A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
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 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…
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…
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…
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_…
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…
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…
Despite the impressive performance of random forests (RF), its theoretical properties have not been thoroughly understood. In this paper, we propose a novel RF framework, dubbed multinomial random forest (MRF), to analyze the \emph{consistency} and \emph{privacy-preservation}. Instead of deterministic greedy split rule…
As datasets capturing human choices grow in richness and scale -- particularly in online domains -- there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity, and Luce's choice axiom. In this work we introduce the Pairwise Choice Markov Cha…
In this paper we purpose a blockwise descent algorithm for group-penalized multiresponse regression. Using a quasi-newton framework we extend this to group-penalized multinomial regression. We give a publicly available implementation for these in R, and compare the speed of this algorithm to a competing algorithm --- w…
Paper develops Bayesian inference for discrete-choice mnp models with Gaussian priors.
problem Estimating parameters of discrete-choice multinomial probit models with Gaussian priors.
method Adapts Fasano and Durante's results to a specific mnp model with zero mean and independent Gaussian priors, simplifying posterior distribution parameters and providing a new variational algorithm.
result Simplified expressions for posterior distribution parameters and a novel variational algorithm.