New method uniquely identifies causal structure from ordinal data.
problem Challenges in causal discovery for categorical data, especially direction of relationships.
method Exploits ordinal information to uniquely identify causal structure.
result Favorable and robust performance compared to state-of-the-art methods.
New method estimates and completes tensors from ordinal data, improving accuracy and efficiency.
problem Estimating and completing tensors from incomplete, ordinal observations.
method Multi-linear cumulative link model with rank-constrained M-estimator.
result The proposed estimator achieves faster convergence and is minimax optimal.
Proposes models to better represent ordinal data with non-unimodal distributions.
problem Real-world ordinal data often have non-unimodal conditional probability distributions.
method Develops approximately unimodal likelihood models to better represent non-unimodal CPDs.
result Proposed models can effectively represent both unimodal and nearly unimodal CPDs.
New methods for ordinal classification of interval-valued data and functional data.
problem Ordinal classification of interval-valued data and functional data.
method Six ordinal classifiers are proposed, including parametric, binary decomposition, logistic regression, distance-based, k-nearest-neighbor, kernel PCA, and random forest methods.
result Considering ordering and interval-valued information improves the accuracy of ordinal classification.
K-Models clusters functional data with ordinal constraints for better interpretability.
problem Challenges in extracting meaningful insights from functional data due to lack of interpretability.
method Integrates ordinal constraints into clustering to improve interpretability and structure identification.
result Enhances interpretability of clustering results while maintaining performance.
We address the task of simultaneous feature fusion and modeling of discrete ordinal outputs. We propose a novel Gaussian process(GP) auto-encoder modeling approach. In particular, we introduce GP encoders to project multiple observed features onto a latent space, while GP decoders are responsible for reconstructing the…
Python package for ordinal regression using gradient boosting.
problem Handling ordinal variables in machine learning.
method Gradient boosting with latent variable framework.
result Performs joint optimization of latent function and threshold vector.
The paper bounds and identifies joint probabilities in causal inference with monotonicity assumptions.
problem Bounding and identifying joint probabilities of potential outcomes and observed variables under monotonicity assumptions.
method Proposes new families of monotonicity assumptions, formulates bounding problem as linear programming, introduces new monotonicity assumption for identification.
result Validated methods through numerical experiments and applied to real-world datasets.
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…
Paper tackles clustering with ordinal comparisons, achieving near-optimal results.
problem Clustering with ordinal comparisons when similarity measures are not available.
method Two-step procedure: estimate similarity matrix from comparisons, then apply SDP clustering.
result Near-optimal recovery of planted clustering using near-optimal number of comparisons.
Proposes a deep learning method for robust ordinal regression under label noise.
problem Label noise in real-world data constrains ordinal regression algorithms.
method Develops a deep learning approach that is robust to label noise and rank consistent.
result Demonstrates robustness to label noise and rank consistency on real data.
A new framework estimates causal effects for ordinal variables.
problem Existing causal inference methods fail for ordinal data.
method Presumes a latent Gaussian DAG model with constrained covariance matrix.
result Closed-form function for ordinal causal effects in latent space.
Binary feedback outperforms ordinal comparisons in ranking recovery.
problem Challenges the conventional wisdom that ordinal comparisons offer richer information.
method Proposes a parametric framework for modeling ordinal paired comparisons, binarizing ordinal data, and proving faster convergence rates for binary comparisons.
result Binarizing ordinal data significantly improves ranking recovery accuracy and exhibits a substantial performance gap.
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 …
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…
Deep neural networks for ordinal outcomes combining image and tabular data.
problem Lack of interpretable models for ordinal outcomes in mixed data types.
method Ordinal Neural Network Transformation Models (ONTRAMs) integrating DL and classical ordinal regression.
result ONTRAMs achieve performance equivalent to standard multi-class DL models but are faster and more interpretable.
This study introduces balanced DRPS and OrderedLogitNN for better QDE of discrete-level questions.
problem Lack of ordinal regression methods and fair evaluation metrics for discrete-level QDE.
method Introduces balanced DRPS and OrderedLogitNN, fine-tunes BERT on RACE++ and ARC datasets.
result OrderedLogitNN outperforms other models on complex QDE tasks.
Study homeomorphism groups of ordinals, proving strong distortion and normal generators.
problem Understanding algebraic and geometric properties of homeomorphism groups of ordinals.
method Analyzing successor ordinals with connections to permutation groups and manifolds.
result Proves strong distortion and normal generators for homeomorphism groups of ordinals.
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.
problem Ordinal response variables in real-world prediction problems are often ignored by conventional classification losses.
method CORN framework using conditional training sets and the chain rule for conditional probability distributions.
result Improves performance substantially compared to the CORAL reference approach without weight-sharing restrictions.
Develops an ordinal-similarity framework for scalable and interpretable representation alignment.
problem Measuring representation similarity in large datasets.
method Triplet and Quadruplet Similarity Indices.
result Demonstrates inherent interpretability, robustness to outliers, and computational efficiency.
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.
problem Lack of edge weight information in existing graph kernels for brain connectivity networks.
method Ordinal pattern kernel for weighted brain connectivity networks.
result The ordinal pattern kernel achieves better classification performance than state-of-the-art graph kernels.
Landmark Ordinal Embedding improves scalability of ordinal embedding.
problem Learning low-dimensional Euclidean representations from ordinal constraints.
method Landmark-based strategy (LOE) that trades statistical efficiency for computational efficiency.
result LOE is significantly more efficient than conventional methods as the number of items grows.
This paper applies deep learning to ordinal regression, modeling it as a binary search.
problem Ordinal regression with deep learning models.
method Formulated ordinal regression as a binary search problem, using recurrent neural networks.
result Deep learning model shows comparable or better predictive power compared to traditional methods.
XOFM explains attribute effects in ordinal regression using piece-wise linear functions.
problem Lack of detailed attribute contributions in existing ordinal regression models.
method XOFM uses piece-wise linear functions to approximate attribute contributions and introduces ordinal transformation.
result XOFM provides superior explainability and state-of-the-art prediction accuracy.
Algorithm finds real line mapping from points under ordinal constraints.
problem Finding a mapping from points to real line under ordinal constraints.
method Approximation algorithm for dense case in O(n7)+(1/ε)O(1/ε1/8)n time. result Computes a solution satisfying (1−O(ε1/8))-fraction of all constraints. Lognormal distribution used for predicting team rankings in an orienteering relay race.
problem Predicting final team rankings in an orienteering relay race.
method Used lognormal distribution and Fenton-Wilkinson approximations for order statistics.
result Accurate predictions of team rankings using order statistics.
The paper identifies and critiques problems with risk matrices using ordinal scales.
problem Problems with risk matrices using ordinal scales.
method Overview of risk assessment process, explanation of fallacies, and suggestions for improvement.
result The paper proposes avoiding risk matrices and using fully quantitative methods instead.
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.
problem Controlling risk in ordinal classification tasks.
method Formulated ordinal classification in conformal risk control framework, proposed loss functions and algorithms.
result Demonstrated effectiveness and analyzed differences in risk control methods.
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…
In this paper, we address the problem of measuring and analysing sensation, the subjective magnitude of one's experience. We do this in the context of the method of triads: the sensation of the stimulus is evaluated via relative judgments of the form: "Is stimulus S_i more similar to stimulus S_j or to stimulus S_k?". …
New framework learns complex AI attitudes from heterogeneous data.
problem Heterogeneous ordinal structure in AI attitudes, poorly captured by existing methods.
method Monotone Gaussian score embedding, BNP complexity discovery, confirmatory fixed-K estimation.
result Reduced holdout MSE by 25.8% over single-graph baseline.
We propose a new variational Bayes estimator for high-dimensional copulas with discrete, or a combination of discrete and continuous, margins. The method is based on a variational approximation to a tractable augmented posterior, and is faster than previous likelihood-based approaches. We use it to estimate drawable vi…
We develop a novel probabilistic generative model based on the variational autoencoder approach. Notable aspects of our architecture are: a novel way of specifying the latent variables prior, and the introduction of an ordinality enforcing unit. We describe how to do supervised, unsupervised and semi-supervised learnin…
New RNN model forecasts unseen time series with little training data.
problem Lack of data for RNNs to generalize well in time series forecasting.
method Proposes a novel RNN-based model that learns shared feature embeddings over quantised time series.
result Accurately forecasts unseen time series with minimal training data.
Proposes a deep ordinal regression framework using optimal transport loss and unimodal output probabilities.
problem Lack of unimodal output probabilities in recent ordinal regression models.
method Introduces a deep learning framework based on optimal transport loss and unimodal output distribution, inspired by the Proportional Odds model.
result Demonstrates improved performance and unimodal output probabilities on real-world datasets compared to existing methods.
Ordinal data is omnipresent in almost all multiuser-generated feedback - questionnaires, preferences etc. This paper investigates modelling of ordinal data with Gaussian restricted Boltzmann machines (RBMs). In particular, we present the model architecture, learning and inference procedures for both vector-variate and …
A new neural network model for ordinal regression.
problem Ordinal regression with non-proportional odds.
method Interpretable neural network for both continuous and discrete responses, training a non-linear neural network as a coefficient function.
result N3POM preserves interpretability while offering flexibility. We introduce two types of ordinal pattern dependence between time series. Positive (resp. negative) ordinal pattern dependence can be seen as a non-paramatric and in particular non-linear counterpart to positive (resp. negative) correlation. We show in an explorative study that both types of this dependence show up in …
A scalable algorithm improves AUC optimization for semi-supervised ordinal regression.
problem Optimizing AUC for semi-supervised ordinal regression with limited labeled data.
method Proposes QS3ORAO using quadruply stochastic gradients for scalable kernelized learning. result Converges to optimal solution at O(1/t) rate, demonstrating efficiency and effectiveness. The study explores how to infer the geometry of space forms from similarity comparisons.
problem Inferring the geometry of space forms from unreliable similarity measurements.
method Introducing ordinal capacity and spread, proving their relation to space form properties, and using statistical analysis of similarity measurements.
result The statistical behavior of ordinal spread variables can identify the underlying space form.
A popular approach for large scale data annotation tasks is crowdsourcing, wherein each data point is labeled by multiple noisy annotators. We consider the problem of inferring ground truth from noisy ordinal labels obtained from multiple annotators of varying and unknown expertise levels. Annotation models for ordinal…
The paper develops distribution-free methods for ordinal classification.
problem Constructing valid prediction sets for ordinal classification problems.
method Leveraging conformal prediction and multiple testing with FWER control.
result The proposed methods achieve satisfactory levels of marginal and class-specific conditional coverages.