs (TrustLOG)

Abstract: Algorithmic fairness is of utmost societal importance, yet the current trend in large-scale machine learning models requires training with massive datasets that are frequently biased. In this context, pre-processing methods that focus on modeling and correcting bias in the data emerge as valuable approaches. In this paper, we propose FairShap, a novel instance-level data re-weighting method for fair algorithmic decision-making through data valuation by means of Shapley Values. FairShap is model-agnostic and easily interpretable, as it measures the contribution of each training data point to a predefined fairness metric. We empirically validate FairShap on several state-of-the-art datasets of different nature, with a variety of training scenarios and models and show how it yields fairer models with similar levels of accuracy than the baselines. We illustrate FairShap’s interpretability by means of histograms and latent space visualizations. Moreover, we perform a utility-fairness study, and ablation and runtime experiments to illustrate the impact of the size of the reference dataset and FairShap’s computational cost depending on the size of the dataset and the number of features. We believe that FairShap represents a promising direction in interpretable and model-agnostic approaches to algorithmic fairness that yield competitive accuracy even when only biased datasets are available.

Type of Publication: Conference Proceeding

Title of Conference: International Conference on Learning Representations (ICLR 2024) workshop on Data-centric Machine Learning Research (DMLR)

Abstract: Manifold-valued measurements exist in numerous applications within computer vision and machine learning. Recent studies have extended Deep Neural Networks (DNNs) to manifolds, and concomitantly, normalization techniques have also been adapted to several manifolds, referred to as Riemannian normalization. Nonetheless, most of the existing Riemannian normalization methods have been derived in an ad hoc manner and only apply to specific manifolds. This paper establishes a unified framework for Riemannian Batch Normalization (RBN) techniques on Lie groups. Our framework offers the theoretical guarantee of controlling both the Riemannian mean and variance. Empirically, we focus on Symmetric Positive Definite (SPD) manifolds, which possess three distinct types of Lie group structures. Using the deformation concept, we generalize the existing Lie groups on SPD manifolds into three families of parameterized Lie groups. Specific normalization layers induced by these Lie groups are then proposed for SPD neural networks. We demonstrate the effectiveness of our approach through three sets of experiments: radar recognition, human action recognition, and electroencephalography (EEG) classification. The code is available at this https URL.

Type of Publication: Conference Proceeding

Title of Conference: International Conference on Learning Representations (ICLR 2024)

Abstract: Current text classification approaches usually focus on the content to be classified. Contextual aspects (both linguistic and extra-linguistic) are usually neglected, even in tasks based on online discussions. Still in many cases the multi-party and multi-turn nature of the context from which these elements are selected can be fruitfully exploited. In this work, we propose a series of experiments on a large dataset for stance detection in English, in which we evaluate the contribution of different types of contextual information, i.e. linguistic, structural and temporal, by feeding them as natural language input into a transformer-based model. We also experiment with different amounts of training data and analyse the topology of local discussion networks in a privacy-compliant way. Results show that structural information can be highly beneficial to text classification but only under certain circumstances (e.g. depending on the amount of training data and on discussion chain complexity). Indeed, we show that contextual information on smaller datasets from other classification tasks does not yield significant improvements. Our framework, based on local discussion networks, allows the integration of structural information, while minimising user profiling, thus preserving their privacy.

Type of Publication: Conference paper

Title of Conference: European Chapter of the Association for Computational Linguistics. EACL 2024.

Abstract: Algorithmic Recourse (AR) is the problem of computing a sequence of actions that – once performed by a user – overturns an undesirable machine decision. It is paramount that the sequence of actions does not require too much effort for users to implement. Yet, most approaches to AR assume that actions cost the same for all users, and thus may recommend unfairly expensive recourse plans to certain users. Prompted by this observation, we introduce PEAR, the first human-in-the-loop approach capable of providing personalized algorithmic recourse tailored to the needs of any end-user. PEAR builds on insights from Bayesian Preference Elicitation to iteratively refine an estimate of the costs of actions by asking choice set queries to the target user. The queries themselves are computed by maximizing the Expected Utility of Selection, a principled measure of information gain accounting for uncertainty on both the cost estimate and the user’s responses. PEAR integrates elicitation into a Reinforcement Learning agent coupled with Monte Carlo Tree Search to quickly identify promising recourse plans. Our empirical evaluation on real-world datasets highlights how PEAR produces high-quality personalized recourse in only a handful of iterations.

Type of Publication: Journal article

Title of Journal: Transactions on Machine Learning Research, ISSN: 2835-8856, 2024.

Abstract: Owing to the power of vision-language foundation models, e.g., CLIP, the area of image synthesis has seen recent important advances. Particularly, for style transfer, CLIP enables transferring more general and abstract styles without collecting the style images in advance, as the style can be efficiently described with natural language, and the result is optimized by minimizing the CLIP similarity between the text description and the stylized image. However, directly using CLIP to guide style transfer leads to undesirable artifacts (mainly written words and unrelated visual entities) spread over the image. In this paper, we propose SpectralCLIP, which is based on a spectral representation of the CLIP embedding sequence, where most of the common artifacts occupy specific frequencies. By masking the band including these frequencies, we can condition the generation process to adhere to the target style properties (e.g., color, texture, paint stroke, etc.) while excluding the generation of larger-scale structures corresponding to the artifacts. Experimental results show that SpectralCLIP prevents the generation of artifacts effectively in quantitative and qualitative terms, without impairing the stylisation quality. We also apply SpectralCLIP to text-conditioned image generation and show that it prevents written words in the generated images. Our code is available at this https URL.

Type of Publication: Conference paper

Title of Journal: IEEE Winter Conference on Application of Computer Vision

Abstract: Fairness is crucial when training a deep-learning discriminative model, especially in the facial domain. Models tend to correlate specific characteristics (such as age and skin color) with unrelated attributes (downstream tasks), resulting in biases which do not correspond to reality. It is common knowledge that these correlations are present in the data and are then transferred to the models during training. This paper proposes a method to mitigate these correlations to improve fairness. To do so, we learn interpretable and meaningful paths lying in the semantic space of a pre-trained diffusion model (DiffAE) — such paths being supervised by contrastive text dipoles. That is, we learn to edit protected characteristics (age and skin color). These paths are then applied to augment images to improve the fairness of a given dataset. We test the proposed method on CelebA-HQ and UTKFace on several downstream tasks with age and skin color as protected characteristics. As a proxy for fairness, we compute the difference in accuracy with respect to the protected characteristics. Quantitative results show how the augmented images help the model improve the overall accuracy, the aforementioned metric, and the disparity of equal opportunity. Code is available at: this URL.

Type of Publication: Conference paper

Title of Journal: IEEE Winter Conference on Application of Computer Vision

Abstract: Large datasets are often affected by cell-wise outliers in the form of missing or erroneous data. However, discarding any samples containing outliers may result in a dataset that is too small to accurately estimate the covariance matrix. Moreover, the robust procedures designed to address this problem require the invertibility of the covariance operator and thus are not effective on high-dimensional data. In this paper, we propose an unbiased estimator for the covariance in the presence of missing values that does not require any imputation step and still achieves near minimax statistical accuracy with the operator norm. We also advocate for its use in combination with cell-wise outlier detection methods to tackle cell-wise contamination in a high-dimensional and low-rank setting, where state-of-the-art methods may suffer from numerical instability and long computation times. To complement our theoretical findings, we conducted an experimental study which demonstrates the superiority of our approach over the state of the art both in low and high dimension settings.

Type of Publication: Conference paper

Title of Journal: Neural Information Processing Systems (NeurIPS)

Abstract: Nonlinear dynamical systems can be handily described by the associated Koopman operator, whose action evolves every observable of the system forward in time. Learning the Koopman operator and its spectral decomposition from data is enabled by a number of algorithms. In this work we present for the first time non-asymptotic learning bounds for the Koopman eigenvalues and eigenfunctions. We focus on time-reversal-invariant stochastic dynamical systems, including the important example of Langevin dynamics. We analyze two popular estimators: Extended Dynamic Mode Decomposition (EDMD) and Reduced Rank Regression (RRR). Our results critically hinge on novel minimax estimation bounds for the operator norm error, that may be of independent interest. Our spectral learning bounds are driven by the simultaneous control of the operator norm error and a novel metric distortion functional of the estimated eigenfunctions. The bounds indicates that both EDMD and RRR have similar variance, but EDMD suffers from a larger bias which might be detrimental to its learning rate. Our results shed new light on the emergence of spurious eigenvalues, an issue which is well known empirically. Numerical experiments illustrate the implications of the bounds in practice..

Type of Publication: Conference paper

Title of Journal: Neural Information Processing Systems (NeurIPS)