Effektiv modellutvelgelse i Tikhonov Regulariseringsrammeverket og preprosessering av spektroskopisk data

Machine learning is a hot topic in today's society. Data sets of varying sizes show up in a number of contexts, and learning from data sets is important for answering many questions. There is a plethora of methods that can be used to extract information from data, and in this thesis we consider primarily the Tikhonov Regularization (TR) framework for regularized linear least squares modeling. TR is a very flexible modeling framework, in the sense that it is easy to adjust the type of regularization used as well as including a priori information about the regression coefficients. The main topic of this thesis is efficient model selection in the TR framework. When using TR regularization for modeling it is necessary to specify one or more model parameters, often called regularization parameters. The regularization parameter can have a significant effect on the quality of the final model, and choosing an appropriate regularization parameter is therefore an important part of the modeling. For large data sets model selection can be time consuming, and it is therefore of interest to obtain efficient methods for selecting between different models. In Paper I it is shown how generalized cross validation can be used for efficient model selection in the TR framework. This discussion continues in Paper III where it is shown how leave-one-out cross validation can be done efficiently in the TR framework. Paper III also suggests a heuristic that can be used for efficient model selection when dealing with data sets with repeated measurements of the same physical sample. Raw data often needs to pre-processed before useful models can be created. Papers I and II deal with pre-processing and modeling of vibrational spectroscopic data in the extended multiplicative signal correction (EMSC) framework. In the EMSC framework unwanted effects in the data are modeled as multiplicative and additive effects. In Paper I it is shown how the correction of additive effects can be done while creating a regression model in the TR framework and why this can in some cases be advantageous. The multiplicative correction in EMSC is based on a single reference spectrum, but for data sets with very different spectra a single reference spectrum might not be sufficient to accurately correct for multiplicative effects in the measured spectra. Paper II discusses how to extend the EMSC framework to include multiple reference spectra as well as how appropriate reference spectra can be obtained automatically. Paper IV considers classification using regularized linear discriminant analysis (RLDA). The link between RLDA and regularized regression is used to argue that the efficient validation criteria discussed in papers I and III also can be used for model validation in RLDA. This is tested empirically and the results indicate that good choices of the regularization parameter can be obtained efficiently using a regression-based criterion

Designing problems introducing the concept of numerical integration in an inquiry-based setting

Research literature argues for the benefits of inquiry-based approaches to provide opportunities for in-depth understanding of mathematics. This paper studies the design of mathematical problems for the purpose of introducing the concept of numerical integration in an inquiry-based setting. We present a series of six developmental stages (represent, refocus, area, accumulate, approximate, and refine) indicating a natural trajectory for students to follow when inquiring on the concept of numerical integration before any formal introduction to the topic. Further, we present a sequence of three problems illustrating how the developmental stages can be applied in problem design

A new formula for fast computation of segmented cross validation residuals in linear regression modelling -- providing efficient regularisation parameter estimation in Ridge Regression and the Tikhonov Regularisation Framework

In the present paper we prove a new theorem, resulting in an exact updating formula for linear regression model residuals to calculate the segmented cross-validation residuals for any choice of cross-validation strategy without model refitting. The required matrix inversions are limited by the cross-validation segment sizes and can be executed with high efficiency in parallel. The well-known formula for leave-one-out cross-validation follows as a special case of our theorem. In situations where the cross-validation segments consist of small groups of repeated measurements, we suggest a heuristic strategy for fast serial approximations of the cross-validated residuals and associated PRESS statistic. We also suggest strategies for quick estimation of the exact minimum PRESS value and full PRESS function over a selected interval of regularisation values. The computational effectiveness of the parameter selection for Ridge-/Tikhonov regression modelling resulting from our theoretical findings and heuristic arguments is demonstrated for several practical applications.Comment: 33 pages, 10 figure, 8 table

Fra papirindustri til Papirbredden : En studie av bruken av kulturminner i byggingen av Drammen Kunnskapspark

I Norge er det flere statlig eide selskaper som deltar som byutviklingsaktører. Felles for disse er at de opererer på og i konkurranse med, det private markedet. Slik sett får man bedrifter som befinner seg et sted mellom privat og offentlig. Ved å belyse Papirbreddenprosjektet søker studien å vise hvordan et prosjekt i grenseland mellom privat og offentlig forvalter kulturminner. Studien ser på aktørenes tilnærminger til bruken av kulturminner som ressurs og belyser ulike syn på governancestrukturers kapasitet, vilje og ønske om å ta samfunnsansvar

Selection of principal variables through a modified Gram–Schmidt process with and without supervision

In various situations requiring empirical model building from highly multivariate measurements, modelling based on partial least squares regression (PLSR) may often provide efficient low-dimensional model solutions. In unsupervised situations, the same may be true for principal component analysis (PCA). In both cases, however, it is also of interest to identify subsets of the measured variables useful for obtaining sparser but still comparable models without significant loss of information and performance. In the present paper, we propose a voting approach for sparse overall maximisation of variance analogous to PCA and a similar alternative for deriving sparse regression models influenced closely related to the PLSR method. Both cases yield pivoting strategies for a modified Gram–Schmidt process and its corresponding (partial) QRfactorisation of the underlying data matrix to manage the variable selection process. The proposed methods include score and loading plot possibilities that are acknowledged for providing efficient interpretations of the related PCA and PLS models in chemometric applications.Selection of principal variables through a modified Gram–Schmidt process with and without supervisionpublishedVersio

Penerapan Pembelajaran Kooperatif Tipe Jigsaw Dalam Meningkatkan Motivasi Dan Hasil Belajar IPA Pada Siswa Kelas VII Semester II SMP Negeri 2 Pulokulon

Permasalahan pokok yang akan dipecahkan lewat Penelitian Tindakan Kelas ini adalah: apakah penerapan model pembelajaran kooperatif tipe jigsaw dapat meningkatkan hasil belajar IPA. Tujuannya untuk meningkatkan motivasi dan hasil belajar siswa dalam mata pelajaran IPA..Penelitian ini merupakan tindakan guru untuk memperbaiki hasil belajar siswa kelas VII SMP Negeri 2 Pulokulon Semester 2 Tahun Pelajaran 2013/2004, dan pelakunya adalah guru IPA. Penelitian dilakukan dalam 2 siklus dan meliputi 4 tahapan, yaitu perencanaan, tindakan,pengamatan dan refleksi.Hasil penelitian menunjukkan bahwa dari keseluruhan siklus yang telah dilakukan motivasi dan perolehan nilai siswa kelas VII SMP Negeri 2 Pulokulon Semester 2 Tahun Pelajaran 2013/2004 mengalami peningkatan dari satu siklus ke siklus berikutnya. Jadi secara keseluruhan siklus yang telah dilakukan, penerapan model pembelajaran kooperatif tipe jigsaw dapat meningkatkan motivasi dan hasil belajar siswa dalam mata pelajaran IPA

Genome-wide risk prediction of common diseases across ancestries in one million people

Peer reviewe

Association studies of up to 1.2 million individuals yield new insights into the genetic etiology of tobacco and alcohol use.

Tobacco and alcohol use are leading causes of mortality that influence risk for many complex diseases and disorders1. They are heritable2,3 and etiologically related4,5 behaviors that have been resistant to gene discovery efforts6-11. In sample sizes up to 1.2 million individuals, we discovered 566 genetic variants in 406 loci associated with multiple stages of tobacco use (initiation, cessation, and heaviness) as well as alcohol use, with 150 loci evidencing pleiotropic association. Smoking phenotypes were positively genetically correlated with many health conditions, whereas alcohol use was negatively correlated with these conditions, such that increased genetic risk for alcohol use is associated with lower disease risk. We report evidence for the involvement of many systems in tobacco and alcohol use, including genes involved in nicotinic, dopaminergic, and glutamatergic neurotransmission. The results provide a solid starting point to evaluate the effects of these loci in model organisms and more precise substance use measures

Genome-wide analysis of 53,400 people with irritable bowel syndrome highlights shared genetic pathways with mood and anxiety disorders.

Irritable bowel syndrome (IBS) results from disordered brain-gut interactions. Identifying susceptibility genes could highlight the underlying pathophysiological mechanisms. We designed a digestive health questionnaire for UK Biobank and combined identified cases with IBS with independent cohorts. We conducted a genome-wide association study with 53,400 cases and 433,201 controls and replicated significant associations in a 23andMe panel (205,252 cases and 1,384,055 controls). Our study identified and confirmed six genetic susceptibility loci for IBS. Implicated genes included NCAM1, CADM2, PHF2/FAM120A, DOCK9, CKAP2/TPTE2P3 and BAG6. The first four are associated with mood and anxiety disorders, expressed in the nervous system, or both. Mirroring this, we also found strong genome-wide correlation between the risk of IBS and anxiety, neuroticism and depression (rg > 0.5). Additional analyses suggested this arises due to shared pathogenic pathways rather than, for example, anxiety causing abdominal symptoms. Implicated mechanisms require further exploration to help understand the altered brain-gut interactions underlying IBS