Maximum-Margin Model for Nearest Prototype Classifiers

In this paper, we study nearest prototype classifiers, which classify data instances into the classes to which their nearest prototypes belong. We propose a maximum-margin model for nearest prototype classifiers. To provide the margin, we define a class-wise discriminant function for instances by the negatives of distances of their nearest prototypes of the class. Then, we define the margin by the minimum of differences between the discriminant function values of instances with respect to the classes they belong to and the values of the other classes. The optimization problem corresponding to the maximum-margin model is a difference of convex functions (DC) program. It is solved using a DC algorithm, which is ak-means-like algorithm, i.e., the members and positions of prototypes are alternately optimized. Through a numerical study, we analyze the effects of hyperparameters of the maximum-margin model, especially considering the classification performance.

Accelerated Difference of Convex functions Algorithm and its Application to Sparse Binary Logistic Regression

In this work, we present a variant of DCA (Difference of Convex function Algorithm) with the aim to improve its convergence speed. The proposed algorithm, named Accelerated DCA (ADCA), consists in incorporating the Nesterov's acceleration technique into DCA. We first investigate ADCA for solving the standard DC program and rigorously study its convergence properties and the convergence rate. Secondly, we develop ADCA for a special case of the standard DC program whose the objective function is the sum of a differentiable with L-Lipschitz gradient function (possibly nonconvex) and a nonsmooth DC function. We exploit the special structure of the problem to propose an efficient DC decomposition for which the corresponding ADCA scheme is inexpensive. As an application, we consider the sparse binary logistic regression problem. Numerical experiments on several benchmark datasets illustrate the efficiency of our algorithm and its superiority over well-known methods.

DC-Programming versus ℓ0-Superiorization for Discrete Tomography

In this paper we focus on the reconstruction of sparse solutions to underdetermined systems of linear equations with variable bounds. The problem is motivated by sparse and gradient-sparse reconstruction in binary and discrete tomography from limited data. To address the ℓ0-minimization problem we consider two approaches: DC-programming and ℓ0-superiorization. We show that ℓ0-minimization over bounded polyhedra can be equivalently formulated as a DC program. Unfortunately, standard DC algorithms based on convex programming often get trapped in local minima. On the other hand, ℓ0-superiorization yields comparable results at significantly lower costs.

Veterans' Labor Force Participation: What Role Does the VA's Disability Compensation Program Play?

We explore time trends in the labor force participation of veterans and non-veterans and investigate whether they are consistent with a rising role for the Department of Veterans Affairs' Disability Compensation (DC) program, which pays benefits to veterans with service-connected disabilities and has grown rapidly since 2000. Using 35 years of March CPS data, we find that veterans' labor force participation declined over time in a way that coincides closely with DC growth and that veterans have become more sensitive to economic shocks. Our findings suggest that DC program growth has contributed to recent declines in veterans' labor force participation.

Block Clustering Based on Difference of Convex Functions (DC) Programming and DC Algorithms

We investigate difference of convex functions (DC) programming and the DC algorithm (DCA) to solve the block clustering problem in the continuous framework, which traditionally requires solving a hard combinatorial optimization problem. DC reformulation techniques and exact penalty in DC programming are developed to build an appropriate equivalent DC program of the block clustering problem. They lead to an elegant and explicit DCA scheme for the resulting DC program. Computational experiments show the robustness and efficiency of the proposed algorithm and its superiority over standard algorithms such as two-mode K-means, two-mode fuzzy clustering, and block classification EM.

Residential facilities and day centres in mental health. Is there any difference?

SummaryAims– We wanted to investigate to what extent and in what characteristics the patients cared in the psychiatric residential facilities (RF) were similar to those in the day-centres (DC), and whether 6-month improvements in the two settings were comparable.Methods– We described 141 patients admitted to the RF and 180 in DC of three mental health service networks in Milan and near Milan. They were evaluated again after six months.Results– In both groups, we identified subgroups of more intensive treatment: 45% of those in residential treatment were in high intensity rehabilitation facilities, and those who followed a residential program of >12 hours/week were 53%. The mean duration of treatment in the residential treatment was 40 months (SD 55.7) and in DC 49.6 months (49.3). The two groups differed in the overall scores of the HoNOS, but differences emerged in the subscales relative to daily life activities and living conditions. Among those in RF, about half had a house, versus 99% among those in DC. After six months, clinically significant modifications were small in both groups.Conclusions– Residential patients had more needs than DC patients. It is possible that some of the residential patients might be treated with intensive DC program, but the absence of a home for the majority of residential facilities patients makes this unlikely.Declaration of Interest: None.