Variable selection via penalized estimation is appealing for dimension reduction. For penalized linear regression, Efron, et al. (2004) introduced the LARS algorithm. Recently, the coordinate descent (CD) algorithm was developed by Friedman, et al. (2007) for penalized linear regression and penalized logistic regression and was shown to gain computational superiority. This paper explores the CD algorithm to penalized Bregman divergence (BD) estimation for a broader class of models, including not only the generalized linear model, which has been well studied in the literature on penalization, but also the quasi-likelihood model, which has been less developed. Simulation study and real data application illustrate the performances of the CD and LARS algorithms in regression estimation, variable selection and classification procedure when the number of explanatory variables is large in comparison to the sample size.

Image processing is a method to perform some operations on an image, in order to get an enhanced image or to extract some useful information from it. The conventional image processing algorithms cannot perform well in scenarios where the training images (source domain) that are used to learn the model have a different distribution with test images (target domain). In fact, the existence of conditional distribution difference across the source and target domains degrades the performance of model. Domain adaptation and transfer learning are promising solutions that aim to generalize a learning model across training and test data with different distributions. In this paper, we address the problem of unsupervised cross domain image processing in which no labels are available in test images. In fact, the proposed method transfers the source and target domains into a shared low dimensional FLDA-based subspace in an unsupervised manner. Our proposed method minimizes the conditional probability distribution difference of the source and target data via Bregman divergence. We provide a projection matrix to map the source and target data into a common subspace on which the between class scatter matrix is maximized and within class scatter matrix and cross domain distributions are minimized. Extensive experiments on 58 cross-domain image classification tasks over six public datasets reveal that our proposed method outperforms the state-of-the-art cross domain image processing approaches.

Image processing is a method to perform some operations on an image, in order to get an enhanced image or to extract some useful information from it. The conventional image processing algorithms cannot perform well in scenarios where the training images (source domain) that are used to learn the model have a different distribution with test images (target domain). Also, many real world applications suffer from a limited number of training labeled data and therefore benefit from the related available labeled datasets to train the model. In this way, since there is the distribution difference across the source and target domains (domain shift problem), the learned classifier on the training set might perform poorly on the test set. Transfer learning and domain adaptation are two outstanding solutions to tackle this challenge by employing available datasets, even with significant difference in distribution and properties, to transfer the knowledge from a related domain to the target domain. The main assumption in domain shift problem is that the marginal or the conditional distribution of the source and the target data is different. Distribution adaptation explicitly minimizes predefined distance measures to reduce the difference in the marginal distribution, conditional distribution, or both. In this paper, we address a challenging scenario in which the source and target domains are different in marginal distributions, and the target images have no labeled data. Most prior works have explored two following learning strategies independently for adapting domains: feature matching and instance reweighting. In the instance reweighting approach, samples in the source data are weighted individually so that the distribution of the weighted source data is aligned to that of the target data. Then, a classifier is trained on the weighted source data. This approach can effectively eliminate unrelated source samples to the target data, but it would reduce the number of samples in adapted source data, which results in an increase in generalization errors of the trained classifier. Conversely, the feature-transform approach creates a feature map such that distributions of both datasets are aligned while both datasets are well distributed in the transformed feature space. In this paper, we show that both strategies are important and inevitable when the domain difference is substantially large. Our proposed using sample-oriented Domain Adaptation for Image Classification (DAIC) aims to reduce the domain difference by jointly matching the features and reweighting the instances across images in a principled dimensionality reduction procedure, and construct new feature representation that is invariant to both the distribution difference and the irrelevant instances. We extend the nonlinear Bregman divergence to measure the difference in marginal, and integrate it with Fisher’ s linear discriminant analysis (FLDA) to construct feature representation that is effective and robust for substantial distribution difference. DAIC benefits pseudo labels of target data in an iterative manner to converge the model. We consider three types of cross-domain image classification data, which are widely used to evaluate the visual domain adaptation algorithms: object (Office+Caltech-256), face (PIE) and digit (USPS, MNIST). We use all three datasets prepared by and construct 34 cross-domain problems. The Office-Caltech-256 dataset is a benchmark dataset for cross-domain object recognition tasks, which contains 10 overlapping categories from following four domains: Amazon (A), Webcam (W), DSLR (D) and Caltech256 (C). Therefore 4 × 3 = 12 cross domain adaptation tasks are constructed, namely A → W, . . ., C → D. USPS (U) and MNIST (M) datasets are widely used in computer vision and pattern recognition tasks. We conduct two handwriting recognition tasks, i. e., usps-mnist and mnist-usps. PIE is a benchmark dataset for face detection task and has 41, 368 face images of size 3232 from 68 individuals. The images were taken by 13 synchronized cameras and 21 flashes, under varying poses, illuminations, and expressions. PIE dataset consists five subsets depending on the different poses as follows: PIE1 (C05, left pose), PIE2 (C07, upward pose), PIE3 (C09, downward pose), PIE4 (C27, frontal pose), PIE5 (C29, right pose). Thus, we can construct 20 cross domain problems, i. e., P1 → P2, P1 → P3, . . ., P5 → P4. We compare our proposed DAIC with two baseline machine learning methods, i. e., NN, Fisher linear discriminant analysis (FLDA) and nine state-of-the-art domain adaptation methods for image classification problems (TSL, DAM, TJM, FIDOS and LRSR). Due to these methods are considered as dimensionality reduction approaches, we train a classifier on the labeled training data (e. g., NN classifier), and then apply it on test data to predict the labels of the unlabeled target data. DAIC efficiently preserves and utilizes the specific information among the samples from different domains. The obtained results indicate that DAIC outperforms several state of-the-art adaptation methods even if the distribution difference is substantially large.

Skeptical theism is one of the theistic responses to the evidential problem of evil. This approach which is included of different ideas, with emphasizing on human cognitive limitations and complicated axiological reality, casts doubt on the claim of gratuitous evil. This article is based on Bergmann’ s idea, who is one of the prominent philosopher in this sphere. He challenges William Rowe’ s inductive argument with his skeptical theses which are based on “ representative” principle. Bergmann’ s articles in this sphere are influential and highly controversial. One of the main objections to his idea is that his skeptical theses lead to moral impasse, both in theoretical (moral justification) and pragmatic aspect. This is against our approach in our everyday moral life. Since this position is not acceptable in everyday moral life, skeptical theism is not acceptable either. Although Bergmann accepts limitations in sphere of value, he doesn’ t think it makes problem for skeptical theism. This article first introduce representative approach of Bergmann then considering objections and responses to them. At least it becomes clear that Bergmann’ s solutions does not response objections rightly.

In recent decades optimal control problems with partial differential equation constraints have been studied extensively. These issues are very complex and the numerical solution of such problems is of great importance. In this article we will discuss the solution of elliptic optimal control problem. First, by using the finite element method we obtain to gain the discrete form of the problem. The obtained discrete problem is actually a large scale constrained optimization problem. Solving this optimization problem with traditional methods is difficult and requires a lot of CPU time and memory.But split Bergman method converts the constrained problem to an unconstrained problem, and hence it saves time and memory requirement. We then use the split Bergman iterative methods for solving this problem, and examples show the speed and accuracy of split Bergman iterative methods for solving this type of problems. We also use the SQP method for solving the problem and compare with split Bergman method.

During the twentieth century of A.C. Khouzestan the most strategic province if Iran, more than any other provinces of this country, has been exposed to separatism. Arab governments, Specially Iraq, have been the greatest planner and obstinate spporter of separation of this part of Iran. Being Arabs and particularly historical desire of the magority of this province inhabitance for separation has been the most important excuse and proof supporting this plan. This research tries to analysis the divergence and convergence degree of Khouzestan Arabs with regard to the major constructing political core of country an national aspiration as well.