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.
Novel simplex-valued distribution improves on existing models.
problem Limitations of existing simplex-valued distributions like Dirichlet.
method Introducing continuous categorical distribution.
result Continuous categorical resolves limitations of Dirichlet.
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.
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 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.
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.
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.
VAIOM models financial returns using continuous input and categorical output.
problem Modeling continuous, noisy, and heterogeneous financial data.
method VAIOM is a decoder-only Transformer that separates input representation from output likelihood.
result VAIOM models outperform fixed single-bar LightGBM baseline in both Test halves.
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…
Efficient optimisation of black-box problems that comprise both continuous and categorical inputs is important, yet poses significant challenges. We propose a new approach, Continuous and Categorical Bayesian Optimisation (CoCaBO), which combines the strengths of multi-armed bandits and Bayesian optimisation to select …
Paper introduces Categorical Normalizing Flows for better handling of categorical data.
problem Limited application of normalizing flows on categorical data due to lack of intrinsic order.
method Categorical Normalizing Flows use continuous transformations to model latent relations in categorical data, optimizing both continuous representation and model likelihood.
result GraphCNF, a permutation-invariant generative model, outperforms state-of-the-art on molecule generation.
We present a framework for learning disentangled and interpretable jointly continuous and discrete representations in an unsupervised manner. By augmenting the continuous latent distribution of variational autoencoders with a relaxed discrete distribution and controlling the amount of information encoded in each latent…
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.
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.
Researchers propose better probabilistic models for deep learning.
problem Using cross-entropy loss for non-categorical data.
method Introducing continuous-categorical distribution and proposing probabilistic alternatives.
result Potential for outperformance in deep learning models with proper probabilistic treatment.
A new method for Gaussian Processes handles mixed continuous and categorical inputs.
problem Modeling cross-correlations between continuous and categorical data.
method Low-Rank Correlation (LRC) method for Gaussian Processes with flexible rank approximation.
result LRC outperforms existing methods in estimating cross-correlations and predicting response surfaces.
Unified Bayesian Optimisation for mixed variables improves performance.
problem Efficient optimisation of problems with both categorical and continuous variables.
method Derive value proposals from the Expected Improvement criterion to optimise both categorical and continuous variables under a single acquisition metric.
result Unified approach significantly outperforms existing methods across mixed-variable tasks.
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.
Partition Tree estimates conditional densities for mixed continuous and categorical variables.
problem Estimating conditional densities for mixed data types.
method Tree-based framework modeling conditional distributions as piecewise-constant densities on adaptive partitions, minimizing conditional negative log-likelihood.
result Improved probabilistic prediction compared to CART-style trees and state-of-the-art methods.
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.
New GP kernel handles mixed-categorical data, improving model accuracy.
problem Improving Gaussian process models for mixed-categorical data.
method Extends continuous exponential kernels to handle mixed-categorical variables.
result The proposed GP model gives higher likelihood and smaller residual error.
Gryffin optimizes categorical variables in materials design, leveraging expert knowledge.
problem Optimizing categorical variables in complex design choices like molecule selection.
method Bayesian optimization with smooth approximations to categorical distributions, incorporating expert knowledge.
result Gryffin accelerates discovery of promising molecules and materials, highlighting relevant correlations.
We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We prove conditions for the asymptotic unbiasedness of the DP-GLM regression mean fu…
Bayesian optimisation tackles high-dimensional categorical and mixed search spaces.
problem Bayesian optimisation on high-dimensional categorical and mixed search spaces is challenging.
method Combining local optimisation with a tailored kernel design.
result Empirically outperforms current baselines in performance and computational costs.
A new model estimates mixed memberships for categorical data with weighted responses.
problem Limited applicability of existing GoM model to weighted categorical data.
method Proposes Weighted Grade of Membership (WGoM) model, relaxing distribution constraints.
result WGoM can describe any response matrix with finite distinct elements.
CARD models predict the distribution of continuous or categorical responses.
problem Uncertainty in predicting continuous or categorical responses.
method Combines denoising diffusion and conditional mean estimation.
result Outperforms state-of-the-art methods in conditional distribution prediction.
LDAO addresses imbalanced regression by learning local distribution structures.
problem Imbalanced regression with sparse target regions difficult for models.
method LDAO learns local distribution structures, models and samples from each, then merges.
result LDAO outperforms state-of-the-art methods on 45 imbalanced datasets.
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 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.
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…
Many real-world functions are defined over both categorical and category-specific continuous variables and thus cannot be optimized by traditional Bayesian optimization (BO) methods. To optimize such functions, we propose a new method that formulates the problem as a multi-armed bandit problem, wherein each category co…
Paper extends sparse alternatives to softmax for continuous domains, enabling efficient attention mechanisms.
problem Efficiently assigning zero probability to irrelevant categories in continuous domains.
method Extend alpha-entmax to continuous domains, introducing continuous-domain attention mechanisms.
result Continuous attention allows attending to time intervals and compact regions, improving text classification, machine translation, and visual question answering.
Paper develops a novel approach for classifying high-dimensional mixed data.
problem Handling datasets with both categorical and continuous variables of high dimensions.
method Location model with Gaussian conditional distributions, kernel smoothing for bandwidth choice, penalized likelihood estimation.
result Competitive performance of the proposed classifier demonstrated through simulations and real data.
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.
The variational autoencoder (VAE) is a generative model with continuous latent variables where a pair of probabilistic encoder (bottom-up) and decoder (top-down) is jointly learned by stochastic gradient variational Bayes. We first elaborate Gaussian VAE, approximating the local covariance matrix of the decoder as an o…
WE constructs GP kernels for mixed inputs using weighted EDMs.
problem Limitation of standard GP models in handling categorical variables.
method WEGP constructs kernel function using weighted EDMs for categorical inputs.
result WEGP improves GP model accuracy in both synthetic and real-world optimization problems.
New gradient estimators for discrete variables improve model training.
problem Training models with discrete latent variables is challenging due to high gradient variance.
method Introduced novel gradient estimators based on importance sampling and statistical couplings, extending to categorical variables.
result Proposed gradient estimators outperform previous methods in systematic experiments.
Improved vector quantization using Gaussian mixtures for better codebook utilization.
problem Training instability and information loss in discrete vector quantization.
method Generalized vector quantization with Gaussian mixture model and aggregated categorical posterior evidence lower bound.
result GM-VQ improves codebook utilization and reduces information loss without heuristics.
A hybrid model for Bayesian optimization handles mixed variables using MCTS for categorical and GP for continuous.
problem Optimizing functions with mixed variable types (continuous, integer, categorical).
method Merges MCTS for categorical and GP for continuous variables, integrates UCTS search strategy, and dynamically selects kernels.
result Hybrid models outperform traditional methods in Bayesian optimization.
SPlit optimizes dataset splitting for better model performance.
problem Improving model performance through optimal dataset splitting.
method Adapting Support Points (SP) algorithm for subsampling and categorical variables in a sequential nearest neighbor approach.
result SPlit significantly improves worst-case testing performance compared to random splitting.
Kendall transformation converts continuous data into categorical vectors for robust information theory.
problem Handling small number of observations and preserving ranking in continuous data.
method Kendall transformation converts ordered features into categorical vectors of pairwise order relations.
result Kendall transformation makes information theory methods applicable to continuous data robustly.
This paper develops sparse alternatives to continuous distributions, including new types of Gaussians and attention mechanisms.
problem Creating flexible continuous distributions with varying support for machine learning applications.
method Defining Ω-regularized prediction maps and Fenchel-Young losses for arbitrary domains, and deriving new types of Gaussians and attention mechanisms. result Sparse alternatives to continuous distributions, including deformed exponential families and β-Gaussians, are introduced. New methods tackle adversarial attacks on categorical sequences, improving model security.
problem Adversarial attacks on categorical sequence models, especially for money transactions and medical fraud.
method Two black-box adversarial attacks: Monte-Carlo and continuous relaxation methods.
result Generated adversarial sequences fool machine learning models but remain close to original ones.
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…
Earth observation embeddings can convert discrete biome maps into continuous representations that better capture ecological variation.
problem Biome maps impose categorical boundaries that compress continuous variation in biotic communities.
method Fit a linear classifier on Earth observation embeddings to predict biome labels.
result Continuous biome representation outperforms discrete biome labels for predicting species occurrence.
Neural network quantization has become an important research area due to its great impact on deployment of large models on resource constrained devices. In order to train networks that can be effectively discretized without loss of performance, we introduce a differentiable quantization procedure. Differentiability can…
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.