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This paper deals with some nonlinear problems which exponential and biexponential decays are involved in. A proof of the quasiconvexity of the error function in some of these problems of optimization is presented. This proof is restricted…
A new package for nonlinear least squares fitting is introduced in this paper. This package implements a recently developed algorithm that, for certain types of nonlinear curve fitting, reduces the number of nonlinear parameters to be…
In this paper we present an algorithm to fit data via exponentials when the error is measured using the max-norm. We prove the necesssary results to show that the algorithm will converge to the best approximation no matter the dataset.
Trust-region (TR) and adaptive regularization using cubics (ARC) have proven to have some very appealing theoretical properties for non-convex optimization by concurrently computing function value, gradient, and Hessian matrix to obtain the…
In this paper we consider the problem of maximizing the Area under the ROC curve (AUC) which is a widely used performance metric in imbalanced classification and anomaly detection. Due to the pairwise nonlinearity of the objective function,…
We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…
The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with latent variables. Many authors modified its simple design to fit more specific situations. For instance, the Expectation (E) step…
The estimation of parameters from data is a common problem in many areas of the physical sciences, and frequently used algorithms rely on sets of simulated data which are fit to data. In this article, an analytic solution for…
The success of reinforcement learning (RL) is fundamentally tied to having a reward function that accurately reflects the task objective. Yet, designing reward functions is notoriously time-consuming and prone to misspecification. To…
Curve fitting is a fundamental technique in engineering and scientific research, serving as a critical tool for extracting insights from data. This study explores the application of various statistical equations to estimate outcomes in…
We study the incremental knapsack problem, where one wishes to sequentially pack items into a knapsack whose capacity expands over a finite planning horizon, with the objective of maximizing time-averaged profits. While various…
Maximum consensus estimation plays a critically important role in robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify…
The relationship between demand and prices of a set of products can be modeled as a linear mapping from logarithmic price changes to logarithmic changes in demand. We consider the problem of estimating the coefficient matrix of this…
Many scientific and engineering applications require fitting regression models that are nonlinear in the parameters. Advances in computer hardware and software in recent decades have made it easier to fit such models. Relative to fitting…
We introduce \underline{F}actor-\underline{A}ugmented \underline{Ma}trix \underline{R}egression (FAMAR) to address the growing applications of matrix-variate data and their associated challenges, particularly with high-dimensionality and…
Deep heteroscedastic regression involves jointly optimizing the mean and covariance of the predicted distribution using the negative log-likelihood. However, recent works show that this may result in sub-optimal convergence due to the…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
Robust estimation is a crucial and still challenging task, which involves estimating model parameters in noisy environments. Although conventional sampling consensus-based algorithms sample several times to achieve robustness, these…
Stochastic-approximation gradient methods are attractive for large-scale convex optimization because they offer inexpensive iterations. They are especially popular in data-fitting and machine-learning applications where the data arrives in…