Context tree selection: A unifying view

Context tree models have been introduced by Rissanen in [25] as a parsimonious generalization of Markov models. Since then, they have been widely used in applied probability and statistics. The present paper investigates non-asymptotic properties of two popular procedures of context tree estimation: Rissanen's algorithm Context and penalized maximum likelihood. First showing how they are related, we prove finite horizon bounds for the probability of over- and under-estimation. Concerning overestimation, no boundedness or loss-of-memory conditions are required: the proof relies on new deviation inequalities for empirical probabilities of independent interest. The under-estimation properties rely on classical hypotheses for processes of infinite memory. These results improve on and generalize the bounds obtained in Duarte et al. (2006) [12], Galves et al. (2008) [18], Galves and Leonardi (2008) [17], Leonardi (2010) [22], refining asymptotic results of Buhlmann and Wyner (1999) [4] and Csiszar and Talata (2006) [9]. (C) 2011 Elsevier B.V. All rights reserved.

Models to predict the distribution and abundance of breeding ducks in Canada

Detailed knowledge of waterfowl abundance and distribution across Canada is lacking, which limits our ability to effectively conserve and manage their populations. We used 15 years of data from an aerial transect survey to model the abundance of 17 species or species groups of ducks within southern and boreal Canada. We included 78 climatic, hydrological, and landscape variables in Boosted Regression Tree models, allowing flexible response curves and multiway interactions among variables. We assessed predictive performance of the models using four metrics and calculated uncertainty as the coefficient of variation of predictions across 20 replicate models. Maps of predicted relative abundance were generated from resulting models, and they largely match spatial patterns evident in the transect data. We observed two main distribution patterns: a concentrated prairie-parkland distribution and a more dispersed pan-Canadian distribution. These patterns were congruent with the relative importance of predictor variables and model evaluation statistics among the two groups of distributions. Most species had a hydrological variable as the most important predictor, although the specific hydrological variable differed somewhat among species. In some cases, important variables had clear ecological interpretations, but in some instances, e.g., topographic roughness, they may simply reflect chance correlations between species distributions and environmental variables identified by the model-building process. Given the performance of our models, we suggest that the resulting prediction maps can be used in future research and to guide conservation activities, particularly within the bounds of the survey area.

CONTEXT TREE SELECTION AND LINGUISTIC RHYTHM RETRIEVAL FROM WRITTEN TEXTS

The starting point of this article is the question "How to retrieve fingerprints of rhythm in written texts?" We address this problem in the case of Brazilian and European Portuguese. These two dialects of Modern Portuguese share the same lexicon and most of the sentences they produce are superficially identical. Yet they are conjectured, on linguistic grounds, to implement different rhythms. We show that this linguistic question can be formulated as a problem of model selection in the class of variable length Markov chains. To carry on this approach, we compare texts from European and Brazilian Portuguese. These texts are previously encoded according to some basic rhythmic features of the sentences which can be automatically retrieved. This is an entirely new approach from the linguistic point of view. Our statistical contribution is the introduction of the smallest maximizer criterion which is a constant free procedure for model selection. As a by-product, this provides a solution for the problem of optimal choice of the penalty constant when using the BIC to select a variable length Markov chain. Besides proving the consistency of the smallest maximizer criterion when the sample size diverges, we also make a simulation study comparing our approach with both the standard BIC selection and the Peres-Shields order estimation. Applied to the linguistic sample constituted for our case study, the smallest maximizer criterion assigns different context-tree models to the two dialects of Portuguese. The features of the selected models are compatible with current conjectures discussed in the linguistic literature.

Using the canonical modelling approach to simplify the simulation of function in functional-structural plant models

Functional-structural plant models that include detailed mechanistic representation of underlying physiological processes can be expensive to construct and the resulting models can also be extremely complicated. On the other hand, purely empirical models are not able to simulate plant adaptability and response to different conditions. In this paper, we present an intermediate approach to modelling plant function that can simulate plant response without requiring detailed knowledge of underlying physiology. Plant function is modelled using a 'canonical' modelling approach, which uses compartment models with flux functions of a standard mathematical form, while plant structure is modelled using L-systems. Two modelling examples are used to demonstrate that canonical modelling can be used in conjunction with L-systems to create functional-structural plant models where function is represented either in an accurate and descriptive way, or in a more mechanistic and explanatory way. We conclude that canonical modelling provides a useful, flexible and relatively simple approach to modelling plant function at an intermediate level of abstraction.

Essays on Machine Learning and Hedonic Models

Thesis (Ph.D.)--University of Washington, 2016-08

3D-2D image registration by nonlinear regression

We propose a 3D-2D image registration method that relates image features of 2D projection images to the transformation parameters of the 3D image by nonlinear regression. The method is compared with a conventional registration method based on iterative optimization. For evaluation, simulated X-ray images (DRRs) were generated from coronary artery tree models derived from 3D CTA scans. Registration of nine vessel trees was performed, and the alignment quality was measured by the mean target registration error (mTRE). The regression approach was shown to be slightly less accurate, but much more robust than the method based on an iterative optimization approach.

Mapping the Pasture Steppe in Bayankhongor, Mongolia: comparison of classification methods, using Landsat-8 and geophysical data

Grasslands in semi-arid regions, like Mongolian steppes, are facing desertification and degradation processes, due to climate change. Mongolia’s main economic activity consists on an extensive livestock production and, therefore, it is a concerning matter for the decision makers. Remote sensing and Geographic Information Systems provide the tools for advanced ecosystem management and have been widely used for monitoring and management of pasture resources. This study investigates which is the higher thematic detail that is possible to achieve through remote sensing, to map the steppe vegetation, using medium resolution earth observation imagery in three districts (soums) of Mongolia: Dzag, Buutsagaan and Khureemaral. After considering different thematic levels of detail for classifying the steppe vegetation, the existent pasture types within the steppe were chosen to be mapped. In order to investigate which combination of data sets yields the best results and which classification algorithm is more suitable for incorporating these data sets, a comparison between different classification methods were tested for the study area. Sixteen classifications were performed using different combinations of estimators, Landsat-8 (spectral bands and Landsat-8 NDVI-derived) and geophysical data (elevation, mean annual precipitation and mean annual temperature) using two classification algorithms, maximum likelihood and decision tree. Results showed that the best performing model was the one that incorporated Landsat-8 bands with mean annual precipitation and mean annual temperature (Model 13), using the decision tree. For maximum likelihood, the model that incorporated Landsat-8 bands with mean annual precipitation (Model 5) and the one that incorporated Landsat-8 bands with mean annual precipitation and mean annual temperature (Model 13), achieved the higher accuracies for this algorithm. The decision tree models consistently outperformed the maximum likelihood ones.

Geometric stopping of a random walk and its applications to valuing equity-linked death benefits

We study discrete-time models in which death benefits can depend on a stock price index, the logarithm of which is modeled as a random walk. Examples of such benefit payments include put and call options, barrier options, and lookback options. Because the distribution of the curtate-future-lifetime can be approximated by a linear combination of geometric distributions, it suffices to consider curtate-future-lifetimes with a geometric distribution. In binomial and trinomial tree models, closed-form expressions for the expectations of the discounted benefit payment are obtained for a series of options. They are based on results concerning geometric stopping of a random walk, in particular also on a version of the Wiener-Hopf factorization.

Finding Methods for Recognizing and Classifying Spare Part Criticality – Case Full Deposit Stripping Machines

The aim of this Master’s thesis is to find a method for classifying spare part criticality in the case company. Several approaches exist for criticality classification of spare parts. The practical problem in this thesis is the lack of a generic analysis method for classifying spare parts of proprietary equipment of the case company. In order to find a classification method, a literature review of various analysis methods is required. The requirements of the case company also have to be recognized. This is achieved by consulting professionals in the company. The literature review states that the analytic hierarchy process (AHP) combined with decision tree models is a common method for classifying spare parts in academic literature. Most of the literature discusses spare part criticality in stock holding perspective. This is relevant perspective also for a customer orientated original equipment manufacturer (OEM), as the case company. A decision tree model is developed for classifying spare parts. The decision tree classifies spare parts into five criticality classes according to five criteria. The criteria are: safety risk, availability risk, functional criticality, predictability of failure and probability of failure. The criticality classes describe the level of criticality from non-critical to highly critical. The method is verified for classifying spare parts of a full deposit stripping machine. The classification can be utilized as a generic model for recognizing critical spare parts of other similar equipment, according to which spare part recommendations can be created. Purchase price of an item and equipment criticality were found to have no effect on spare part criticality in this context. Decision tree is recognized as the most suitable method for classifying spare part criticality in the company.

Predicting smear negative pulmonary tuberculosis with classification trees and logistic regression: a cross-sectional study

Abstract Background Smear negative pulmonary tuberculosis (SNPT) accounts for 30% of pulmonary tuberculosis cases reported yearly in Brazil. This study aimed to develop a prediction model for SNPT for outpatients in areas with scarce resources. Methods The study enrolled 551 patients with clinical-radiological suspicion of SNPT, in Rio de Janeiro, Brazil. The original data was divided into two equivalent samples for generation and validation of the prediction models. Symptoms, physical signs and chest X-rays were used for constructing logistic regression and classification and regression tree models. From the logistic regression, we generated a clinical and radiological prediction score. The area under the receiver operator characteristic curve, sensitivity, and specificity were used to evaluate the model's performance in both generation and validation samples. Results It was possible to generate predictive models for SNPT with sensitivity ranging from 64% to 71% and specificity ranging from 58% to 76%. Conclusion The results suggest that those models might be useful as screening tools for estimating the risk of SNPT, optimizing the utilization of more expensive tests, and avoiding costs of unnecessary anti-tuberculosis treatment. Those models might be cost-effective tools in a health care network with hierarchical distribution of scarce resources.

Spatial Assessment of Erosion and its Impact on Soil Fertility in the Tajik Foothills

Efficient planning of soil conservation measures requires, first, to understand the impact of soil erosion on soil fertility with regard to local land cover classes; and second, to identify hot spots of soil erosion and bright spots of soil conservation in a spatially explicit manner. Soil organic carbon (SOC) is an important indicator of soil fertility. The aim of this study was to conduct a spatial assessment of erosion and its impact on SOC for specific land cover classes. Input data consisted of extensive ground truth, a digital elevation model and Landsat 7 imagery from two different seasons. Soil spectral reflectance readings were taken from soil samples in the laboratory and calibrated with results of SOC chemical analysis using regression tree modelling. The resulting model statistics for soil degradation assessments are promising (R2=0.71, RMSEV=0.32). Since the area includes rugged terrain and small agricultural plots, the decision tree models allowed mapping of land cover classes, soil erosion incidence and SOC content classes at an acceptable level of accuracy for preliminary studies. The various datasets were linked in the hot-bright spot matrix, which was developed to combine soil erosion incidence information and SOC content levels (for uniform land cover classes) in a scatter plot. The quarters of the plot show different stages of degradation, from well conserved land to hot spots of soil degradation. The approach helps to gain a better understanding of the impact of soil erosion on soil fertility and to identify hot and bright spots in a spatially explicit manner. The results show distinctly lower SOC content levels on large parts of the test areas, where annual crop cultivation was dominant in the 1990s and where cultivation has now been abandoned. On the other hand, there are strong indications that afforestations and fruit orchards established in the 1980s have been successful in conserving soil resources.

A systematized workflow for assessing land resources using readily available spatial datasets

Land degradation as well as land conservation maps at a (sub-) national scale are critical for pro-ject planning for sustainable land management. It has long been recognized that online accessible and low-cost raster data sets (e.g. Landsat imagery, SRTM-DEM’s) provide a readily available basis for land resource assessments for developing countries. However, choice of spatial, tempo-ral and spectral resolution of such data is often limited. Furthermore, while local expert knowl-edge on land degradation processes is abundant, difficulties are often encountered when linking existing knowledge with modern approaches including GIS and RS. The aim of this study was to develop an easily applicable, standardized workflow for preliminary spatial assessments of land degradation and conservation, which also allows the integration of existing expert knowledge. The core of the developed method consists of a workflow for rule-based land resource assess-ment. In a systematic way, this workflow leads from predefined land degradation and conserva-tion classes to field indicators, to suitable spatial proxy data, and finally to a set of rules for clas-sification of spatial datasets. Pre-conditions are used to narrow the area of interest. Decision tree models are used for integrating the different rules. It can be concluded that the workflow presented assists experts from different disciplines in col-laboration GIS/RS specialists in establishing a preliminary model for assessing land degradation and conservation in a spatially explicit manner. The workflow provides support when linking field indicators and spatial datasets, and when determining field indicators for groundtruthing.

Maximizing the number of polychronous groups in spiking networks

In this paper we investigate the effect of biasing the axonal connection delay values in the number of polychronous groups produced for a spiking neuron network model. We use an estimation of distribution algorithm (EDA) that learns tree models to search for optimal delay configurations. Our results indicate that the introduced approach can be used to considerably increase the number of such groups.