Multidimensional Test Assembly Using Mixed-Integer Linear Programming: An Application of Kullback-Leibler Information.

This study aims to investigate the effect of different item exposure controlling strategies on item selection methods in the context of multidimensional computerized adaptive testing (MCAT). Additionally, this study aims to examine to what extend the restrictive threshold (RT) and the restrictive progressive (RPG) exposure methods suppress the item exposure rates and increase the exposure rates of underexposed items without losing psychometric precision in MCAT. For this purpose, the performance of four item selection methods with and without exposure controls are evaluated and compared so as to determine how results differ when item exposure controlling strategies are applied with Monte-Carlo simulation method. The four item selection methods employed in this study are D-optimality, Kullback–Leibler information (KLP), the minimized error variance of linear combination score with equal weight (V1), the composite score with optimized weight (V2). On the other hand, the maximum priority index (MPI) method proposed for unidimensional CAT and two other item exposure control methods, that are RT and RPG methods proposed for cognitive diagnostic CAT, are adopted. The results show that: (1) KLP, D-optimality, and V1 performed better in recovering domain scores, and all outperformed V2 with respect to precision; (2) although V1 and V2 offer improved item bank usage rates, KLP, D-optimality, V1, and V2 produced an unbalanced distribution of item exposure rates; (3) all exposure control strategies improve the exposure uniformity greatly and with very little loss in psychometric precision; (4) RPG and MPI perform similarly in exposure control, and outperformed RT exposure control method.

ABSTRACTConcentration of a diffusing substance in a medium was derived in various cases of uni-dimensional diffusion, including in a semi-infinite medium and a plate-shaped medium. Multi-dimensional diffusion involves boundary conditions in each coordinate direction. The algorithm dealing with uni-dimensional case becomes very complicated in multi-dimensional cases. This study proposes an algorithm, which is called the complementary method, that combines complementary functions of the normalized solution in uni-dimensional diffusion case by multiplication to solve those in various multi-dimensional diffusion cases with dramatically simplified mathematics. Besides, the complementary method is used to solve various kinds of boundary conditions for multi-dimensional diffusion.

The purpose of this study was to conduct a real-time multidimensional computerized adaptive test (MCAT) using data from a previous paper-pencil test (PPT) regarding the grammar and vocabulary dimensions of an end-of-term proficiency exam conducted on students in a preparatory class at a university. An item pool was established through four separate 50-item sets applied in four different semesters. The fit between unidimensional, multi-unidimensional and bifactor IRT models was compared during item calibration, with the bifactor model providing the best fit for all data sets. This was followed by a hybrid simulation for 36 conditions obtained using six item selection methods, two ability estimation methods and three termination rules. The statistics and graphs obtained indicate D-rule item selection, maximum a posteriori (MAP) ability estimation and standard error termination rule as the best algorithm for the real-time MCAT application. With the minimum number of items to be administered determined as 10, the real-time application conducted on 99 examinees yielded an average number of items of 13.4. The PPT format proficiency exam consists of 50 items, leading to the conclusion that the examinees participating in the real-time MCAT are administered an average of 74.4% fewer items than the PPT. Additionally, 86 of the examinees answered between 10-13 items. The item pool use rate is 30%. Lastly, the correlation between the PPT scores and general trait scores of 32 examinees was calculated as .77.

This paper first discusses the relationship between Kullback–Leibler information (KL) and Fisher information in the context of multi-dimensional item response theory and is further interpreted for the two-dimensional case, from a geometric perspective. This explication should allow for a better understanding of the various item selection methods in multi-dimensional adaptive tests (MAT) which are based on these two information measures. The KL information index (KI) method is then discussed and two theorems are derived to quantify the relationship between KI and item parameters. Due to the fact that most of the existing item selection algorithms for MAT bear severe computational complexity, which substantially lowers the applicability of MAT, two versions of simplified KL index (SKI), built from the analytical results, are proposed to mimic the behavior of KI, while reducing the overall computational intensity.

Several constitutive theories have been proposed in the literature to model the viscoelastic response of materials, including widely used rheological constitutive models. These models are characterized by certain parameters (“time constants”) that define the time scales over which the material relaxes. These parameters are primarily obtained from stress relaxation experiments using curve-fitting techniques. However, the question of how best to estimate these time constants remains open. As a step towards answering this question, we propose an optimal experimental design approach based on ideas from information geometry, namely Fisher information and Kullback–Leibler divergence. The material is modeled as a spring element in parallel with multiple Maxwell elements and described using a one- or two-term Prony series. Treating the time constants as unknowns, we develop expressions for the Fisher information and Kullback–Leibler divergence that allow us to maximize information gain from experimental data. Based on the results of this study, we propose that the largest time constant estimated from a stress relaxation experiment for a linear viscoelastic material should be at most one-fifth of the total time of the experiment in order to maximize information gain. Our results also provide confirmation that the equilibrium modulus of the material cannot be reliably determined from curve-fitting to data from a stress relaxation experiment.

This study investigated item exposure control procedures under various combinations of item pool characteristics and ability distributions in computerized adaptive testing based on the partial credit model. Three variables were manipulated: item pool characteristics (120 items for each of easy, medium, and hard item pools), two ability distributions (normally distributed and negatively skewed data), and three exposure control procedures (randomesque procedure, progressive–restricted procedure, and maximum information procedure). A number of measurement precision indexes such as descriptive statistics, correlations between known and estimated ability levels, bias, root mean squared error, and average absolute difference, exposure rates, item usage, and item overlap were computed to assess the impact of matched or nonmatched item pool and ability distributions on the accuracy of ability estimation and the performance of exposure control procedures. As expected, the medium item pool produced better precision of measurement than both the easy and hard item pools. The progressive–restricted procedure performed better in terms of maximum exposure rates, item average overlap, and pool utilization than both the randomesque procedure and the maximum information procedure. The easy item pool with the negatively skewed data as a mismatched condition produced the worst performance.

Wald’s (1947) sequential probability ratio test can be implemented as an adaptive test for classifying examinees into categories. However, current implementations use an item selection method that is either random or based on Fisher information (FI), a criterion related to optimized examinee trait estimates. In this study, a method based on Kullback-Leibler information (KLI) was evaluated. Simulation studies were conducted for two- and three-category classifications in which item selection methods based on FI and KLI were compared. Results showed that testing algorithms using KLI-based item selection performed better than or as well as those using FI-based item selection.

Facial Expressions play major role in interpersonal communication and imparting intelligence to computer for identifying facial expressions is a crucial task. In this paper we present an efficient preprocessing algorithm combined with feature extraction using Local Binary Patterns (LBP) followed by classification using Kullback Leibler (KL) divergence. Firstly Viola Jones algorithm is used to detect pair of eyes using which effective part of face is obtained which is further processed to eliminate illumination effect. LBP operator is then applied on the preprocessed image to extract local features represented by histogram. Template histograms for seven basic expressions using training images are formed which are compared with the test histogram distribution using an efficient KL divergence for dissimilarity measure. This algorithm is implemented on JAFFE database resulting in a high classification accuracy of 95.24%.

In this work, we first consider the discrete version of Fisher information measure and then propose Jensen–Fisher information, to develop some associated results. Next, we consider Fisher information and Bayes–Fisher information measures for mixing parameter vector of a finite mixture probability mass function and establish some results. We provide some connections between these measures with some known informational measures such as chi-square divergence, Shannon entropy, Kullback–Leibler, Jeffreys and Jensen–Shannon divergences.

In this paper, the problem of bearings-only tracking with a single sensor is studied via the theory of information geometry, where Fisher information matrix plays the role of Riemannian metric. Under a given tracking scenario, the Fisher information distance between two targets is approximately calculated over the window of surveillance region and is compared to the corresponding Kullback Leibler divergence. It is demonstrated that both "distances" provide a contour map that describes the information difference between the location of a target and a specified point. Furthermore, an analytical result for the optimal heading of a given constant speed sensor is derived based on the the properties of statistical manifolds.

Voice conversion with SI-DNN and KL divergence based mapping without parallel training data

Our previous works suggest that fractal-based texture features are very useful for detection, segmentation and classification of posterior-fossa (PF) pediatric brain tumor in multimodality MRI. In this work, we investigate and compare efficacy of our texture features such as fractal and multifractional Brownian motion (mBm), and intensity along with another useful level-set based shape feature in PF tumor segmentation. We study feature selection and ranking using Kullback -Leibler Divergence (KLD) and subsequent tumor segmentation; all in an integrated Expectation Maximization (EM) framework. We study the efficacy of all four features in both multimodality as well as disparate MRI modalities such as T1, T2 and FLAIR. Both KLD feature plots and information theoretic entropy measure suggest that mBm feature offers the maximum separation between tumor and non-tumor tissues in T1 and FLAIR MRI modalities. The same metrics show that intensity feature offers the maximum separation between tumor and non-tumor tissue in T2 MRI modality. The efficacies of these features are further validated in segmenting PF tumor using both single modality and multimodality MRI for six pediatric patients with over 520 real MR images.

In this article, we study the helium atom confined in a spherical impenetrable cavity by using informational measures. We use the Ritz variational method to obtain the energies and wave functions of the confined helium atom as a function of the cavity radius . As trial wave functions we use one uncorrelated function and five explicitly correlated basis sets in Hylleraas coordinates with different degrees of electronic correlation. We computed the Shannon entropy, Fisher information, Kullback–Leibler entropy, Tsallis entropy, disequilibrium and Fisher–Shannon complexity, as a function of . We found that these entropic measures are sensitive to electronic correlation and can be used to measure it. As expected these entropic measures are less sensitive to electron correlation in the strong confinement regime ( a.u.).

A two-stage location and capacity determination method based on data-driven distributed robust optimization is proposed to address the uncertainty in the selection and capacity determination of grid connected optical storage charging stations on highways. Stage 1: Obtain the location of the charging point based on Monte Carlo simulation method, and use an integer programming model to determine the location of the charging station. Stage 2 takes into account the interests of charging stations and user satisfaction, establishes a data-driven distributed robust optimization fixed capacity model, constructs a probability distribution fuzzy set centered on empirical probability distribution through KL (Kullback Leibler) divergence to describe uncertainty, and uses risk theory to transform the distributed robust optimization model into a mixed integer linear programming problem, thereby optimizing the number of charging stations and optical storage capacity in the charging station. Finally, the proposed method is validated and sensitivity analysis is conducted through a circular road network. The results indicate that the proposed method is feasible and effective. Configuring optical storage equipment can reduce the annual lifespan cost. By controlling KL divergence tolerance, sample size, range, charging power, etc., the economy and robustness of the system can be effectively balanced.

Data-driven model-independent reconstructions of the dark energy equation of state $w(z)$ are presented using Planck 2015 era CMB, BAO, SNIa and Lyman-$\alpha$ data. These reconstructions identify the $w(z)$ behaviour supported by the data and show a bifurcation of the equation of state posterior in the range $1.5{<}z{<}3$. Although the concordance $\Lambda$CDM model is consistent with the data at all redshifts in one of the bifurcated spaces, in the other a supernegative equation of state (also known as `phantom dark energy') is identified within the $1.5 \sigma$ confidence intervals of the posterior distribution. To identify the power of different datasets in constraining the dark energy equation of state, we use a novel formulation of the Kullback--Leibler divergence. This formalism quantifies the information the data add when moving from priors to posteriors for each possible dataset combination. The SNIa and BAO datasets are shown to provide much more constraining power in comparison to the Lyman-$\alpha$ datasets. Further, SNIa and BAO constrain most strongly around redshift range $0.1-0.5$, whilst the Lyman-$\alpha$ data constrains weakly over a broader range. We do not attribute the supernegative favouring to any particular dataset, and note that the $\Lambda$CDM model was favoured at more than $2$ log-units in Bayes factors over all the models tested despite the weakly preferred $w(z)$ structure in the data.