ERA ranking representability: The missing link between ordinal regression and multi-class classification

Can a multi-class classification model in some situations be simplified to an ordinal regression model without sacrificing performance? We try to answer this question from a theoretical point of view for one-versus-one multi-class ensembles. To that end, sufficient conditions are derived for which a one-versus-one ensemble becomes ranking representable, i.e. conditions for which the ensemble can be reduced to a ranking or ordinal regression model such that a similar performance on training data is measured. As performance measure, we use the area under the ROC curve (AUC) and its reformulation in terms of graphs. For the three-class case, this results in a new type of cycle transitivity for pairwise AUCs that can be verified by solving an integer quadratic program. Moreover, solving this integer quadratic program can be avoided, since its solution converges for an infinite data sample to a simple form, resulting in a deviation bound that becomes tighter with increasing sample size

Méthodes d'apprentissage statistique pour le ranking : théorie, algorithmes et applications

Multipartite ranking is a statistical learning problem that consists in ordering observations that belong to a high dimensional feature space in the same order as the labels, so that the observations with the highest label appear at the top of the list. This work aims to understand the probabilistic nature of the multipartite ranking problem in order to obtain theoretical guarantees for ranking algorithms. In this context, the output of a ranking algorithm takes the form of a scoring function, a function that maps the space of the observation to the real line which order is induced using the values on the real line. The contributions of this manuscript are the following : First, we focus on the characterization of optimal solutions to multipartite ranking. The second research theme is the design of algorithms to produce scoring functions. We offer two methods, the first using an aggregation procedure, the second an approximation scheme. Finally, we return to the binary ranking problem to establish adaptive minimax rate of convergence.Le ranking multipartite est un problème d'apprentissage statistique qui consiste à ordonner les observations qui appartiennent à un espace de grande dimension dans le même ordre que les labels, de sorte que les observations avec le label le plus élevé apparaissent en haut de la liste. Cette thèse vise à comprendre la nature probabiliste du problème de ranking multipartite afin d'obtenir des garanties théoriques pour les algorithmes de ranking. Dans ce cadre, la sortie d'un algorithme de ranking prend la forme d'une fonction de scoring, une fonction qui envoie l'espace des observations sur la droite réelle et l'ordre finale est construit en utilisant l'ordre induit par la droite réelle. Les contributions de ce manuscrit sont les suivantes : d'abord, nous nous concentrons sur la caractérisation des solutions optimales de ranking multipartite. Le deuxième thème de recherche est la conception d'algorithmes pour produire des fonctions de scoring. Nous proposons deux méthodes, la première utilisant une procédure d'agrégation, la deuxième un schema d'approximation. Enfin, nous revenons au problème de ranking binaire afin d'établir des vitesse minimax adaptives de convergences

Visual Scene Understanding by Deep Fisher Discriminant Learning

Modern deep learning has recently revolutionized several fields of classic machine learning and computer vision, such as, scene understanding, natural language processing and machine translation. The substitution of feature hand-crafting with automatic feature learning, provides an excellent opportunity for gaining an in-depth understanding of large-scale data statistics. Deep neural networks generally train models with huge numbers of parameters, facilitating efficient search for optimal and sub-optimal spaces of highly non-convex objective functions. On the other hand, Fisher discriminant analysis has been widely employed to impose class discrepancy, for the sake of segmentation, classification, and recognition tasks. This thesis bridges between contemporary deep learning and classic discriminant analysis, to accommodate some important challenges in visual scene understanding, i.e. semantic segmentation, texture classification, and object recognition. The aim is to accomplish specific tasks in some new high-dimensional spaces, covered by the statistical information of the datasets under study. Inspired by a new formulation of Fisher discriminant analysis, this thesis introduces some novel arrangements of well-known deep learning architectures, to achieve better performances on the targeted missions. The theoretical justifications are based upon a large body of experimental work, and consolidate the contribution of the proposed idea; Deep Fisher Discriminant Learning, to several challenges in visual scene understanding

On the ERA ranking representability of pairwise bipartite ranking functions

AbstractIn domains like decision theory and social choice theory it is known for a long time that stochastic transitivity properties yield necessary and sufficient conditions for the ranking or utility representability of reciprocal preference relations. In this article we extend these results for reciprocal preference relations originating from the pairwise comparison of random vectors in a machine learning context. More specifically, the expected ranking accuracy (ERA) is such a reciprocal relation that occurs in multi-class classification problems, when ranking or utility functions are fitted to the data in a pairwise manner. We establish necessary and sufficient conditions for which these pairwise bipartite ranking functions can be simplified to a single ranking function such that the pairwise expected ranking accuracies of both models coincide. Similarly as for more common reciprocal preference relations, cycle transitivity plays a crucial role in this new setting. We first consider the finite sample case, for which expected ranking accuracy can be estimated by means of the area under the ROC curve (AUC), and subsequently, we further generalize these results to the underlying distributions. It turns out that the ranking representability of pairwisely compared random vectors can be expressed elegantly in a distribution-independent way by means of a specific type of cycle transitivity, defined by a conjunctor that is closely related to the algebraic product

Study on open science: The general state of the play in Open Science principles and practices at European life sciences institutes

Nowadays, open science is a hot topic on all levels and also is one of the priorities of the European Research Area. Components that are commonly associated with open science are open access, open data, open methodology, open source, open peer review, open science policies and citizen science. Open science may a great potential to connect and influence the practices of researchers, funding institutions and the public. In this paper, we evaluate the level of openness based on public surveys at four European life sciences institute

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Wigner negativity on the sphere

The rise of quantum information theory has largely vindicated the long-held belief that Wigner negativity is an indicator of genuine nonclassicality in quantum systems. This thesis explores its manifestation in spin-j systems using the spherical Wigner function. Common symmetric multi-qubit states are studied and compared. Spin coherent states are shown to never have vanishing Wigner negativity. Pure states that maximize negativity are determined and analyzed using the Majorana stellar representation. The relationship between negativity and state mixedness is discussed, and polytopes characterizing unitary orbits of lower-bounded Wigner functions are studied. Results throughout are contrasted with similar works on symmetric state entanglement and other forms of phase-space nonclassicality