arXiv research

Binary feedback outperforms ordinal comparisons in ranking recovery.

Recent work by Locatello et al. (2018) has shown that an inductive bias is required to disentangle factors of interest in Variational Autoencoder (VAE). Motivated by a real-world problem, we propose a setting where such bias is introduced by providing pairwise ordinal comparisons between instances, based on the desired…

Paper tackles clustering with ordinal comparisons, achieving near-optimal results.

In the absence of prior knowledge, ordinal embedding methods obtain new representation for items in a low-dimensional Euclidean space via a set of quadruple-wise comparisons. These ordinal comparisons often come from human annotators, and sufficient comparisons induce the success of classical approaches. However, colle…

The study explores how to infer the geometry of space forms from similarity comparisons.

Existing ordinal embedding methods usually follow a two-stage routine: outlier detection is first employed to pick out the inconsistent comparisons; then an embedding is learned from the clean data. However, learning in a multi-stage manner is well-known to suffer from sub-optimal solutions. In this paper, we propose a…

In supervised learning, we typically leverage a fully labeled dataset to design methods for function estimation or prediction. In many practical situations, we are able to obtain alternative feedback, possibly at a low cost. A broad goal is to understand the usefulness of, and to design algorithms to exploit, this alte…

The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like this often come from human judgments. To account for errors and variation in jud…

In recent years it has become popular to study machine learning problems in a setting of ordinal distance information rather than numerical distance measurements. By ordinal distance information we refer to binary answers to distance comparisons such as $d(A,B)<d(C,D)$. For many problems in machine learning and statist…

To investigate objects without a describable notion of distance, one can gather ordinal information by asking triplet comparisons of the form "Is object $x$ closer to $y$ or is $x$ closer to $z$?" In order to learn from such data, the objects are typically embedded in a Euclidean space while satisfying as many triplet …

This paper applies deep learning to ordinal regression, modeling it as a binary search.

We consider the problem of embedding unweighted, directed k-nearest neighbor graphs in low-dimensional Euclidean space. The k-nearest neighbors of each vertex provides ordinal information on the distances between points, but not the distances themselves. We use this ordinal information along with the low-dimensionality…

Data in the form of pairwise comparisons arises in many domains, including preference elicitation, sporting competitions, and peer grading among others. We consider parametric ordinal models for such pairwise comparison data involving a latent vector $w^* \in \mathbb{R}^d$ that represents the "qualities" of the $d$ ite…

Motivated by generating personalized recommendations using ordinal (or preference) data, we study the question of learning a mixture of MultiNomial Logit (MNL) model, a parameterized class of distributions over permutations, from partial ordinal or preference data (e.g. pair-wise comparisons). Despite its long standing…

We propose a new constrained-optimization formulation for deep ordinal classification, in which uni-modality of the label distribution is enforced implicitly via a set of inequality constraints over all the pairs of adjacent labels. Based on (c-1) constraints for c labels, our model is non-parametric and, therefore, mo…

We address the classical problem of hierarchical clustering, but in a framework where one does not have access to a representation of the objects or their pairwise similarities. Instead, we assume that only a set of comparisons between objects is available, that is, statements of the form "objects $i$ and $j$ are more …

The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous algorithms have been proposed to solve this problem. However, there does not exist a fai…

Rank aggregation systems collect ordinal preferences from individuals to produce a global ranking that represents the social preference. Rank-breaking is a common practice to reduce the computational complexity of learning the global ranking. The individual preferences are broken into pairwise comparisons and applied t…

Reinforcement learning usually makes use of numerical rewards, which have nice properties but also come with drawbacks and difficulties. Using rewards on an ordinal scale (ordinal rewards) is an alternative to numerical rewards that has received more attention in recent years. In this paper, a general approach to adapt…

Proposes models to better represent ordinal data with non-unimodal distributions.

An efficient algorithm selects the correct number of latent dimensions in multidimensional probit models.

A new framework estimates causal effects for ordinal variables.

In applications such as recommendation systems and revenue management, it is important to predict preferences on items that have not been seen by a user or predict outcomes of comparisons among those that have never been compared. A popular discrete choice model of multinomial logit model captures the structure of the …

New method uniquely identifies causal structure from ordinal data.

New methods for ordinal classification of interval-valued data and functional data.

Probability distributions produced by the cross-entropy loss for ordinal classification problems can possess undesired properties. We propose a straightforward technique to constrain discrete ordinal probability distributions to be unimodal via the use of the Poisson and binomial probability distributions. We evaluate …

Learning from triplet comparison data has been extensively studied in the context of metric learning, where we want to learn a distance metric between two instances, and ordinal embedding, where we want to learn an embedding in an Euclidean space of the given instances that preserves the comparison order as well as pos…

Many real-world datasets are labeled with natural orders, i.e., ordinal labels. Ordinal regression is a method to predict ordinal labels that finds a wide range of applications in data-rich domains, such as natural, health and social sciences. Most existing ordinal regression approaches work well for independent and id…

The real-world data is often susceptible to label noise, which might constrict the effectiveness of the existing state of the art algorithms for ordinal regression. Existing works on ordinal regression do not take label noise into account. We propose a theoretically grounded approach for class conditional label noise i…

New framework estimates treatment effects based on preferences.

Improved motion prediction for self-driving cars using trajectory sets and auxiliary losses.

A game-theoretic approach to multi-criteria ranking from ordinal data.

Deep neural networks for ordinal outcomes combining image and tabular data.

This study introduces balanced DRPS and OrderedLogitNN for better QDE of discrete-level questions.

This paper analyzes OCBA algorithms' convergence rates for DEDS optimization.

Study homeomorphism groups of ordinals, proving strong distortion and normal generators.

Ordinal regression is aimed at predicting an ordinal class label. In this paper, we consider its semi-supervised formulation, in which we have unlabeled data along with ordinal-labeled data to train an ordinal regressor. There are several metrics to evaluate the performance of ordinal regression, such as the mean absol…

Proposes a new method for rank-consistent ordinal regression without weight-sharing constraints.

Develops an ordinal-similarity framework for scalable and interpretable representation alignment.

Ordinal data are often seen in real applications. Regular multicategory classification methods are not designed for this data type and a more proper treatment is needed. We consider a framework of ordinal classification which pools the results from binary classifiers together. An inherent difficulty of this framework i…

When eliciting judgements from humans for an unknown quantity, one often has the choice of making direct-scoring (cardinal) or comparative (ordinal) measurements. In this paper we study the relative merits of either choice, providing empirical and theoretical guidelines for the selection of a measurement scheme. We pro…

A new kernel measures brain network similarities, improving disease classification.

Algorithm finds real line mapping from points under ordinal constraints.

The paper identifies and critiques problems with risk matrices using ordinal scales.

Ordinal Data are those where a natural order exist between the labels. The classification and pre-processing of this type of data is attracting more and more interest in the area of machine learning, due to its presence in many common problems. Traditionally, ordinal classification problems have been approached as nomi…

We propose a novel method for automatic pain intensity estimation from facial images based on the framework of kernel Conditional Ordinal Random Fields (KCORF). We extend this framework to account for heteroscedasticity on the output labels(i.e., pain intensity scores) and introduce a novel dynamic features, dynamic ra…

In many real-world prediction tasks, class labels include information about the relative ordering between labels, which is not captured by commonly-used loss functions such as multi-category cross-entropy. Recently, the deep learning community adopted ordinal regression frameworks to take such ordering information into…

Develops methods to control risk in ordinal classification tasks.