Related papers: Robust Numerical Methods for Nonlinear Regression

Improvement of time series forecasting accuracy through combining multiple models is an important as well as a dynamic area of research. As a result, various forecasts combination methods have been developed in literature. However, most of…

For many nonlinear Bayesian state estimation problems, the posterior recursion is not analytically tractable, leading to algorithms that are influenced by numerical approximation errors. These algorithms depend on parameters that affect the…

We propose an active-learning method for nonlinear minimax regression. Given a nonlinear function that can be arbitrarily evaluated over a compact set, we fit a surrogate model, such as a feedforward neural network, by minimizing the…

A biomechanical model often requires parameter estimation and selection in a known but complicated nonlinear function. Motivated by observing that data from a head-neck position tracking system, one of biomechanical models, show…

A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…

Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…

Likelihood-free approaches are appealing for performing inference on complex dependence models, either because it is not possible to formulate a likelihood function, or its evaluation is very computationally costly. This is the case for…

Ordinary least square (OLS), maximum likelihood (ML) and robust methods are the widely used methods to estimate the parameters of a linear regression model. It is well known that these methods perform well under some distributional…

Methods for reasoning under uncertainty are a key building block of accurate and reliable machine learning systems. Bayesian methods provide a general framework to quantify uncertainty. However, because of model misspecification and the use…

Reliable predictions from systems biology models require knowing whether parameters can be estimated from available data, and with what certainty. Identifiability analysis reveals whether parameters are learnable in principle (structural…

Random graph models are widely used to understand network properties and graph algorithms. Key to such analyses are the different parameters of each model, which affect various network features, such as its size, clustering, or degree…

In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…

Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…

High-dimensional predictive models, those with more measurements than observations, require regularization to be well defined, perform well empirically, and possess theoretical guarantees. The amount of regularization, often determined by…

Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…

We address the tracking problem for a class of uncertain non-affine nonlinear systems with high relative degrees, performing non-repetitive tasks. We propose a rigorously proven, robust adaptive learning control scheme that relies on a…

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…

Real-life mobile phone data may contain noisy instances, which is a fundamental issue for building a prediction model with many potential negative consequences. The complexity of the inferred model may increase, may arise overfitting…

Accurate knowledge of the state variables in a dynamical system is critical for effective control, diagnosis, and supervision, especially when direct measurements of all states are infeasible. This paper presents a novel approach to…

In the context of computer models, calibration is the process of estimating unknown simulator parameters from observational data. Calibration is variously referred to as model fitting, parameter estimation/inference, an inverse problem, and…