Kernel density classification and boosting: an L2 sub analysis

Kernel density estimation is a commonly used approach to classification. However, most of the theoretical results for kernel methods apply to estimation per se and not necessarily to classification. In this paper we show that when estimating the difference between two densities, the optimal smoothing parameters are increasing functions of the sample size of the complementary group, and we provide a small simluation study which examines the relative performance of kernel density methods when the final goal is classification. A relative newcomer to the classification portfolio is “boosting”, and this paper proposes an algorithm for boosting kernel density classifiers. We note that boosting is closely linked to a previously proposed method of bias reduction in kernel density estimation and indicate how it will enjoy similar properties for classification. We show that boosting kernel classifiers reduces the bias whilst only slightly increasing the variance, with an overall reduction in error. Numerical examples and simulations are used to illustrate the findings, and we also suggest further areas of research

From the Diary of a Traveller: South Africa in 1923 / ﻣﻦ ﻳﻮﻣﻴﺎﺕ ﻣﺳﺎﻓﺮﺓ: ﺟﻨﻮﺏ ﺃﻓﺮﻳﻘﻴﺎ ﻓﻲ ١٩٢٣

[This essay introduces prominent figures who undertook a journey in a South African bush in 1923, and presents an extract from the unpublished trek journal of Margaret Gillett, née Clark, daughter of a well-known Somerset family. She and her husband were liberal-minded activists. Jan Christian Smuts, an international statesman and Prime Minister of South Africa accompanied them on this journey, as well as Illtyd Buller Pole-Evans, a botanist and an ecologist. In this extract, the diarist describes the landscape, flora and fauna, as well as encounters with Chief Malabok and the native inhabitants, including a gift exchange ceremony. ﺗﻘﺪﻡ ﻫﺬﻩ ﺍﻟﻤﻘﺎﻟﺔ ﺷﺨﺼﻴﺎﺕ ﻣﺮﻣﻮﻗﺔ ﻗﺎﻣﺖ ﺑﺮﺣﻠﺔ ﻓﻲ ﺃﺩﻏﺎﻝ ﺟﻨﻮﺏ ﺃﻓﺮﻳﻘﻴﺎ ﻓﻲ ٬١٩٢٣ ﻣﺴﺘﺸﻬﺪﺓ ﺑﻤﻘﺘﻄﻔﺎﺕ ﻣﻦ ﻳﻮﻣﻴﺎﺕ ﺍﻟﺮﺣﻠﺔ ﻟﻤﺮﺟﺮﻳﺖ ﻛﻼﺭﻙ ﺟﻴﻠﻴﺖ٬ ﺍﺑﻨﺔ ﻋﺎﺋﻠﺔ ﻣﻌﺮﻭﻓﺔ ﻣﻦ ﺳﻮﻣﺮﺳﺖ٬ ﻭﺍﻟﺘﻲ ﻛﺎﻧﺖ ﻫﻲ ﻭﺯﻭﺟﻬﺎ ﻣﻦ ﺍﻟﻨﺎﺷﻄﻴﻦ ﺍﻟﻤﺘﺤﺮﺭﻳﻦ ﻓﻜﺮﻳﺎﹰ٠ ﻭﻗﺪ ﺻﺎﺣﺒﻬﻤﺎ ﻓﻲ ﺍﻟﺮﺣﻠﺔ ﻛﻞ ﻣﻦ ﺟﺎﻥ ﻛﺮﻳﺴﺘﻴﺎﻥ ﺳﻤﺘﺲ٬ ﺍﻟﺴﻴﺎﺳﻲ ﺍﻟﺪﻭﻟﻲ ﻭﺭﺋﻴﺲ ﻭﺯﺭﺍﺀ ﺟﻨﻮﺏ ﺃﻓﺮﻳﻘﻴﺎ٬ ﻭﭘﻮﻝ-ﺇﻳﭭﺎﻧﺰ٬ ﻋﺎﻟﻢ ﺍﻟﻨﺒﺎﺗﺎﺕ ﻭﺍﻟﺒﻴﺌﺔ٠ ﻭﻓﻲ ﻫﺬﻩ ﺍﻟﻤﻘﺘﻄﻔﺎﺕ٬ ﺗﺼﻒ ﺻﺎﺣﺒﺔ ﺍﻟﻴﻮﻣﻴﺎﺕ ﺍﻟﻄﺒﻴﻌﻴﺔ٬ ﻭﺍﻟﺰﻫﻮﺭ ﻭﺍﻟﻨﺒﺎﺗﺎﺕ٬ ﻭﻟﻘﺎﺀﺍﺗﻬﺎ ﻣﻊ ﺍﻟﺰﻋﻴﻢ ﻣﺎﻻ ﺑﻮﻙ ﻭﺍﻟﺴﻜﺎﻥ ﺍﻷﺻﻠﻴﻦ٬ ﺑﻤﺎ ﻓﻲ ﺫﻟﻚ ﻣﺮﺍﺳﻢ ﺗﺒﺎﺩﻝ ﺍﻟﻬﺪﺍﻳﺎ٠