Florian Yger

TMLR Journal 2025 Journal Article

Geometry-Aware visualization of high dimensional Symmetric Positive Definite matrices

• Thibault de Surrel
• Sylvain Chevallier
• Fabien Lotte
• Florian Yger

Symmetric Positive Definite (SPD) matrices are pervasive in machine learning, from data features (such as covariance matrices) to optimization process.These matrices induce a Riemannian structure, where the curvature plays a critical role in the success of approaches based on those geometries. Yet, for ML practitioners wanting to visualize SPD matrices, the existing (flat) Euclidean approaches will hide the curvature of the manifold. To overcome this lack of expressivity in the existing algorithms, we introduce Riemannian versions of two state-of-the-art techniques, namely t-SNE and Multidimensional Scaling. Therefore, we are able to reduce a set of $c \times c$ SPD matrices into a set of $2 \times 2$ SPD matrices in order to capture the curvature information and avoid any distortion induced by flattening the representation in an Euclidean setup. Moreover, our approaches pave the way for targeting more general dimensionality reduction applications while preserving the geometry of the data. We performed experiments on controlled synthetic dataset to ensure that the low-dimensional representation preserves the geometric properties of both SPD Gaussians and geodesics. We also conduct experiments on various real datasets, such as video, anomaly detection, brain signal and others.

ICML Conference 2025 Conference Paper

Wrapped Gaussian on the manifold of Symmetric Positive Definite Matrices

• Thibault de Surrel
• Fabien Lotte
• Sylvain Chevallier
• Florian Yger

Circular and non-flat data distribution are prevalent across diverse domains of data science, yet their specific geometric structures often remain underutilized in machine learning frameworks. A principled approach to accounting for the underlying geometry of such data is pivotal, particularly when extending statistical models, like the pervasive Gaussian distribution. In this work, we tackle those issue by focusing on the manifold of symmetric positive definite matrices, a key focus in information geometry. We introduced a non-isotropic wrapped Gaussian by leveraging the exponential map, we derive theoretical properties of this distribution and propose a maximum likelihood framework for parameter estimation. Furthermore, we reinterpret established classifiers on SPD through a probabilistic lens and introduce new classifiers based on the wrapped Gaussian model. Experiments on synthetic and real-world datasets demonstrate the robustness and flexibility of this geometry-aware distribution, underscoring its potential to advance manifold-based data analysis. This work lays the groundwork for extending classical machine learning and statistical methods to more complex and structured data.

UAI Conference 2022 Conference Paper

Multi-winner approval voting goes epistemic

• Tahar Allouche
• Jérôme Lang
• Florian Yger

Epistemic voting interprets votes as noisy signals about a ground truth. We consider contexts where the truth consists of a set of objective winners, knowing a lower and upper bound on its cardinality. A prototypical problem for this setting is the aggregation of multi-label annotations with prior knowledge on the size of the ground truth. We posit noise models, for which we define rules that output an optimal set of winners. We report on experiments on multi-label annotations (which we collected).

AAAI Conference 2022 Conference Paper

Truth-Tracking via Approval Voting: Size Matters

• Tahar Allouche
• Jérôme Lang
• Florian Yger

Epistemic social choice aims at unveiling a hidden ground truth given votes, which are interpreted as noisy signals about it. We consider here a simple setting where votes consist of approval ballots: each voter approves a set of alternatives which they believe can possibly be the ground truth. Based on the intuitive idea that more reliable votes contain fewer alternatives, we define several noise models that are approval voting variants of the Mallows model. The likelihoodmaximizing alternative is then characterized as the winner of a weighted approval rule, where the weight of a ballot decreases with its cardinality. We have conducted an experiment on three image annotation datasets; they conclude that rules based on our noise model outperform standard approval voting; the best performance is obtained by a variant of the Condorcet noise model.

ICML Conference 2021 Conference Paper

Mediated Uncoupled Learning: Learning Functions without Direct Input-output Correspondences

• Ikko Yamane
• Junya Honda
• Florian Yger
• Masashi Sugiyama

Ordinary supervised learning is useful when we have paired training data of input $X$ and output $Y$. However, such paired data can be difficult to collect in practice. In this paper, we consider the task of predicting $Y$ from $X$ when we have no paired data of them, but we have two separate, independent datasets of $X$ and $Y$ each observed with some mediating variable $U$, that is, we have two datasets $S_X = \{(X_i, U_i)\}$ and $S_Y = \{(U’_j, Y’_j)\}$. A naive approach is to predict $U$ from $X$ using $S_X$ and then $Y$ from $U$ using $S_Y$, but we show that this is not statistically consistent. Moreover, predicting $U$ can be more difficult than predicting $Y$ in practice, e. g. , when $U$ has higher dimensionality. To circumvent the difficulty, we propose a new method that avoids predicting $U$ but directly learns $Y = f(X)$ by training $f(X)$ with $S_{X}$ to predict $h(U)$ which is trained with $S_{Y}$ to approximate $Y$. We prove statistical consistency and error bounds of our method and experimentally confirm its practical usefulness.

NeurIPS Conference 2019 Conference Paper

Theoretical evidence for adversarial robustness through randomization

• Rafael Pinot
• Laurent Meunier
• Alexandre Araujo
• Hisashi Kashima
• Florian Yger
• Cedric Gouy-Pailler
• Jamal Atif

This paper investigates the theory of robustness against adversarial attacks. It focuses on the family of randomization techniques that consist in injecting noise in the network at inference time. These techniques have proven effective in many contexts, but lack theoretical arguments. We close this gap by presenting a theo- retical analysis of these approaches, hence explaining why they perform well in practice. More precisely, we make two new contributions. The first one relates the randomization rate to robustness to adversarial attacks. This result applies for the general family of exponential distributions, and thus extends and unifies the previous approaches. The second contribution consists in devising a new upper bound on the adversarial risk gap of randomized neural networks. We support our theoretical claims with a set of experiments.

UAI Conference 2018 Conference Paper

Graph-based Clustering under Differential Privacy

• Rafael Pinot
• Anne Morvan
• Florian Yger
• Cédric Gouy-Pailler
• Jamal Atif

In this paper, we present the first differentially private clustering method for arbitraryshaped node clusters in a graph. This algorithm takes as input only an approximate Minimum Spanning Tree (MST) T released under weight differential privacy constraints from the graph. Then, the underlying nonconvex clustering partition is successfully recovered from cutting optimal cuts on T. As opposed to existing methods, our algorithm is theoretically well-motivated. Experiments support our theoretical findings.

NeurIPS Conference 2018 Conference Paper

Uplift Modeling from Separate Labels

• Ikko Yamane
• Florian Yger
• Jamal Atif
• Masashi Sugiyama

Uplift modeling is aimed at estimating the incremental impact of an action on an individual's behavior, which is useful in various application domains such as targeted marketing (advertisement campaigns) and personalized medicine (medical treatments). Conventional methods of uplift modeling require every instance to be jointly equipped with two types of labels: the taken action and its outcome. However, obtaining two labels for each instance at the same time is difficult or expensive in many real-world problems. In this paper, we propose a novel method of uplift modeling that is applicable to a more practical setting where only one type of labels is available for each instance. We show a mean squared error bound for the proposed estimator and demonstrate its effectiveness through experiments.

ICML Conference 2012 Conference Paper

Adaptive Canonical Correlation Analysis Based On Matrix Manifolds

• Florian Yger
• Maxime Berar
• Gilles Gasso
• Alain Rakotomamonjy