http://103.7.193.12:8080/xmlui/handle/123456789/42 DEPARTMENT OF STATISTICS (STT) 2026-04-17T16:56:35Z http://103.7.193.12:8080/xmlui/handle/123456789/762 Kernel Choice for Unsupervised Kernel Methods Alam, Md. Ashad In kernel methods, choosing a suitable kernel is indispensable for favorable results. While cross-validation is a useful method of the kernel and parameter choice for supervised learning such as the support vector machines, there are no well-founded methods, have been established in general for unsupervised learning. We focus on kernel principal component analysis (kernel PCA) and kernel canonical correlation analysis (kernel CCA), which are the nonlinear extension of principal component analysis (PCA) and canonical correlation analysis (CCA), respectively. Both of these methods have been used effectively for extracting nonlinear features and reducing dimensionality. As a kernel method, kernel PCA and kernel CCA also suffer from the problem of kernel choice. Although cross-validation is a popular method of choosing hyperparameters, it is not applicable straightforwardly to choose a kernel and the number of components in kernel PCA and kernel CCA. It is important, thus, to develop a well-founded method for choosing hyperparameters of the unsupervised methods. In kernel PCA, it is not possible to use cross-validation for choosing hyperparameters because of the incomparable norms given by different kernels. The first goal of the dissertation is to propose a method for choosing hyperparameters in kernel PCA (the kernel and the number of components) based on cross-validation for the comparable reconstruction errors of pre-images in the original space. The experimental results of synthesized and real-world datasets demonstrate that the proposed method successfully selects an appropriate kernel and the number of components in kernel PCA in terms of visualization and classification errors on the principal components. The results imply that the proposed method enables the automatic design of hyperparameters in kernel PCA. XIV In recent years, the influence function of kernel PCA and a robust kernel PCA has been theoretically derived. One observation of their analysis is that kernel PCA with a bounded kernel such as Gaussian is robust in that sense the influence function does not diverged, while for kernel PCA with unbounded kernels for example polynomial the influence function goes to infinity. This can be understood by the boundedness of the transformed data onto the feature space by a bounded kernel. While this is not a result of kernel CCA but for kernel PCA, it is reasonable to expect that kernel CCA with a bounded kernel is also robust. This consideration motivates us to do some empirical studies on the robustness of kernel CCA. It is essential to know how kernel CCA is effected by outliers and to develop measures of accuracy. Therefore, we do intend to study a number of conventional robust estimates and kernel CCA with different functions but fixed parameter of kernel. The second goal of the dissertation is to discuss five canonical correlation coefficients and investigate their performances (robustness) by influence function, sensitivity curve, qualitative robustness index and breakdown point using different type of simulated datasets. The final goal of the dissertation is to extract the limitations of cross-validation for the kernel CCA, and to propose a new regularization approach to overcome the limitations of kernel CCA. As we demonstrate for Gaussian kernels, the cross-validation errors for kernel CCA tend to decrease as the bandwidth parameter of the kernel decreases, which provides inappropriate features with all the data concentrated in a few points. This is caused by the ill-posedness of the kernel CCA with the cross-validation. To solve this problem, we propose to use constraints on the 4th order moments of canonical variables in addition to the variances. Experiments on synthesized and real world datasets including human action recognition for a robot demonstrate that the proposed higher-order regularized kernel CCA can be applied effectively with the cross-validation to find appropriate kernel and regularization parameters. Methods using positive definite kernel (PDK), kernel methods play an increasingly prominent role to solve various problems in statistical machining learning such as, web design, pattern recognition, human action recognition for a robot, computational protein function perdition, remote sensing data analysis and in many other research fields. Due to the kernel trick and reproducing property, we can use linear techniques in feature spaces without knowing explicit forms of either the feature map or feature spaces. It offers versatile tools to process, analyze, and compare many types of data and offers state-of-the-art performance. Nowadays, PDK has become a popular tool for the most branches of statistical machine learning e.g., supervised learning, unsupervised learning, reinforcement learning, non-parametric inference and so on. Many methods have been proposed to kernel methods, which include support vector machine (SVM, Boser et al., 1992), kernel ridge regression (KRR, Saunders et al., 1998), kernel principal component analysis (kernel PCA, Schélkopf et al., 1998), kernel canonical correlation analysis (kernel CCA, Akaho, 2001, Bach and Jordan, 2002), Bayesian inference with positive definite kernels (kernel Bayes’ rule, Fukumizu et al., 2013), gradient-based kernel dimension reduction for regression (gKDR, Fukumizu and Leng, 2014), kernel two-sample test (Gretton, 2012) and so on. 2014-09-01T00:00:00Z http://103.7.193.12:8080/xmlui/handle/123456789/684 STATISTICAL ANALYSIS OF FOOD EXPENDITURE BEHAVIOR OF AN NGO SUPPORTED FARMERS’ FAMILIES IN DINAJPUR: AN APPLICATION OF LA/AIDS MODEL Kumer, Ashim This study analyzed aggregate food expenditure data of marginal and small farmers` families’ collected from the Dinajpur District in the north-western Bangladesh. The Linear Approximate Almost Ideal Demand System (LA/AIDS) method is used to estimate food expenditure and demand function for aggregating the seven food categories. In order to observe the impact of per capita monthly food expenditure, prices of different commodities, household size, dependency ratio, sex, age, food security status and occupation of the household head on the budget share. The study was based on among the NGO beneficiaries program LRP-45 (ActionAid Bangladesh), Ghorgahat and Katabari union in dinajpur District. The food demand and expenditure behavior analysed by sample of size of 165 household was drawn from the enumerated household of 4936 employing simple random sampling method. The AIDS model fits better for all the items as the adjusted R2 values under consideration the regression through-the -origin model as a solution to the problem of Heteroscedasticity. The results revealed that, the allocation of household total monthly expenditure on food items. The mean budget share for Cereals, Roots and Pulses, Vegetables, Rich foods, Milk & Sugar, Oil & Spices and Drugs & Other Luxuries was (52%, 9.5%, 14.6%, 3.0%, 6.8%, 5.8%, & 7.7%) respectively. The empirical findings of the estimated seven expenditure equations are summarized. The expenditure elasticities for food groups are elastic, except cereals, vegetables, and oil & spices. The implication is that food groups of cereals, vegetables, and spices are necessities in the Bangladeshi diet. Roots & pulses, rich foods, milk & sugar, and luxuries foods are luxury goods. Marshallian and Hicksian elasticity calculated from the model were between 1 and -1 making the products less responsive to price changes. The uncompensated own-price elasticties for the food items for cereals (-0.43), vegetables (-1.07), milk & sugar (-0.67), oil & spices (0.83) and luxuries (-1.04) were inelastic, showing that consumers were not sensitive to the price in adjusting their consumption of corresponding items. However, for vegetables, roots & pulses, own-price elasticity of demand were close to one (0.68) implying that quantity demanded for this item changes by almost the same percentage with the price change. That is, if the prices of these food items decreased, then the demand for those food increased. For example, if price of rich foods falls by 10 percent, then demand for rich foods would increase by 19.6 percent. Compensated own and cross-price elasriceties of demand for oil & spices, and rich foods in this case were substitutes. Consumer’s demand behavior is fundamental to understand the demand side of the market. Demand analysts are continuously finding for specifications and functional forms of demand equations which are initials concerned with finding out how the demand for a product will alter as certain specified variables change. The most consistent patterns of consumer demand is the Engel’s Law (1857) which states that as income rises, budget’s share spent on food tends to decline. The estimation of Engel’s models and hence Engel’s curves has a long tradition in empirical economic research. Moreover, in working with Engel’s curve, one important assumption is that consumer’s purchase is mostly influenced by his or her level of income, total expenditure and does not depend on the 2015-12-01T00:00:00Z http://103.7.193.12:8080/xmlui/handle/123456789/681 Maternal Morbidity and Mortality Status among Indigenous People in North-West Bangladesh: A Study in Dinajpur District AKTAR, MST. SUMAIA The present study was conducted among the plain land indigenous families in Dinajpur, the North-west region of Bangladesh to identify the source-demographic and economic condition, health access systems, the maternal morbidity and mortality and its determinants. This study was carried out in the six upazilas namely Dinajpur sadar, Birgang, Nowabganj, Fulbari, Biral and Chirirbandr in the Dinajpur district where most of the indigenous people live. Using appropriate sample size estimating formula, a total of 223currently married women having at least one child of under five years old were interviewed for data collection with simple random sampling method. The collected data were analysed using univariate, bivariate and multivariate analyses. This study comes up with the fact that maternal health status of plain land indigenous people in North-west of Bangladesh is also poor as national level of the country compared to desired level. This study shows that more than one-third of women have access to health care services, which can be one of the most important factors in their poor health. In most cases, indigenous women (mothers’) faced common problems during pregnancies like headache, eye vision, cough/fever, excessive vomiting tendency and morning sickness. But major complications of excessive bleeding, obstructive labor, long-term labor, eclampsia, and membrane are also seen as their delivery period because most midwives help with delivery, those who do not have any formal training or education. Practice for delivering care and current use of contraception are also lower among the indigenous mothers. But in case of family planning and contraceptive use indicators these studied statistics (CPR=67. 2) were relatively better than national average. Maternal mortality situations are also not in desired level due to the practice of preservation by traditional midwives. The mothers cannot afford expensive health care and medical facilities due to their poor financial condition and for own cultural heritage. On the other hand, the indigenous society is still passing through adverse situations regarding their socioeconomic condition and standard obstetric care facilities. The factors associated with the use of lower health care and contraceptive use are found that age of respondents, mothers' education, husband's education and occupation, financial condition, distance to the service center and access to mass media are significant. This study recommends that community health centers/ health care in public and private enterprise will have to increase. Government, NGOs, United Nations Population Fund (UNFPA) and other development partners will have to implement various programs and projects. This chapter attempts to highlight the research background, problem statement, scope and significance of the research. To have the idea of the research area, this chapter gives the research questions and the objectives of the study. Finally, the concept of the key words used in the title and the outline or composition of the dissertation is included here. 1.1 Background of the study The primary census report of 2011gives the number of ethnic population groups of Bangladesh as 27.According to the census of 2011 (Source: Population Census 2011, BBS) The total number of indigenous people in Dinajpur district of Bangladesh was 1,43,425. However, these figures are a gross underestimation. The indigenous peoples are one of the largest tribes residing in the north- west districts of Bangladesh. Besides Bangladesh, the indigenous tribe can also be observed in the neighboring West Bengal and Bihar states of India. The indigenous peoples who are largely concentrated in the districts of Rajshahi, Naogaon, Dinajpur and Rangpur are one of the oldest tribal groups in Bangladesh (Ref: http://en.wikipedia.org/wiki/Santhal_people as on 03 February, 2014). They are mainly hunters and gatherers. They largely depend on the common pool resources (CPR) like forests, bees andharesand above all on the Agra economy for their livelihood. 2016-06-01T00:00:00Z http://103.7.193.12:8080/xmlui/handle/123456789/675 SPOUSAL VIOLENCE AND AUTONOMY STATUS AMONG MARRIED EMPLOYED WOMEN: A STUDY IN NORTH-WESTERN REGION OF BANGLADESH HAQUE, MD. MOZAHIDUL The present study used various statistical tools to measure the prevalence and associated factors of spousal violence and also to examine women's autonomy and decision-making power among married employed women in North-Western region of Bangladesh. The study was conducted in the two selected districts of the region viz., Dinajpur and Thakurgaon, where, 150 married employed women were selected using random sampling technique. A structured questionnaire used to collect a bulk of socio-demographic & economic characteristics and information regarding spousal violence & women's autonomy in decision-making within their household. The study found that about 42.0% women had non-abusive relationship with their husband and 58.0% women were victim of spousal violence. Among the violent women 48.0% women were moderately abused and 10.0% women were seriously abused. According to pattern of violence, about 41% women experienced physical violence, 68.0% experienced sexual violence and 63% experienced psychological violence. The study also found that mainly age of respondent, education level of respondent, occupation of respondent, respondent's monthly income, age of husband, education level of husband, husband's monthly income, total monthly family expenditure and land size of household were significantly associated with spousal violence. Physical violence increased with the increase of age of respondent, marital duration & age of husband and decreased when the age at the time of present marriage and total monthly family expenditure increases. Sexual violence decreased when the age of respondent and age of husband increases. And also psychological violence increased with the increase of marital duration & age of husband and decreased when the age at the time of present marriage, respondent's monthly income, husband's monthly income, and total monthly family expenditure increases. Again the study results showed that overall 25% of the women were participated in all the three areas of decision-making, 37% in two areas of decision-making, and 26.0% participated in at least one of the three areas of decision-making (i.e. freedom of movement, or decision-making regarding children, or HH task and decision). About 46.0% women had autonomy to make decision about their movement, 67% women had autonomy to make decision regarding children and 63% women had autonomy to make decision about household task and decision. Also the study results showed that mainly age of respondent, occupation of respondent, respondent's monthly income, age of husband, occupation of husband, husband's monthly family expenditure from own income and total monthly family expenditure were significantly associated with women's autonomy in decision-making Autonomy of movement of married employed women increased with the increase of husband's monthly income and total monthly family expenditure. Autonomy of decision-making regarding children increased when respondent's monthly income increases. And also autonomy of decision-making regarding HH task and decision increased when the age of respondent increases. To raise awareness among community members/family members that violence against women (VAW) is an extreme violation of women's human rights, is a criminal offense under the law, and also has bad consequences on the immediate family, employment and future generations. Educational and religious institutes are an ideal place where awareness of violence in relationships can be built and healthy ways of forming intimate relationships can be taught to challenge violence against women. 2015-12-01T00:00:00Z