arXiv research

New method for epidemic model inference using multinomial approximations.

We derive error estimates for multinomial approximations of American options in a multidimensional jump--diffusion Merton's model. We assume that the payoffs are Markovian and satisfy Lipschitz type conditions. Error estimates for such type of approximations were not obtained before. Our main tool is the strong approxi…

The paper develops approximations for Pearson's chi-square statistic and applies them to confidence intervals.

Efficient RL algorithm for multinomial logistic MDPs with provable guarantees.

The paper proposes an efficient method to scale Bayesian inference for mixed multinomial logit models to very large datasets.

New algorithm reduces reinforcement learning regret by adapting to interaction variability.

We give an exposition and numerical studies of upper hedging prices in multinomial models from the viewpoint of linear programming and the game-theoretic probability of Shafer and Vovk. We also show that, as the number of rounds goes to infinity, the upper hedging price of a European option converges to the solution of…

For the problem of multi-class linear classification and feature selection, we propose approximate message passing approaches to sparse multinomial logistic regression (MLR). First, we propose two algorithms based on the Hybrid Generalized Approximate Message Passing (HyGAMP) framework: one finds the maximum a posterio…

We develop an approximate formula for evaluating a cross-validation estimator of predictive likelihood for multinomial logistic regression regularized by an $\ell_1$-norm. This allows us to avoid repeated optimizations required for literally conducting cross-validation; hence, the computational time can be significantl…

Approximates large Random Forest models to save space.

We consider probabilistic multinomial probit classification using Gaussian process (GP) priors. The challenges with the multiclass GP classification are the integration over the non-Gaussian posterior distribution, and the increase of the number of unknown latent variables as the number of target classes grows. Expecta…

Paper introduces a new text clustering model using Beta-Liouville priors.

Efficiently models categorical data with low to medium class overlap, improving accuracy over standard distributions.

This paper presents a multinomial method for option pricing when the underlying asset follows an exponential Variance Gamma process. The continuous time Variance Gamma process is approximated by a discrete time Markov chain with the same firsts four cumulants. This approach is particularly convenient for pricing Americ…

The paper tackles learning mixtures of two multinomial logits, showing identifiability and presenting an algorithm.

New conjugate priors improve Bayesian inference for multinomial probit models.

DMNL bandits optimize assortment choices balancing relevance and diversity.

New algorithms improve MPBART for HIV patient data.

Generative Adversarial Networks (GAN) have limitations when the goal is to generate sequences of discrete elements. The reason for this is that samples from a distribution on discrete objects such as the multinomial are not differentiable with respect to the distribution parameters. This problem can be avoided by using…

We improve MoE models for classification with rigorous guarantees and practical methods.

Study on inequalities for multinomial variables.

A new algorithm reduces the time and space complexity for multinomial logistic bandits.

We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black--Scholes (BS) market converge to the corresponding quantities for similar American options in the multidimensional BS market with path dependent payoffs. In comparison to previous papers we conside…

Under the Fundamental Review of the Trading Book (FRTB) capital charges for the trading book are based on the coherent expected shortfall (ES) risk measure, which show greater sensitivity to tail risk. In this paper it is argued that backtesting of expected shortfall - or the trading book model from which it is calcula…

We improve Gaussian copula models for imputing mixed data types with precise approximations.

This paper studies the geometry of minimum-volume confidence sets for multinomial parameters.

New algorithms reduce regret in reinforcement learning with MNL approximations.

Optimal design for multinomial logit models improves assortment selection efficiency.

PIANO speeds up multinomial logistic regression solving.

Log-concavity proven for multinomial likelihoods under specific constraints.

BEGIN network models binary data without parametric assumptions.

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…

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…

The paper proposes a method to test properties of the optimal assortment in multinomial logit models.

New method tests risk measures for various distortions.

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…

Study optimizes product assortment for retailers with repeated exposures and patience costs.

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.

The abstract reviews models for analyzing count data.

Beam search improves UQ in LLMs by reducing duplicates and variance.

Two algorithms achieve optimal regret with limited adaptivity in multinomial logistic bandits.

New algorithm reduces switching costs in multinomial logit bandit problems.

The paper proves asymptotic normality for multinomial logistic regression on null covariates.

FisherSFT selects informative examples to fine-tune LLMs efficiently.

Deviance-style normalization for sparse, jointly overdispersed count matrices

Paper introduces new methods for modeling categorical data.

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…