Does correction for guessing improve the realism in absolute and relative frequency judgements?

The present study investigated the effects of three factors on the level of realism in frequency judgements. These factors were: Instruction (No correction for guessing/Correction for guessing), Format (whether the frequency judgements were made in terms of absolute numbers or in percent) and Difficulty level (easy/hard set of questions). All three factors were found to have a significant effect on the level of the frequency judgements and their realism. In addition, there were no interaction effects. The results suggest that the level and the realism of frequency judgements are both affected by different factors. Correction for guessing improved the realism in frequency judgements, however, only on the set of easy questions and markedly only in the relative format

Recovery of primal solution in dual subgradient schemes

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007.Includes bibliographical references (p. 97-99).In this thesis, we study primal solutions for general optimization problems. In particular, we employ the subgradient method to solve the Lagrangian dual of a convex constrained problem, and use a primal-averaging scheme to obtain near-optimal and near-feasible primal solutions. We numerically evaluate the performance of the scheme in the framework of Network Utility Maximization (NUM), which has recently drawn great research interest. Specifically for the NUM problems, which can have concave or nonconcave utility functions and linear constraints, we apply the dual-based decentralized subgradient method with averaging to estimate the rate allocation for individual users in a distributed manner, due to its decomposability structure. Unlike the existing literature on primal recovery schemes, we use a constant step-size rule in view of its simplicity and practical significance. Under the Slater condition, we develop a way to effectively reduce the amount of feasibility violation at the approximate primal solutions, namely, by increasing the value initial dual iterate; moreover, we extend the established convergence results in the convex case to the more general and realistic situation where the objective function is convex. In particular, we explore the asymptotical convergence properties of the averaging sequence, the tradeoffs involved in the selection of parameter values, the estimation of duality gap for particular functions, and the bounds for the amount of constraint violation and value of primal cost per iteration. Numerical experiments performed on NUM problems with both concave and nonconcave utility functions show that, the averaging scheme is more robust in providing near-optimal and near-feasible primal solutions, and it has consistently better performance than other schemes in most of the test instances.by Jing Ma.S.M

Convergent upper bounds in global minimization with nonlinear equality constraints

We address the problem of determining convergent upper bounds in continuous non-convex global minimization of box-constrained problems with equality constraints. These upper bounds are important for the termination of spatial branch-and-bound algorithms. Our method is based on the theorem of Miranda which helps to ensure the existence of feasible points in certain boxes. Then, the computation of upper bounds at the objective function over those boxes yields an upper bound for the globally minimal value. A proof of convergence is given under mild assumptions. An extension of our approach to problems including inequality constraints is possible

Doctor of Philosophy

dissertationWe present a method for absolutely quantifying pharmacokinetic parameters in dynamic contrast-enhanced (DCE)-MRI. This method, known as alternating mini-mization with model (AMM), involves jointly estimating the arterial input function (AIF) and pharmacokinetic parameters from a characteristic set of measured tissue concentration curves. By blindly estimating the AIF, problems associated with AIF measurement in pharmacokinetic modeling, such as signal saturation, flow and partial volume eff ects, and small arterial lumens can be ignored. The blind estimation method described here introduces a novel functional form for the AIF, which serves to simplify the estimation process and reduce the deleterious e ffects of noise on the deconvolution process. Computer simulations were undertaken to assess the performance of the estimation process as a function of the input tissue curves. A con fidence metric for the estimation quality, based on a linear combination of the SNR and diversity of the input curves, is presented. This con fidence metric is then used to allow for localizing the region from which input curves are drawn. Local blood supply to any particular region can then be blindly estimated, along with some measure of con fidence for that estimation. Methods for evaluating the utility of the blind estimation algorithm on clinical data are presented, along with preliminary results on quantifying tissue parameters in soft-tissue sarcomas. The AMM method is applied to in vivo data from both cardiac perfusion and breast cancer scans. The cardiac scans were conducted using a dual-bolus protocol, which provides a measure of truth for the AIF. Twenty data sets were processed with this method, and pharmacokinetic parameter values derived from the blind AIF were compared with those derived from the dual-bolus measured AIF. For seventeen of the twenty datasets there were no statistically signifi cant differences in Ktrans estimates. The cardiac AMM method presented here provides a way to quantify perfusion of myocardial tissue with a single injection of contrast agent and without a special pulse sequence. The resulting parameters are similar to those given by the dual bolus method. The breast cancer scans were processed with the AMM method and the results were compared to an analysis done with the semiquantitative DCE-MRI scans. The e ffects of the temporal sampling rate of the data on the AMM method are examined. The ability of the AMM-derived parameters to distinguish benign and malignant tumors is compared to more conventional methods

Active Mean Fields for Probabilistic Image Segmentation: Connections with Chan-Vese and Rudin-Osher-Fatemi Models

Segmentation is a fundamental task for extracting semantically meaningful regions from an image. The goal of segmentation algorithms is to accurately assign object labels to each image location. However, image-noise, shortcomings of algorithms, and image ambiguities cause uncertainty in label assignment. Estimating the uncertainty in label assignment is important in multiple application domains, such as segmenting tumors from medical images for radiation treatment planning. One way to estimate these uncertainties is through the computation of posteriors of Bayesian models, which is computationally prohibitive for many practical applications. On the other hand, most computationally efficient methods fail to estimate label uncertainty. We therefore propose in this paper the Active Mean Fields (AMF) approach, a technique based on Bayesian modeling that uses a mean-field approximation to efficiently compute a segmentation and its corresponding uncertainty. Based on a variational formulation, the resulting convex model combines any label-likelihood measure with a prior on the length of the segmentation boundary. A specific implementation of that model is the Chan-Vese segmentation model (CV), in which the binary segmentation task is defined by a Gaussian likelihood and a prior regularizing the length of the segmentation boundary. Furthermore, the Euler-Lagrange equations derived from the AMF model are equivalent to those of the popular Rudin-Osher-Fatemi (ROF) model for image denoising. Solutions to the AMF model can thus be implemented by directly utilizing highly-efficient ROF solvers on log-likelihood ratio fields. We qualitatively assess the approach on synthetic data as well as on real natural and medical images. For a quantitative evaluation, we apply our approach to the icgbench dataset

Integrated Offline and Online Decision Making under Uncertainty

open3noThis work has been partially supported by the H2020 Project AI4EU (g.a. 825619), the VIRTUSProject (CCSEB-00094) and the Emilia-Romagna Region.This paper considers multi-stage optimization problems under uncertainty that involve distinct offline and online phases. In particular it addresses the issue of integrating these phases to show how the two are often interrelated in real-world applications. Our methods are applicable under two (fairly general) conditions: 1) the uncertainty is exogenous; 2) it is possible to define a greedy heuristic for the online phase that can be modeled as a parametric convex optimization problem. We start with a baseline composed by a two-stage offline approach paired with the online greedy heuristic. We then propose multiple methods to tighten the offline/online integration, leading to significant quality improvements, at the cost of an increased computation effort either in the offline or the online phase. Overall, our methods provide multiple options to balance the solution quality/time trade-off, suiting a variety of practical application scenarios. To test our methods, we ground our approaches on two real cases studies with both offline and online decisions: an energy management problem with uncertain renewable generation and demand, and a vehicle routing problem with uncertain travel times. The application domains feature respectively continuous and discrete decisions. An extensive analysis of the experimental results shows that indeed offline/online integration may lead to substantial benefits.openDe Filippo, Allegra; Lombardi, Michele; Milano, MichelaDe Filippo, Allegra; Lombardi, Michele; Milano, Michel