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Ordinal response model is a popular and commonly used regression for ordered categorical data in a wide range of fields such as medicine and social sciences. However, it is empirically known that the existence of ``outliers'', combinations…
This study proposes an interpretable neural network-based non-proportional odds model (N$^3$POM) for ordinal regression. N$^3$POM is different from conventional approaches to ordinal regression with non-proportional models in several ways:…
A probabilistic expert system emulates the decision-making ability of a human expert through a directional graphical model. The first step in building such systems is to understand data generation mechanism. To this end, one may try to…
Prior work has shown that causal structure can be uniquely identified from observational data when these follow a structural equation model whose error terms have equal variances. We show that this fact is implied by an ordering among…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
In this paper we propose a new methodology to represent the results of the robust ordinal regression approach by means of a family of representative value functions for which, taken two alternatives $a$ and $b$, the following two conditions…
Probabilistic conditioning is concerned with the identification of a distribution of a random variable $X$ given a random variable $Y$. It is a cornerstone of scientific and engineering applications where modeling uncertainty is key. This…
Many variables of interest in clinical medicine, like disease severity, are recorded using discrete ordinal categories such as normal/mild/moderate/severe. These labels are used to train and evaluate disease severity prediction models.…
The size and complexity of software and hardware systems have significantly increased in the past years. As a result, it is harder to guarantee their correct behavior. One of the most successful methods for automated verification of…
Biplot Methods allow for the simultaneous representation of individuals and variables of a data matrix. For Binary or Nominal data, Logistic biplots have been recently developed to extend the classical linear representations for continuous…
The recent wide adoption of Electronic Medical Records (EMR) presents great opportunities and challenges for data mining. The EMR data is largely temporal, often noisy, irregular and high dimensional. This paper constructs a novel ordinal…
We derive some simple relations that demonstrate how the posterior convergence rate is related to two driving factors: a "penalized divergence" of the prior, which measures the ability of the prior distribution to propose a nonnegligible…
This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information is unknown and can depend on both predictors and…
Ordinal Patterns are a time-series data analysis tool used as a preliminary step to construct the Permutation Entropy which itself allows the same characterization of dynamics as chaotic or regular as more theoretical constructs such as the…
Paired comparison data, where users evaluate items in pairs, play a central role in ranking and preference learning tasks. While ordinal comparison data intuitively offer richer information than binary comparisons, this paper challenges…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
Simulating longitudinal data from specified marginal structural models is a crucial but challenging task for evaluating causal inference methods and informing study design. While data generation typically proceeds in a fully conditional…
Ordered Weighted $L_{1}$ (OWL) regularized regression is a new regression analysis for high-dimensional sparse learning. Proximal gradient methods are used as standard approaches to solve OWL regression. However, it is still a burning issue…
The Poisson distribution is the default choice of likelihood for probabilistic models of count data. However, due to the equidispersion contraint of the Poisson, such models may have predictive uncertainty that is artificially inflated.…