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.
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…
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…
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…
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.
Scaling multinomial logistic regression to datasets with very large number of data points and classes is challenging. This is primarily because one needs to compute the log-partition function on every data point. This makes distributing the computation hard. In this paper, we present a distributed stochastic gradient d…
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…
In this paper, we study different discrete data clustering methods, which use the Model-Based Clustering (MBC) framework with the Multinomial distribution. Our study comprises several relevant issues, such as initialization, model estimation and model selection. Additionally, we propose a novel MBC method by efficientl…
Dropout has been witnessed with great success in training deep neural networks by independently zeroing out the outputs of neurons at random. It has also received a surge of interest for shallow learning, e.g., logistic regression. However, the independent sampling for dropout could be suboptimal for the sake of conver…
Multinomial Logistic Regression is a well-studied tool for classification and has been widely used in fields like image processing, computer vision and, bioinformatics, to name a few. Under a supervised classification scenario, a Multinomial Logistic Regression model learns a weight vector to differentiate between any …
We introduce the author-topic model, a generative model for documents that extends Latent Dirichlet Allocation (LDA; Blei, Ng, & Jordan, 2003) to include authorship information. Each author is associated with a multinomial distribution over topics and each topic is associated with a multinomial distribution over words.…
Construction of tight confidence regions and intervals is central to statistical inference and decision making. This paper develops new theory showing minimum average volume confidence regions for categorical data. More precisely, consider an empirical distribution p generated from n iid real…
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…
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 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…
In latent Dirichlet allocation (LDA), topics are multinomial distributions over the entire vocabulary. However, the vocabulary usually contains many words that are not relevant in forming the topics. We adopt a variable selection method widely used in statistical modeling as a dimension reduction tool and combine it wi…
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 text classification tasks are known to be highly domain-dependent. Unfortunately, the availability of training data can vary drastically across domains. Worse still, for some domains there may not be any annotated data at all. In this work, we propose a multinomial adversarial network (MAN) to tackle the text clas…
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…
The paper proposes a method to test properties of the optimal assortment in multinomial logit models.
problem Uncertainty quantification for the optimal assortment in multinomial logit models.
method The paper proposes a novel inferential framework to test properties of the optimal assortment in multinomial logit models, reducing the problem to detecting the sign change point of marginal revenue gaps.
result The asymptotic normality of the marginal revenue gap estimator and the construction of a maximum statistic to detect the sign change point.
The logistic normal distribution has recently been adapted via the transformation of multivariate Gaus- sian variables to model the topical distribution of documents in the presence of correlations among topics. In this paper, we propose a probit normal alternative approach to modelling correlated topical structures. O…
We define a new method to estimate centroid for text classification based on the symmetric KL-divergence between the distribution of words in training documents and their class centroids. Experiments on several standard data sets indicate that the new method achieves substantial improvements over the traditional classi…
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…