Related papers: Statistical inference for a stochastic generalized…
The standard odds ratio of logistic regression is foundational but limited to individual explanatory variables. This work derives a multivariable odds ratio that applies to all the explanatory variables in all their combinations.
We develop a probabilistic characterisation of trajectorial expansion rates in non-autonomous stochastic dynamical systems that can be defined over a finite time interval and used for the subsequent uncertainty quantification in Lagrangian…
We study the problem of distributed adaptive estimation over networks where nodes cooperate to estimate physical parameters that can vary over both space and time domains. We use a set of basis functions to characterize the space-varying…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
We consider the homogeneous stochastic differential equation with unknown parameter to be estimated. We prove that the standard maximum likelihood estimate is strongly consistent under very mild conditions. There are also established the…
We develop a new continuous-time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models. The algorithm continuously updates the SDE model's parameters using an…
This paper describes how to convert a machine learning problem into a series of map-reduce tasks. We study logistic regression algorithm. In logistic regression algorithm, it is assumed that samples are independent and each sample is…
Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…
As the size of modern data sets exceeds the disk and memory capacities of a single computer, machine learning practitioners have resorted to parallel and distributed computing. Given that optimization is one of the pillars of machine…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…
In this article we consider the estimation of static parameters for partially observed diffusion process with discrete-time observations over a fixed time interval. In particular, we assume that one must time-discretize the partially…
To accurately reproduce measurements from the real world, simulators need to have an adequate model of the physical system and require the parameters of the model be identified. We address the latter problem of estimating parameters through…
Within the calibration of material models, often the numerical results of a simulation model $y$ are compared with the experimental measurements $y^*$. Usually, the differences between measurements and simulation are minimized using least…
Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. A more general class…
We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…
Spatial generalized linear mixed models (SGLMMs) are popular and flexible models for non-Gaussian spatial data. They are useful for spatial interpolations as well as for fitting regression models that account for spatial dependence, and are…
This paper presents a numerical method to implement the parameter estimation method using response statistics that was recently formulated by the authors. The proposed approach formulates the parameter estimation problem of It\^o drift…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…