Categorical d-separation criterion simplifies probability graph analysis.
problem Detecting causal relationships in probability distributions.
method Introducing categorical definitions for causal models and d-separation.
result Abstract version of d-separation criterion applies to various probability theories.
The paper compares one-hot encoding to Naïve Bayes for categorical variables.
problem Incorrect one-hot encoding affects Naïve Bayes performance.
method Mathematical and experimental analysis of PoB vs. categorical Naïve Bayes.
result Posterior probabilities are usually greater in the PoB case, but agree on the maximum a posteriori class label.
A framework estimates categorical distributions under constraints, ensuring generality and uniqueness.
problem Estimating categorical distributions summarizing sample data under marginal constraints.
method Theoretical framework + Iterative Proportional Fitting (IPF) to estimate the distribution.
result A unique categorical distribution of Maximum Entropy under marginal constraints exists and is estimated.
Efficient algorithm for Bayesian networks reduces marginal probability distribution computation.
problem Exact computation of marginal probability distribution is NP-hard for categorical variables in Bayesian networks.
method Divide-and-conquer approach exploiting graphical properties of Bayesian networks.
result Novel algorithm outperforms state-of-the-art methods in classification and cancer subtype identification.
A method for diffusion on probability simplex for generative models.
problem Tension between continuous and discrete data in diffusion models.
method Proposes using softmax function applied to Ornstein-Uhlenbeck Process on probability simplex.
result Method extends to bounded image generation.
Researchers study the normalizing constant of a continuous categorical distribution.
problem Understanding the normalizing constant of the continuous categorical distribution.
method Characterize numerical behavior and present theoretical and methodological advances.
result The normalizing constant can be written in closed form using elementary functions.
A new gradient estimator for categorical distributions reduces bias and variance.
problem Intractability of gradients for categorical distributions in discrete latent variable models.
method CatLog-Derivative trick and IndeCateR gradient estimator.
result IndeCateR reduces bias and variance of gradients for categorical distributions.
A new method for categorical variational inference using discrete normalizing flows.
problem Challenges in optimizing variational approximations for discrete latent variables.
method Differentiable reparameterization using a mixture of discrete normalizing flows.
result Improves optimization of evidence lower bound and reduces sensitivity to hyperparameters.
The problem of categorical data analysis in high dimensions is considered. A discussion of the fundamental difficulties of probability modeling is provided, and a solution to the derivation of high dimensional probability distributions based on Bayesian learning of clique tree decomposition is presented. The main contr…
AdOBEst-LDP improves privacy-preserving frequency estimation for categorical data.
problem Estimating categorical distributions online while preserving privacy.
method AdOBEst-LDP uses adaptive randomized response mechanism to enhance future data utility.
result AdOBEst-LDP selects optimal subset for LDP mechanism with high probability.
The paper derives a formula for factorizing categorical data to improve Bayes classifiers.
problem Improving the accuracy of Bayes classifiers by effectively factoring multidimensional data.
method Derives an explicit formula for calculating the marginal likelihood of a factorized categorical dataset.
result The derived formula can be used to select the best factorization for constructing a Bayes classifier.
Neural networks utilize the softmax as a building block in classification tasks, which contains an overconfidence problem and lacks an uncertainty representation ability. As a Bayesian alternative to the softmax, we consider a random variable of a categorical probability over class labels. In this framework, the prior …
The Gumbel-max trick and its extensions simplify sampling from categorical distributions in machine learning.
problem Sampling from categorical distributions with unnormalized probabilities.
method Extensions of the Gumbel-max trick for various applications.
result Simplified and efficient methods for sampling and gradient estimation.
Applied Data Scientists throughout various industries are commonly faced with the challenging task of encoding high-cardinality categorical features into digestible inputs for machine learning algorithms. This paper describes a Bayesian encoding technique developed for WeWork's lead scoring engine which outputs the pro…
Neural framework for conditional OT maps learns from categorical and continuous variables.
problem Learning conditional optimal transport maps between complex distributions.
method Hypernetwork generates adaptive transport layer parameters based on conditioning variables.
result Our method outperforms simpler conditioning methods in comprehensive ablation studies.
A new method for Gaussian process regression with categorical inputs.
problem Challenges in building a predictive and computationally efficient Gaussian process with categorical inputs.
method Distributional encoding based on maximum mean discrepancy and Wasserstein distance.
result State-of-the-art predictive performance on various datasets.
We propose a new model for supervised learning to rank. In our model, the relevance labels are assumed to follow a categorical distribution whose probabilities are constructed based on a scoring function. We optimize the training objective with respect to the multivariate categorical variables with an unbiased and low-…
SFM matches flows on statistical manifolds for better discrete generation.
problem Discrete generation on statistical manifolds with strong prior assumptions.
method Statistical Flow Matching (SFM) on manifold of categorical distributions using Fisher information metric.
result SFM achieves higher sampling quality and likelihood than other models.
Categorical variables are a natural choice for representing discrete structure in the world. However, stochastic neural networks rarely use categorical latent variables due to the inability to backpropagate through samples. In this work, we present an efficient gradient estimator that replaces the non-differentiable sa…
Wasserstein gradient boosting predicts probability distributions for supervised learning.
problem Distribution-valued supervised learning where outputs are probability distributions.
method Fits a new weak learner to Wasserstein gradients of loss functionals of probability distributions.
result Superior performance in probabilistic prediction compared to existing methods.
This work assesses DNNs for estimating conditional probabilities.
problem Lack of uncertainty characterization in DNNs for probabilistic applications.
method Investigates DNNs' ability to estimate conditional probabilities using synthetic and real-world datasets.
result DNNs' precision in estimating conditional probabilities is influenced by probability density and inter-categorical sparsity.
Unified discrete diffusion for categorical data simplifies training and sampling.
problem Training and sampling in discrete diffusion models for categorical data.
method Mathematical simplifications and elegant unification of discrete-time and continuous-time discrete diffusion.
result Unified Simplified Discrete Denoising Diffusion (USD3) outperforms SOTA baselines.
This paper generalizes Moody's correlated binomial default distribution for homogeneous (exchangeable) credit portfolio, which is introduced by Witt, to the case of inhomogeneous portfolios. As inhomogeneous portfolios, we consider two cases. In the first case, we treat a portfolio whose assets have uniform default cor…
Geometric Variational Inference improves efficiency in complex probability distributions.
problem Efficiently accessing information in non-linear and high-dimensional probability distributions.
method Geometric Variational Inference (geoVI) uses Riemannian geometry and the Fisher information metric to construct a coordinate transformation.
result geoVI provides a more efficient variational approximation by a normal distribution, demonstrated on various problems.
AdaCat improves density estimation and planning in autoregressive models.
problem Efficiently modeling sharp density changes in continuous data.
method Adaptive Categorical Discretization (AdaCat) for autoregressive models.
result Improves density estimation and planning in various data types.
New framework detects outliers in non-IID categorical data.
problem Existing outlier detection methods fail in non-IID data.
method Value-value graph-based representation and outlierness propagation.
result Significant improvement in AUC on complex data sets.
A new method for optimizing models with categorical variables using diffusion.
problem Optimizing models with categorical variables, especially in discrete distributions.
method Introducing ReDGE, a diffusion-based soft reparameterization method for categorical distributions.
result ReDGE consistently matches or outperforms existing gradient-based methods in experiments.
We consider the problem of sequential learning from categorical observations bounded in [0,1]. We establish an ordering between the Dirichlet posterior over categorical outcomes and a Gaussian posterior under observations with N(0,1) noise. We establish that, conditioned upon identical data with at least two observatio…
ESRLCM clusters similar responses, more broadly than traditional models.
problem Clustering multivariate categorical data with common response patterns.
method Bayesian Equivalence Set Restricted Latent Class Model (ESRLCM).
result ESRLCM identifies clusters with similar item response probabilities.
A new method generates mixed-type features in tabular data with improved realism and accuracy.
problem Generating mixed-type features combining discrete and continuous data is challenging.
method A cascaded approach: first generates low-resolution categorical and coarse numerical features, then uses these in a high-resolution flow matching model.
result The model significantly improves detection scores, generating more realistic samples and capturing distributional details.
Generative model for high-dimensional categorical data using Gaussian-Dirichlet fields.
problem Efficiently modeling and predicting high-dimensional categorical data.
method Combines Dirichlet and Gaussian processes for spatio-temporal modeling.
result Model accurately approximates categorical data in unobserved locations.
CADM proposes a cluster-specific distance metric for categorical data clustering.
problem Inadequate distance metrics for categorical data, especially varying within clusters.
method Cluster-customized adaptive distance metric for categorical data.
result Achieved competitive performance in categorical data clustering.
UNTIE learns representations of coupled categorical data.
problem Challenges in learning from unlabeled categorical data with complex couplings.
method UNTIE approach for unsupervised representation learning of heterogeneous couplings.
result UNTIE significantly improves categorical data representations on 25 diverse datasets.
Distributional approaches to value-based reinforcement learning model the entire distribution of returns, rather than just their expected values, and have recently been shown to yield state-of-the-art empirical performance. This was demonstrated by the recently proposed C51 algorithm, based on categorical distributiona…
New RL algorithm minimizes distributional learning error.
problem Improving distributional reinforcement learning for better error minimization.
method Proposes a new model-based algorithm with theoretical minimax optimality.
result Proves minimax optimality for approximating return distributions.
Paper introduces new methods for modeling categorical data.
problem Training generative models on categorical data like text and segmentation.
method Argmax Flows and Multinomial Diffusion models.
result Models outperform existing methods in log-likelihood.
Quantum probability theory reveals hidden structure in joint probability distributions.
problem Understanding hidden structure in joint probability distributions.
method Modeling joint probability distributions as density operators and applying partial trace.
result Decoding extra information in reduced density operators that captures subsystem interactions.
Multivariate categorical data occur in many applications of machine learning. One of the main difficulties with these vectors of categorical variables is sparsity. The number of possible observations grows exponentially with vector length, but dataset diversity might be poor in comparison. Recent models have gained sig…
Paper examines trade/no trade patterns in illiquid stocks, highlighting effects of varying zero returns probabilities.
problem Detecting long-run trade/no trade effects in illiquid stocks with varying zero returns probabilities.
method Proposes a framework considering constant and time-varying zero returns probabilities, analyzing trade/no trade categorical sequences.
result Long-run trade/no trade effects may be spuriously detected in presence of non-constant zero returns probabilities.
Posterior conformal prediction improves prediction interval validity for subgroups.
problem Marginal and conditional prediction interval validity for subgroups.
method Modeling conditional nonconformity score distribution as a mixture of cluster distributions.
result PCP produces tighter prediction intervals, especially for well-represented clusters.
A method for representing and comparing categorical trajectories using multivariate functional principal components.
problem Statistical description and comparison of categorical trajectories.
method Transforming categorical trajectories into binary indicator functions and applying multivariate functional principal components analysis.
result Consistent estimators of mean trajectories and covariance functions are obtained under weak regularity assumptions.
A new method uses Mean Field Games to optimize mixture models of Bernoulli and categorical distributions.
problem Optimizing parameters of finite mixture models of Bernoulli and categorical distributions.
method Mean Field Games theory applied to multi-population systems.
result The Mean Field Games approach provides a method to compute mixture model parameters.
Categorical distributions are ubiquitous in machine learning, e.g., in classification, language models, and recommendation systems. However, when the number of possible outcomes is very large, using categorical distributions becomes computationally expensive, as the complexity scales linearly with the number of outcome…
Gradient-based methods can be biased by distributional asymmetries in bivariate categorical data.
problem Gradient-based causal discovery methods can be biased by distributional asymmetries in bivariate categorical data.
method Identified and examined two distributional biases: Marginal Distribution Asymmetry and Marginal Distribution Shift Asymmetry. Employed two simple models to demonstrate and control these biases.
result Gradient-based methods can be biased by distributional asymmetries, and these biases can be controlled.
The paper proposes a test to determine the number of latent classes in ordinal categorical data.
problem Determining the correct number of latent classes in latent class models with ordinal categorical data.
method The test statistic centers the largest singular value of a normalized residual matrix by a simple sample-size adjustment.
result The test statistic converges to zero under the null hypothesis and exceeds a fixed positive constant under an under-fitted alternative.
Unified CI test for categorical and ordinal data maintains power in high dimensions.
problem Rapid degradation of statistical power in existing CI tests for high-dimensional conditioning variables.
method Unified CI test for categorical and ordinal data, maintaining reasonable calibration and power in high dimensions.
result Our test outperforms existing baselines in model testing and structure learning for dense directed graphical models.
Anomaly detection plays an important role in modern data-driven security applications, such as detecting suspicious access to a socket from a process. In many cases, such events can be described as a collection of categorical values that are considered as entities of different types, which we call heterogeneous categor…
In this work we present Discrete Attend Infer Repeat (Discrete-AIR), a Recurrent Auto-Encoder with structured latent distributions containing discrete categorical distributions, continuous attribute distributions, and factorised spatial attention. While inspired by the original AIR model andretaining AIR model's capabi…