We propose the nuclear norm penalty as an alternative to the ridge penalty for regularized multinomial regression. This convex relaxation of reduced-rank multinomial regression has the advantage of leveraging underlying structure among the response categories to make better predictions. We apply our method, nuclear pen…
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48 results for “multinomial outcomes”
New algorithm for maximizing revenue in multinomial logistic bandits.
problem Maximizing revenue in scenarios with multiple outcomes.
method MNL-UCB algorithm based on upper confidence bounds.
result Achieves regret with small dependency on constants.
Paper certifies intersection of minimum-volume confidence sets for multinomial outcomes.
problem Certifying intersection of minimum-volume confidence sets for multinomial outcomes.
method Exploits likelihood ordering to induce halfspace constraints, enabling adaptive geometric partitioning and computable bounds on p-values.
result Efficient and provably sound algorithm for certifying intersection, disjointness, or indeterminate result.
Random forest models predict CLABSI risk in hospital admissions, with static models performing similarly to dynamic ones.
problem Predicting CLABSI risk in hospital admissions using EHR data with competing risks.
method Comparison of static and dynamic random forest models for binary, multinomial, survival, and competing risks outcomes.
result Static and dynamic random forest models perform similarly in predicting CLABSI risk, with multinomial models having the lowest computation times.
Two algorithms achieve optimal regret with limited adaptivity in multinomial logistic bandits.
problem Achieving optimal regret with limited adaptivity in multinomial logistic bandits.
method Presented two algorithms, B-MNL-CB and RS-MNL, for batched and rarely-switching paradigms.
result Achieved regret with limited adaptivity.
A new method for optimizing stakes in a single event with multiple outcomes.
problem Maximizing expected log wealth in a single event with multiple outcomes.
method Using implicit state positions to derive the optimal stake formula.
result A compact formula and greedy algorithm for support selection.
New algorithms improve MPBART for HIV patient data.
problem Improving inference for multinomial outcomes in HIV patient data.
method Introduced two new algorithms for fitting MPBART.
result Better performance in MCMC convergence and predictive accuracy.
Improved regret bound for multinomial logistic bandits with non-linearity.
problem Maximizing rewards in multinomial logistic bandits with non-linear feedback.
method Extended the definition of to multinomial setting and proposed an efficient algorithm.
result Minimax-optimal regret bound of , improving over existing guarantees.
A new algorithm reduces the time and space complexity for multinomial logistic bandits.
problem High-dimensional feedback in multinomial logistic bandits makes existing algorithms inefficient.
method Integrates frequent directions matrix sketching into OFUL-MLogB to reduce time and space complexity.
result Achieves a regret bound of .
This paper studies the geometry of minimum-volume confidence sets for multinomial parameters.
problem Determining if minimum-volume confidence sets for multinomial outcomes are disjoint.
method Enumerating and covering the continuous regions of the exact p-value function to study the geometry of minimum-volume confidence sets.
result The geometry of minimum-volume confidence sets for multinomial parameters is studied, providing insights into their structure and properties.
Fused Multinomial Logistic Regression Utilizing Summary-Level External Machine-learning Informationstat.ME
Proposes a method to use external machine-learning predictions in multinomial logistic regression.
problem Improving statistical inference using summary-level external machine-learning predictions.
method Empirical-likelihood framework incorporating moment constraints from external nonparametric machine-learning predictions.
result Fused estimator achieves strict efficiency gain over primary-only estimator under mild conditions.
Improved online confidence bounds for multinomial logistic models in bandits.
problem Achieving optimal regret in multinomial logistic bandits with bounded parameters and outcomes.
method Deriving an improved online confidence bound and proposing OFU-MNL++ and OFU-MNL algorithms.
result Achieved variance-dependent optimal regret for MNL bandits.
Fast Maximum Likelihood Estimation and Supervised Classification for the Beta-Liouville Multinomialstat.ML
Efficiently models categorical data with low to medium class overlap, improving accuracy over standard distributions.
problem Poor parameter estimates and accuracy in multinomial and Dirichlet multinomial distributions when assumptions are violated.
method Introduces Beta-Liouville multinomial distribution and efficient estimation methods.
result Beta-Liouville multinomial outperforms standard distributions on two out of four datasets.
We combine fine-grained spatially referenced census data with the vote outcomes from the 2016 US presidential election. Using this dataset, we perform ecological inference using distribution regression (Flaxman et al, KDD 2015) with a multinomial-logit regression so as to model the vote outcome Trump, Clinton, Other / …
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…
The paper studies causal effects of multiple treatments in healthcare databases with rare outcomes.
problem Estimating causal effects of multiple treatments in healthcare databases with rare outcomes.
method The paper designs three sets of simulations and compares the operating characteristics of three types of methods: Bayesian Additive Regression Trees (BART), regression adjustment on multivariate spline of generalized propensity scores (RAMS), and inverse probability of treatment weighting (IPTW) with multinomial logistic regression or generalized boosted models.
result BART and RAMS provide lower bias and mean squared error compared to IPTW methods.
Study on inequalities for multinomial variables.
problem Understanding concentration inequalities for multinomial variables.
method Investigation of Dirichlet and Multinomial random variables.
result Results on concentration inequalities for multinomial variables.
PIANO speeds up multinomial logistic regression solving.
problem Handling large datasets and many classes in logistic regression.
method Parallel iterative algorithm based on Majorization Minimization.
result PIANO converges to a stationary point of Multinomial and Sparse Multinomial Logistic Regression.
Log-concavity proven for multinomial likelihoods under specific constraints.
problem Log-concavity of multinomial likelihoods under interval censoring constraints.
method Proved log-concavity by showing M-convex subsets of the discrete simplex.
result Likelihood function is completely log-concave.
To model categorical response variables given their covariates, we propose a permuted and augmented stick-breaking (paSB) construction that one-to-one maps the observed categories to randomly permuted latent sticks. This new construction transforms multinomial regression into regression analysis of stick-specific binar…
New method tests risk measures for various distortions.
problem Testing risk measures for different distortions.
method Stratification and randomization of risk levels.
result Method performs well in numerical case studies.
The sparse group lasso optimization problem is solved using a coordinate gradient descent algorithm. The algorithm is applicable to a broad class of convex loss functions. Convergence of the algorithm is established, and the algorithm is used to investigate the performance of the multinomial sparse group lasso classifi…
Many practical modeling problems involve discrete data that are best represented as draws from multinomial or categorical distributions. For example, nucleotides in a DNA sequence, children's names in a given state and year, and text documents are all commonly modeled with multinomial distributions. In all of these cas…
Sparse multinomial logistic regression for multiclass classification with feature selection.
problem High-dimensional multiclass classification with a focus on sparse models.
method Penalized maximum likelihood with complexity penalty, feature selection using group Lasso and Slope classifiers.
result Achievement of minimax order in both small and large number of classes regimes.
Don't Throw Away Your Beams: Improving Consistency-based Uncertainties in LLMs via Beam Searchstat.ML
Beam search improves UQ in LLMs by reducing duplicates and variance.
problem Peaked distributions in multinomial sampling lead to duplicates and high variance in uncertainty estimates.
method Employ beam search to generate candidates for consistency-based UQ, providing a theoretical lower bound and empirical evaluation.
result Beam search achieves smaller error than multinomial sampling, leading to state-of-the-art UQ performance.
New algorithm reduces switching costs in multinomial logit bandit problems.
problem Minimizing switching costs in multinomial logit bandit problems.
method Proposed AT-DUCB and FH-DUCB algorithms with low assortment switching costs.
result AT-DUCB and FH-DUCB algorithms achieve almost optimal minimax regret with low switching costs.
The paper proves asymptotic normality for multinomial logistic regression on null covariates.
problem Classical asymptotic normality results fail in high-dimensional multinomial logistic models.
method Developed asymptotic normality and chi-square results for multinomial logistic MLE on null covariates.
result Validated new methodology to test feature significance in high-dimensional classification problems.
Deviance-style normalization for sparse, jointly overdispersed count matrices
problem Jointly overdispersed count matrices
method Dirichlet-multinomial deviance residualization
result Preserves exact sparsity, evaluates in constant time, recovers multinomial residual
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.
This article proposes Multinomial Probit Bayesian Additive Regression Trees (MPBART) as a multinomial probit extension of BART - Bayesian Additive Regression Trees (Chipman et al (2010)). MPBART is flexible to allow inclusion of predictors that describe the observed units as well as the available choice alternatives. T…
Enhances random forest consistency and introduces DMRF for improved performance.
problem Improving the consistency and efficiency of random forest algorithms.
method Strengthened proof methods and propose DMRF algorithm.
result DMRF achieves better theoretical and experimental performance than previous variants.
Efficient RL algorithm for multinomial logistic MDPs with provable guarantees.
problem Model-based RL for episodic MDPs with unknown transition probabilities.
method Upper confidence bound-based algorithm for exploration-exploitation balance.
result Achieves regret bound for multinomial logistic models.
The paper proposes an efficient method to scale Bayesian inference for mixed multinomial logit models to very large datasets.
problem Efficiency in Bayesian inference for mixed multinomial logit models on large datasets.
method Amortized Variational Inference with stochastic backpropagation, automatic differentiation, and GPU acceleration.
result The proposed method achieves significant computational speedups over traditional methods for large datasets.
A new model uses neural networks for consistent discrete choice analysis.
problem Difficulties in specifying utility functions in RUM models.
method Alternative-Specific and Shared weights Neural Network (ASS-NN) model.
result ASS-NN provides consistent outcomes without specifying utility form.
Proposes a new model for context-dependent decision-making.
problem Constant preference parameters in decision models are too rigid.
method Introduces Context-aware Bayesian mixed multinomial logit model using neural networks.
result Models context-dependent intra-respondent heterogeneity effectively.
A Class of Conjugate Priors for Multinomial Probit Models which Includes the Multivariate Normal Onestat.ME
New conjugate priors improve Bayesian inference for multinomial probit models.
problem Lack of tractable conjugate priors for efficient Bayesian inference in multinomial probit models.
method Unified skew-normal (SUN) distributions as conjugate priors, leading to improved posterior inference and classification.
result Improved computational methods for posterior inference and classification, especially in high dimensions.
A model selection approach for clustering a multinomial sequence with non-negative factorizationstat.ML
We consider a problem of clustering a sequence of multinomial observations by way of a model selection criterion. We propose a form of a penalty term for the model selection procedure. Our approach subsumes both the conventional AIC and BIC criteria but also extends the conventional criteria in a way that it can be app…
Count data take on non-negative integer values and are challenging to properly analyze using standard linear-Gaussian methods such as linear regression and principal components analysis. Generalized linear models enable direct modeling of counts in a regression context using distributions such as the Poisson and negati…
New method calculates DMN log-likelihood faster.
problem Precise and fast computation of DMN log-likelihood.
method Derived a closed form expression using gamma function properties.
result Closed form calculation is faster with same accuracy.
Comparison data arises in many important contexts, e.g. shopping, web clicks, or sports competitions. Typically we are given a dataset of comparisons and wish to train a model to make predictions about the outcome of unseen comparisons. In many cases available datasets have relatively few comparisons (e.g. there are on…
Hierarchical mixtures of Unigram models for short text clustering: The role of Beta-Liouville priorsstat.ML
Paper introduces a new text clustering model using Beta-Liouville priors.
problem Clustering short text data.
method Develops a hierarchical mixture model with Beta-Liouville priors for short text clustering.
result The Beta-Liouville distribution offers a more flexible correlation structure for short text clustering.
The paper develops approximations for Pearson's chi-square statistic and applies them to confidence intervals.
problem Finding confidence intervals for strictly convex functions of discrete distribution weights.
method Non-asymptotic local normal approximation for multinomial probabilities, deriving bounds and coupling inequalities.
result Developed methods to find confidence intervals for negative entropy of discrete distributions.
Sigma-Pi-Sigma neural networks (SPSNNs) as a kind of high-order neural networks can provide more powerful mapping capability than the traditional feedforward neural networks (Sigma-Sigma neural networks). In the existing literature, in order to reduce the number of the Pi nodes in the Pi layer, a special multinomial P_…
Proved a combinatorial conjecture in machine learning.
problem None explicitly stated in the abstract.
method Binomial and multinomial sums identities.
result Proved a combinatorial conjecture.
FJS method improves multinomial classification accuracy.
problem Improving multinomial classification accuracy under dataset shift.
method Derive FJS representation and propose alternative methods.
result Factorizable joint shift is not fully identifiable without additional assumptions.
The paper tackles learning mixtures of two multinomial logits, showing identifiability and presenting an algorithm.
problem Learning an arbitrary mixture of two multinomial logits.
method Reduction to solving a system of univariate quartic equations, followed by an algorithm using polynomial and linear samples.
result Identifiability of the mixture models may only fail on an algebraic variety of negligible measure.
New method for epidemic model inference using multinomial approximations.
problem Inference in stochastic epidemic models with partial observations.
method Recursive multinomial approximations to integrate over unobserved variables.
result Accuracy demonstrated through real and simulated data.
New test for comparing high-dimensional text data.
problem Testing equality of multinomial distributions in high dimensions.
method Proposed a test statistic with asymptotic normality under null.
result Achieves optimal detection boundary across parameter space.