Asymptotic Normality of Support Vector Machine Variants and Other Regularized Kernel Methods

In nonparametric classification and regression problems, regularized kernel methods, in particular support vector machines, attract much attention in theoretical and in applied statistics. In an abstract sense, regularized kernel methods (simply called SVMs here) can be seen as regularized M-estimators for a parameter in a (typically infinite dimensional) reproducing kernel Hilbert space. For smooth loss functions, it is shown that the difference between the estimator, i.e.\ the empirical SVM, and the theoretical SVM is asymptotically normal with rate $\sqrt{n}$. That is, the standardized difference converges weakly to a Gaussian process in the reproducing kernel Hilbert space. As common in real applications, the choice of the regularization parameter may depend on the data. The proof is done by an application of the functional delta-method and by showing that the SVM-functional is suitably Hadamard-differentiable

Qualitative Robustness of Support Vector Machines

Support vector machines have attracted much attention in theoretical and in applied statistics. Main topics of recent interest are consistency, learning rates and robustness. In this article, it is shown that support vector machines are qualitatively robust. Since support vector machines can be represented by a functional on the set of all probability measures, qualitative robustness is proven by showing that this functional is continuous with respect to the topology generated by weak convergence of probability measures. Combined with the existence and uniqueness of support vector machines, our results show that support vector machines are the solutions of a well-posed mathematical problem in Hadamard's sense

The Cause of Inorganic Compounds from Auto-flocculated Algal Solids and Their Effect on the Solid and Biocrude Products of Conventional Hydrothermal Liquefaction

The recent increase in demand for more sustainable and renewable alternatives to both energy and other commercial products has given rise to a modern bioeconomy. With advances in the life sciences, various biomass resources and conversion techniques have been explored to create such products. Often overseen within a bioeconomy, however, is the need for sustainable and renewable means of nutrient recovery, and since 2015 the National Science Foundation, along with several other federal agencies, has invested over $100 million to explore new, innovative processes that are both physical and biological that address the global rise in food, energy, and water. Referred to as the Food, Energy, and Water Nexus, a primary objective of such research is to discover “means of extending resources via methods such as recycling, recovery, and reuse.” Hydrothermal liquefaction (HTL) of algal biomass has been proven to be an effective wet, thermochemical technique for the conversion of biomass to a high quality biocrude oil product. Furthermore, the subcritical water conditions of HTL provide an outstanding environment for the inorganic,0 solid synthesis of high-valued biomaterials and catalysts. The Feedstock to Tailpipe Initiative at the University of Kansas was one of the first to trial HTL on algal solids that were cultivated in wastewater effluent. In addition to an enhanced biocrude product, HTL of wastewater-cultivated algal solids produced a high amount HTL solids unlike several other algal HTL research had previously observed. Further analysis of these HTL solids indicated they were a calcium phosphate material known as hydroxyapatite (HAp), Ca5(PO4)3OH. With a proven proof of concept that HTL of wastewater-cultivated algal solids yields an abundance of HTL solids and an upgraded biocrude product, the major research thrust of this dissertation was to understand the chemical and biological characteristics that created these results. A high ash and calcium content in the wastewater-culitvated algal solids was known to be caused due to the addition of lime, Ca(OH)2, during the wastewater treatment process to control the alkalinity, or buffering capacity, of the wastewater effluent. Thus, Lab- and bench-scale light rack tanks and raceway ponds, respectively, were utilized to grow Chlorella kessleri in BG-11 media with augmented calcium concentrations. All algal cultivation and harvesting were overseen by the collaborating environmental engineers. Algal solid characterization was divided amongst the collaborators and primary author while all HTL reactions and extractions were overseen by the primary author. A majority of the HTL products were also characterized by the primary author with additional analysis and experimentation performed by the collaborator. Light rack experiments aided in discovering the cause for high ash or inorganic capture within the algal solids. Auto-flocculation is an effective dewatering technique that utilizes external coagulants that causes microalgae to flocculate and condense at the bottom of the growth tanks. An increase in pH of 10 or 11 causes solids to precipitate from algal growth media and act as natural coagulants for the auto-flocculation of algal solids. These precipitated solids from auto-flocculation are the cause of the high calcium and ash content in the algal solids. X-ray diffraction (XRD) revealed the primary, crystalline structure of auto-flocculated and wastewater-cultivated algal solids was calcite or CaCO3. Algal solids cultivated in the light racks with various Ca:P molar ratios also showed that an increased calcium content causes a nearly 100% recovery of phosphorus in the HTL solid product. Identical P-recovery in the solid-phase was also observed from the previous HTL of wastewater-cultivated algal solids. Thus, auto-flocculation and subsequent HTL of algal solids provides excellent means for sustainable, renewable P-recovery. A uniform HAp or alternative calcium phosphate structure, such as tricalcium phosphate (TCP) Ca3(PO4)2, were not observed in the HTL solids produced from auto-flocculated algal solids that were cultivated in the light racks. Thus, inorganic and biological model compounds were reacted at identical, conventional HTL conditions (350°C for 60 minutes). Calcite and trisodium phosphate, Na3PO4, were the primary inorganic model compounds used to create a uniform calcium phosphate HTL solid. Initial results were unsuccessful and identical XRD patterns of the HTL solids from duplicate reactions were unachievable. However, the addition of silicon dioxide, SiO2, did enhance the intensity of calcium phosphate structures in the XRD patterns of HTL solids both from the inorganic model compounds and previously auto-flocculated algal solids. The largest discovery from the experimentation of model compounds was a technique for measuring inorganic carbon, (CO32-) within a solid sample through thermal gravimetric analysis (TGA). Calcium carbonate degrades between 600-800°C releasing CO2 and resulting in CaO. TGA allows one to measure the mass lost due to CO2, and from stoichiometry, one can determine the initial mass of CaCO3 with less than 1% error. A greater error occurs, however, when applying this technique to measuring the amount of carbonate in algal solids. The additional organic, biomass of algal solids delays the degradation of CO3 within the algal solids. Correlated trends from both TGA-measured carbonate and the theoretical carbonate as determined through water chemistry modeling for the algal solids justified further use TGA method for measuring carbonate. Carbohydrate, lipid, and protein biological compounds were also reacted at conventional HTL conditions both with and without the addition of various, previously observed, inorganic compounds. Nutritional supplement, soy protein was the only biological compound that produced a viable biocrude product for analysis. Despite several combinations of HTL reactions with different biological and inorganic model compounds, substantial changes to the organic biocrude product were not observed with HAp. The lack of success in proving HAp could be acting as a catalyst and cause in-situ biocrude upgrading aids in further determination and exploration for other causes for the enhanced biocrude properties observed from the HTL of auto-flocculated algal solids. The final raceway study was a comprehensive overview for the previous observations and conclusions from the light rack and model compound studies. The larger raceway ponds allowed for ample algal solid production from both N- and P-limited growth media. Furthermore, algal solids were auto-flocculated and harvested at various growth stages to alter both their inorganic composition, in terms of bio-P and solid-P, as well as their biomolecular content. The theory and original hypothesis proposed by the collaboration was the aqueous phosphorus that remains in solution would precipitate as solid, amorphous calcium phosphate. Thus, algal solids cultivated in N-limited media created algal solids with a majority of theoretical solid-P sustained throughout all growth stages while the theoretical amount of solid-P decreased as algal growth accumulated in P-limited media. The hypothesis that amorphous calcium phosphate precipitates from solution was confirmed with the observance of calcium phosphate structures in the algal solid ash. The amount of amorphous calcium phosphate in the algal solids could be further estimated using the previous TGA-method for estimating the carbonate. The balance of calcium not stoichiometrically correlated to the mass of carbonate was assumed to be associated with amorphous calcium phosphate. Similar, correlating trends between the theoretical solid-P, the estimated percent of calcium as calcium phosphate, and the calcium phosphate structure in the algal solids’ ash confirmed the initial hypothesis that amorphous calcium phosphate precipitates and is captured within the algal solids. Uniform calcium phosphate structures in the HTL solids were also produced from algal solids that contained a majority of amorphous calcium phosphate. Thus, the algal growth media and growth stage ultimately decide the final structure of the HTL solids. Finally, the algal growth media and growth stage impacted the biocrude composition as well. A decrease in long chain amides and C20 hydrocarbons that had previously been observed in the biocrude produced by the HTL of wastewater-cultivated algal solids also only appeared from N-limited, stationary-stage, auto-flocculated algal solids cultivated in the raceway. The uniqueness of the results leads to believe that the N-limited, semi-batch cultivation of algal solids from wastewater effluent may be the cause for improvements in the biocrude as opposed to the HTL solids. However, substantial variances were observed in biocrude properties from algal solids cultivated in the same growth media and harvested from the same growth stage with only the inorganic composition varying. Furthermore, biocrude with the highest H/C molar ratio was achieved when complimented with HTL solids with a primarily calcite structure. Thus, it is suggested that future work focus on the impact and role of CaCO3 during the HTL of algal solids

Data-Based Decisions under Complex Uncertainty

Decision theory is, in particular in economics, medical expert systems and statistics, an important tool for determining optimal decisions under uncertainty. In view of applications in statistics, the present book is concerned with decision problems which are explicitly data-based. Since the arising uncertainties are often too complex to be described by classical precise probability assessments, concepts of imprecise probabilities (coherent lower previsions, F-probabilities) are applied. Due to the present state of research, some basic groundwork has to be done: Firstly, topological properties of different concepts of imprecise probabilities are investigated. In particular, the concept of coherent lower previsions appears to have advantageous properties for applications in decision theory. Secondly, several decision theoretic tools are developed for imprecise probabilities. These tools are mainly based on concepts developed by L. Le Cam and enable, for example, a definition of sufficiency in case of imprecise probabilities for the first time. Building on that, the article [A. Buja, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 65 (1984) 367-384] is reinvestigated in the only recently available framework of imprecise probabilities. This leads to a generalization of results within the Huber-Strassen theory concerning least favorable pairs or models. Results obtained by these investigations can also be applied afterwards in order to justify the use of the method of natural extension, which is fundamental within the theory of imprecise probabilities, in data-based decision problems. It is shown by means of the theory of vector lattices that applying the method of natural extension in decision problems does not affect the optimality of decisions. However, it is also shown that, in general, the method of natural extension suffers from a severe instability. The book closes with an application in statistics in which a minimum distance estimator is developed for imprecise probabilities. After an investigation concerning its asymptotic properties, an algorithm for calculating the estimator is given which is based on linear programming. This algorithm has led to an implementation of the estimator in the programming language R which is publicly available as R package "imprProbEst". The applicability of the estimator (even for large sample sizes) is demonstrated in a simulation study

Journal of African Christian Biography: v. 4, no. 1

A publication of the Dictionary of African Christian Biography with U.S. offices located at the Center for Global Christianity and Mission at Boston University. This issue focuses on: 1. Introducing African Christian Biography. 2. Modern African Church History and the Streetlight Effect. 3. Both African and Christian. 4. Musicians and Composers in African Christianity. 5. Yared. 6. John Knox Bokwe. 7. Recent Print and Digital Resources Related to Christianity in Africa. 8. Guidelines for Article Contributors. 9. Suggested Interview Guidelines and Questions. 10. Guidelines for Book Reviewers