Improved image ranking model using ordinal distance metric learning and multidimensional scaling.
problem Ranking images based on known ranked images.
method Proposes an improved linear ordinal distance metric learning approach using multidimensional scaling.
result Demonstrates improved ranking performance and speed over the linear distance metric learning model.
Given a geodesic space (E, d), we show that full ordinal knowledge on the metric d-i.e. knowledge of the function D d : (w, x, y, z) → 1 d(w,x)≤d(y,z) , determines uniquely-up to a constant factor-the metric d. For a subspace En of n points of E, converging in Hausdorff distance to E, we construct a met…
Paper introduces novel distances for clustering ordinal time series.
problem Clustering ordinal time series with discrete response.
method Introduces two novel distances and fuzzy clustering algorithms.
result Fuzzy clustering algorithms accurately group series from similar stochastic processes.
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…
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.
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…
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…
Optimal bounds proven for ordinal embedding convergence rate.
problem Optimal bounds for ordinal embedding convergence rate in 1D.
method Utilized results from additive number theory and conducted computational experiments.
result Proved optimal bounds for convergence rate in 1D.
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.
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…
A new method clusters categorical data by learning their optimal order and distance.
problem Clustering categorical data lacks a well-defined metric space.
method Order distance metric learning for categorical data.
result Superior clustering accuracy on categorical and mixed datasets.
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.
The Wasserstein probability metric has received much attention from the machine learning community. Unlike the Kullback-Leibler divergence, which strictly measures change in probability, the Wasserstein metric reflects the underlying geometry between outcomes. The value of being sensitive to this geometry has been demo…
BinConv improves time series forecasting by preserving ordinal information in a classification framework.
problem Lack of ordinal information in existing classification-based time series forecasting methods.
method Cumulative Binary Encoding (CBE) and BinConv architecture.
result BinConv achieves superior performance in time series forecasting compared to existing methods.
The paper develops a Gaussian process model for predicting chemical efficacy.
problem Statistical methodologies for analyzing chemical databases are limited.
method Conditional Gaussian process models with Tanimoto distance and a scaling parameter.
result Predictive performance improves when accounting for chemical space correlation.
Algorithm learns nearest neighbor graph from noisy distance queries.
problem Learning nearest neighbor graph from noisy distance samples.
method Active algorithm to find graph with high probability, analyzing query complexity.
result Empirically and theoretically efficient, needing only O(n log(n)Delta^-2) queries.
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.
The paper introduces uncertainty estimates for embedding objects based on noisy triplet comparisons.
problem Learning from ordinal data without a distance metric.
method Bootstrap and Bayesian approaches to estimate uncertainty for embedding algorithms.
result Empirical uncertainty estimates are well-calibrated and useful for selecting parameters or quantifying uncertainty.
Paper proposes an unbiased classifier from triplet comparison data.
problem Learning a classifier from triplet comparison data.
method Empirical risk minimization framework with an unbiased estimator.
result The proposed method achieves better performance than baseline methods.
Optimizes risk assessment tools using mixed-integer programming.
problem Challenges in healthcare risk assessment due to label scarcity and asymmetric misclassification costs.
method Jointly optimizes scoring weights and category thresholds via mixed-integer programming (MIP).
result Prevents label-scarce category collapse and achieves more accurate risk categorization.
Ordinal embedding methods estimate perceptual scales from relative judgments.
problem Measuring subjective sensation using relative judgments.
method Ordinal embedding from machine learning applied to method of triads.
result Ordinal embedding allows estimating perceptual scales from few judgments, non-monotonous functions, and multi-dimensional scales.
A new perceptual adjustment query for metric learning reduces complexity in high-dimensional data.
problem Metric learning in high-dimensional data with limited human feedback.
method Inverted measurement scheme and two-stage estimator for PAQs.
result Sample complexity guarantees for the two-stage estimator of metric learning from PAQs.
New STH distance finds patterns in event timeseries without resampling.
problem Lack of efficient analysis methods for event and state timeseries.
method Define STE-ts, propose STH, leveraging both time and state duration.
result Improved precision and computation time compared to resampled metrics.
A diagonal metric sum_{i=1}^n g_{ii} dx_i^2 is termed Guichard_k if sum_{i=1}^{n-k}g_{ii}-sum_{i=n-k+1}^n g_{ii}=0. A hypersurface in R^{n+1} is isothermic_k if it admits line of curvature co-ordinates such that its induced metric is Guichard_k. Isothermic_1 surfaces in R^3 are the classical isothermic surfaces in R^3.…
SurvCORN predicts survival curves using conditional ordinal ranking networks.
problem Challenges in survival analysis with censored data.
method SurvCORN: Conditional Ordinal Ranking Neural Network.
result SurvCORN improves accuracy in predicting time-to-event outcomes.
Proposes a new deep ordinal classification model enforcing label uni-modality.
problem Deep ordinal classification with label consistency issues.
method Non-parametric uni-modality constraints via inequality constraints.
result Improves scalability and performance in ordinal classification tasks.
Adapts deep reinforcement learning to ordinal rewards.
problem Using numerical rewards in reinforcement learning has drawbacks; ordinal rewards offer an alternative.
method Develops a general approach to converting reinforcement learning algorithms to ordinal reward systems, including Ordinal Deep Q-Networks.
result Ordinal Deep Q-Networks perform comparably to numerical variants on engineered problems and better on simpler reward signals.
Proposes a new loss function for distributional learning.
problem Learning sparse and singular distributions.
method Entropy-regularized optimal transport and Fenchel duality.
result Geometric loss results in unconstrained convex objective functions.
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.
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.
Develops multi-task learning models for ordinal regression with heterogeneous data.
problem Tackling ordinal regression for heterogeneous, non-IID data.
method Sparse and deep multi-task learning approaches.
result Proposed MTOR models improve prediction performance.
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.
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.
Graph Convolutional Networks improve prosthetic sensation interpretation.
problem Improving neuroprosthetic performance and sensory information stability.
method Applied Graph Convolutional Networks (GCNs) to interpret neuronal spiking activity.
result GCN model achieved 73.5% performance on ordinal regression task.
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 …
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.
We propose a simple probabilistic model to explain the spatial structure of the rent distribution of housing market in city of Sapporo. Here we modify the mathematical model proposed by Gauvin et. al. Especially, we consider the competition between two distances, namely, the distance between house and center, and the d…
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.
Identifies feature relevance bounds for ordinal regression models.
problem Interpreting ordinal regression models is challenging due to variable dependencies.
method Identifies feature relevance bounds explicitly differentiating between strongly and weakly relevant features.
result Identification of feature relevance bounds for ordinal regression models.
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.
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.