We propose to solve a label ranking problem as a structured output regression task. In this view, we adopt a least square surrogate loss approach that solves a supervised learning problem in two steps: a regression step in a well-chosen feature space and a pre-image (or decoding) step. We use specific feature maps/embeddings for ranking data, which convert any ranking/permutation into a vector representation. These embeddings are all well-tailored for our approach, either by resulting in consistent estimators, or by solving trivially the pre-image problem which is often the bottleneck in structured prediction. Their extension to the case of incomplete or partial rankings is also discussed. Finally, we provide empirical results on synthetic and real-world datasets showing the relevance of our method.

However, the common assumption both in theoretical and in applied works is that the observed rankings are noisy in the sense that they do not always correspond to the ground-truth ranking.

This paper presents an interesting approach to the label ranking problem, by first casting it as a Structured Prediction problem that can be optimized using a surrogate least square methodology, and then demonstrating an embedding representation that captures a couple of common ranking loss functions -- most notable being the Kendall-Tau distance. Overall I liked the paper and found a decent mix of method, theory and experiments (though I would have liked to see more convincing experimentation as further detailed below). In particular I liked the demonstration of the Kendall tau distance and Hamming distances to be representable in this embedding formulation/ That said I had a few concerns with this work as well: - Specifically the empirical results were not very convincing. While this may not have been a problem for a theory-first paper, part of the appeal of an approach like this it is supposed to work in practice. Unfortunately with the current (some what limited) set of experiments I am not entirely convinced. For example: This only looked at a couple of very specific (and not particularly common loss functions) with the evals only measuring Kendall Tau.

Several machine learning methods allow for abstaining from uncertain predictions. While being common for settings like conventional classification, abstention has been studied much less in learning to rank. We address abstention for the label ranking setting, allowing the learner to declare certain pairs of labels as being incomparable and, thus, to predict partial instead of total orders. In our method, such predictions are produced via thresholding the probabilities of pairwise preferences between labels, as induced by a predicted probability distribution on the set of all rankings. We formally analyze this approach for the Mallows and the Plackett-Luce model, showing that it produces proper partial orders as predictions and characterizing the expressiveness of the induced class of partial orders. These theoretical results are complemented by experiments demonstrating the practical usefulness of the approach.

Label ranking is the task of inferring a total order over a predefined set of labels for each given instance. We present a general framework for batch learning of label ranking functions from supervised data. We assume that each instance in the training data is associated with a list of preferences over the label-set, however we do not assume that this list is either com- plete or consistent. This enables us to accommodate a variety of ranking problems. In contrast to the general form of the supervision, our goal is to learn a ranking function that induces a total order over the entire set of labels.

Several machine learning methods allow for abstaining from uncertain predictions. While being common for settings like conventional classification, abstention has been studied much less in learning to rank. We address abstention for the label ranking setting, allowing the learner to declare certain pairs of labels as being incomparable and, thus, to predict partial instead of total orders. In our method, such predictions are produced via thresholding the probabilities of pairwise preferences between labels, as induced by a predicted probability distribution on the set of all rankings. We formally analyze this approach for the Mallows and the Plackett-Luce model, showing that it produces proper partial orders as predictions and characterizing the expressiveness of the induced class of partial orders.

Rank aggregation for complete rankings: The standard Borda method [10] is a well-established greedy heuristic for RAP, which is intuitive and simple to compute for complete rankings. This method has the advantage of being simple and fast, but the obtained solutions may be far from the true optima.

Limb deficiency severely affects the daily lives of amputees and drives efforts to provide functional robotic prosthetic hands to compensate this deprivation. Convolutional neural network-based computer vision control of the prosthetic hand has received increased attention as a method to replace or complement physiological signals due to its reliability by training visual information to predict the hand gesture. Mounting a camera into the palm of a prosthetic hand is proved to be a promising approach to collect visual data. However, the grasp type labelled from the eye and hand perspective may differ as object shapes are not always symmetric. Thus, to represent this difference in a realistic way, we employed a dataset containing synchronous images from eye- and hand- view, where the hand-perspective images are used for training while the eye-view images are only for manual labelling. Electromyogram (EMG) activity and movement kinematics data from the upper arm are also collected for multi-modal information fusion in future work. Moreover, in order to include human-in-the-loop control and combine the computer vision with physiological signal inputs, instead of making absolute positive or negative predictions, we build a novel probabilistic classifier according to the Plackett-Luce model. To predict the probability distribution over grasps, we exploit the statistical model over label rankings to solve the permutation domain problems via a maximum likelihood estimation, utilizing the manually ranked lists of grasps as a new form of label. We indicate that the proposed model is applicable to the most popular and productive convolutional neural network frameworks.

In multiclass classification, the goal is to learn how to predict a random label $Y$, valued in $\mathcal{Y}=\{1,\; \ldots,\; K \}$ with $K\geq 3$, based upon observing a r.v. $X$, taking its values in $\mathbb{R}^q$ with $q\geq 1$ say, by means of a classification rule $g:\mathbb{R}^q\to \mathcal{Y}$ with minimum probability of error $\mathbb{P}\{Y\neq g(X) \}$. However, in a wide variety of situations, the task targeted may be more ambitious, consisting in sorting all the possible label values $y$ that may be assigned to $X$ by decreasing order of the posterior probability $\eta_y(X)=\mathbb{P}\{Y=y \mid X \}$. This article is devoted to the analysis of this statistical learning problem, halfway between multiclass classification and posterior probability estimation (regression) and referred to as label ranking here. We highlight the fact that it can be viewed as a specific variant of ranking median regression (RMR), where, rather than observing a random permutation $\Sigma$ assigned to the input vector $X$ and drawn from a Bradley-Terry-Luce-Plackett model with conditional preference vector $(\eta_1(X),\; \ldots,\; \eta_K(X))$, the sole information available for training a label ranking rule is the label $Y$ ranked on top, namely $\Sigma^{-1}(1)$. Inspired by recent results in RMR, we prove that under appropriate noise conditions, the One-Versus-One (OVO) approach to multiclassification yields, as a by-product, an optimal ranking of the labels with overwhelming probability. Beyond theoretical guarantees, the relevance of the approach to label ranking promoted in this article is supported by experimental results.