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.
Two approaches improve parameter learning in various mixture models.
Detecting and recovering labels in binomial logistic mixtures is challenging due to an information gap.
A new tree model, GRST, improves option pricing without log-normality assumptions.
The paper models stock returns using -Gaussians and negative binomials.
Develops a model for RNA-seq data clustering.
Survival MDN uses invertible functions to speed up survival analysis models.
Paper optimizes clustering for multi-layer networks and discrete mixtures.
By developing data augmentation methods unique to the negative binomial (NB) distribution, we unite seemingly disjoint count and mixture models under the NB process framework. We develop fundamental properties of the models and derive efficient Gibbs sampling inference. We show that the gamma-NB process can be reduced …
We compare two statistical models of three binary random variables. One is a mixture model and the other is a product of mixtures model called a restricted Boltzmann machine. Although the two models we study look different from their parametrizations, we show that they represent the same set of distributions on the int…
The traditional Minkowski distances are induced by the corresponding Minkowski norms in real-valued vector spaces. In this work, we propose novel statistical symmetric distances based on the Minkowski's inequality for probability densities belonging to Lebesgue spaces. These statistical Minkowski distances admit closed…
The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process f…
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset of the sample to be dependent on the sample size, a feature not presented in a …
Count data, for example the number of observed cases of a disease in a city, often arise in the fields of healthcare analytics and epidemiology. In this paper, we consider performing regression on multivariate data in which our outcome is a count. Specifically, we derive log-likelihood functions for finite mixtures of …
Paper establishes universal lower bounds and optimal rates for clustering sub-exponential mixture models.
We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet distributions, Negative binomial regression, Poisson-Gamma hierarchical models, …
Develops Bayesian inference methods for gamma models.
The paper improves Fisher-Pitman tests for Poisson mixtures, detecting autism-related genes.
The study tightens bounds on binomial probabilities and minimums using KL-divergence.
Efficient Bayesian variable selection for binomial and negative binomial data.
We construct a binomial tree model fitting all moments to the approximated geometric Brownian motion. Our construction generalizes the classical Cox-Ross-Rubinstein, the Jarrow-Rudd, and the Tian binomial tree models. The new binomial model is used to resolve a discontinuity problem in option pricing.
Extends CRR model with q-binomial random walks for asset pricing.
We construct a binomial model for a guaranteed minimum withdrawal benefit (GMWB) rider to a variable annuity (VA) under optimal policyholder behaviour. The binomial model results in explicitly formulated perfect hedging strategies funded using only periodic fee income. We consider the separate perspectives of the insur…
Correction for Error estimates for binomial approximations of game options [math.PR/0607123]
In this paper, we develop a general theory of truncated inverse binomial sampling. In this theory, the fixed-size sampling and inverse binomial sampling are accommodated as special cases. In particular, the classical Chernoff-Hoeffding bound is an immediate consequence of the theory. Moreover, we propose a rigorous and…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let be an arbitrary distribution over an interval which is -close (in total variation distance) to an unknown probability distribution $…
Using techniques from the theories of convex polytopes, lattice paths, and indirect influences on directed manifolds, we construct continuous analogues for the binomial coefficients and the Catalan numbers. Our approach for constructing these analogues can be applied to a wide variety of combinatorial sequences. As an …
The theme in this paper is the recombining binomial tree to price American put option when the underlying stock follows constant elasticity of variance(CEV) process. Recombining nodes of binomial tree are decided from finite difference scheme to emulate CEV process and the tree has a linear complexity. Also it is deriv…
We introduce a Bayesian nonparametric regression model for data with multiway (tensor) structure, motivated by an application to periodontal disease (PD) data. Our outcome is the number of diseased sites measured over four different tooth types for each subject, with subject-specific covariates available as predictors.…
Transformer learns to estimate negative binomial parameters efficiently.
We construct algorithms via binomial approximations for computation of prices of game put options and obtain estimates of approximation errors.
In the present paper we show that the Binomial-tree approach for pricing, hedging, and risk assessment of Convertible bonds in the framework of the Tsiveriotis-Fernandes model has serious drawbacks. Key words: Convertible bonds, Binomial tree, Tsiveriotis-Fernandes model, Convertible bond pricing, Convertible bond Gree…
We present a consensus Monte Carlo algorithm that scales existing Bayesian nonparametric models for clustering and feature allocation to big data. The algorithm is valid for any prior on random subsets such as partitions and latent feature allocation, under essentially any sampling model. Motivated by three case studie…
The paper resolves a counterexample showing convergence of expected utility in binomial models.
We consider learning parameters of Binomial Hidden Markov Models, which may be used to model DNA methylation data. The standard algorithm for the problem is EM, which is computationally expensive for sequences of the scale of the mammalian genome. Recently developed spectral algorithms can learn parameters of latent va…
Improved concentration inequalities for sub-Weibull variables enhance statistical and machine learning applications.
We characterize the combinatorial structure of conditionally-i.i.d. sequences of negative binomial processes with a common beta process base measure. In Bayesian nonparametric applications, such processes have served as models for latent multisets of features underlying data. Analogously, random subsets arise from cond…
We justify and give error estimates for binomial approximations of game (Israeli) options in the Black--Scholes market with Lipschitz continuous path dependent payoffs which are new also for usual American style options. We show also that rational (optimal) exercise times and hedging self-financing portfolios of binomi…
This paper provides formulas for minimum cost super-hedging in a multi-asset binomial market.
Develops a new filtration for asset pricing models.
We extend the classical Cox-Ross-Rubinstein binomial model in two ways. We first develop a binomial model with time-dependent parameters that equate all moments of the pricing tree increments with the corresponding moments of the increments of the limiting Itô price process. Second, we introduce a new trinomial model i…
This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial processes, i.e., by processes with fixed size binary increments at sampling points. …
PSO optimizes model parameters in nonstandard distributions.
Closed-form pricing method for multi-asset options.
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in learning theory and generalization bounds for unbounded loss functions.
Proved a combinatorial conjecture in machine learning.
New framework for portfolio management using binomial markets and game theory.
Motivated by the need of the linking records across various databases, we propose a novel graphical model based classifier that uses a mixture of Poisson distributions with latent variables. The idea is to derive insight into each pair of hypothesis records that match by inferring its underlying latent rate of error us…
The study models credit risk using Merton's framework and binomial trees.