Modeling Efficient Classification as a Process of Confidence Assessment and Delegation

In visual object detection and recognition, classifiers have two interesting characteristics: accuracy and speed. Accuracy depends on the complexity of the image features and classifier decision surfaces. Speed depends on the hardware and the computational effort required to use the features and decision surfaces. When attempts to increase accuracy lead to increases in complexity and effort, it is necessary to ask how much are we willing to pay for increased accuracy. For example, if increased computational effort implies quickly diminishing returns in accuracy, then those designing inexpensive surveillance applications cannot aim for maximum accuracy at any cost. It becomes necessary to find trade-offs between accuracy and effort. We study efficient classification of images depicting real-world objects and scenes. Classification is efficient when a classifier can be controlled so that the desired trade-off between accuracy and effort (speed) is achieved and unnecessary computations are avoided on a per input basis. A framework is proposed for understanding and modeling efficient classification of images. Classification is modeled as a tree-like process. In designing the framework, it is important to recognize what is essential and to avoid structures that are narrow in applicability. Earlier frameworks are lacking in this regard. The overall contribution is two-fold. First, the framework is presented, subjected to experiments, and shown to be satisfactory. Second, certain unconventional approaches are experimented with. This allows the separation of the essential from the conventional. To determine if the framework is satisfactory, three categories of questions are identified: trade-off optimization, classifier tree organization, and rules for delegation and confidence modeling. Questions and problems related to each category are addressed and empirical results are presented. For example, related to trade-off optimization, we address the problem of computational bottlenecks that limit the range of trade-offs. We also ask if accuracy versus effort trade-offs can be controlled after training. For another example, regarding classifier tree organization, we first consider the task of organizing a tree in a problem-specific manner. We then ask if problem-specific organization is necessary.

Drops That Open Worlds : Image of Water in the Poetry of Euphrase Kezilahabi

Euphrase Kezilahabi on tansanialainen kirjailija, joka ensimmäisenä julkaisi swahilinkielisen vapaalla mitalla kirjoitetun runokokoelman. Perinteisessä swahilirunoudessa tiukat muotosäännöt ovat tärkeitä, ja teos synnytti kiivasta keskustelua. Runoteokset Kichomi ( Viilto , Kipu , 1974) ja Karibu Ndani ( Tervetuloa sisään , 1988) sekä Kezilahabin muu tuotanto voidaan nähdä uuden sukupolven taiteena. Kezilahabi on arvostettu runoilija, mutta hänen runojaan ei aiemmin ole käännetty englanniksi (yksittäisiä säkeitä lukuunottamatta), eikä juurikaan tutkittu yksityiskohtaisesti. Yleiskuvaan pyrkivissä lausunnoissa Kezilahabin runouden on hyvin usein määritelty olevan poliittista. Monet Kezilahabin runoista ottavatkin kantaa yhteiskunnallisiin kysymyksiin, mutta niiden pohdinta on kuitenkin runoissa vain yksi taso. Sen lisäksi Kezilahabin lyriikassa on paljon muuta ennen kartoittamatonta tämä tutkimus keskittyy veden kuvaan (the image of water). Kezilahabi vietti lapsuutensa saarella Victoria-järven keskellä, ja hänen vesikuvastonsa on rikasta. Tutkimuskysymyksenä on, mitä veden kuva runoteoksissa Kichomi ja Karibu Ndani esittää. Runojen analysoinnissa ja tulkinnassa on tarkasteltu myös sitä, miten äänteellinen taso osallistuu kuvien luomiseen. Tutkimuksen määritelmä kuvasta pohjautuu osittain Hugh Kennerin näkemykseen, jonka mukaan oleellista kuvassa on kirjaimellinen taso. Kennerin lähtökohtaan on yhdistetty John Shoptawin teoriaa, joka korostaa runon äänteellisen puolen tärkeyttä merkityksen muodostumisessa. Foneemien analyysissä vaikutteena on ollut Reuven Tsurin teoria. Analyysiosio osoittaa, että veden kuva edustaa ja käsittelee teoksissa lukuisia teemoja: elämää, kuolemaa, fyysistä vetovoimaa, runoutta, mielikuvitusta ja (ali)tajuntaa sekä moraalia. Veden kuvan tutkimuksen pohjalta on nähtävissä, että Kezilahabin filosofia asettuu elävä/kuollut- ja elämä/kuolema dikotomioiden ulkopuolelle.

Boundedness and convergence of singular integrals on fractal type sets

The topic of this dissertation lies in the intersection of harmonic analysis and fractal geometry. We particulary consider singular integrals in Euclidean spaces with respect to general measures, and we study how the geometric structure of the measures affects certain analytic properties of the operators. The thesis consists of three research articles and an overview. In the first article we construct singular integral operators on lower dimensional Sierpinski gaskets associated with homogeneous Calderón-Zygmund kernels. While these operators are bounded their principal values fail to exist almost everywhere. Conformal iterated function systems generate a broad range of fractal sets. In the second article we prove that many of these limit sets are porous in a very strong sense, by showing that they contain holes spread in every direction. In the following we connect these results with singular integrals. We exploit the fractal structure of these limit sets, in order to establish that singular integrals associated with very general kernels converge weakly. Boundedness questions consist a central topic of investigation in the theory of singular integrals. In the third article we study singular integrals of different measures. We prove a very general boundedness result in the case where the two underlying measures are separated by a Lipshitz graph. As a consequence we show that a certain weak convergence holds for a large class of singular integrals.

Modeling Asymmetries in Financial Data with Multiplicative Error Models

This thesis addresses modeling of financial time series, especially stock market returns and daily price ranges. Modeling data of this kind can be approached with so-called multiplicative error models (MEM). These models nest several well known time series models such as GARCH, ACD and CARR models. They are able to capture many well established features of financial time series including volatility clustering and leptokurtosis. In contrast to these phenomena, different kinds of asymmetries have received relatively little attention in the existing literature. In this thesis asymmetries arise from various sources. They are observed in both conditional and unconditional distributions, for variables with non-negative values and for variables that have values on the real line. In the multivariate context asymmetries can be observed in the marginal distributions as well as in the relationships of the variables modeled. New methods for all these cases are proposed. Chapter 2 considers GARCH models and modeling of returns of two stock market indices. The chapter introduces the so-called generalized hyperbolic (GH) GARCH model to account for asymmetries in both conditional and unconditional distribution. In particular, two special cases of the GARCH-GH model which describe the data most accurately are proposed. They are found to improve the fit of the model when compared to symmetric GARCH models. The advantages of accounting for asymmetries are also observed through Value-at-Risk applications. Both theoretical and empirical contributions are provided in Chapter 3 of the thesis. In this chapter the so-called mixture conditional autoregressive range (MCARR) model is introduced, examined and applied to daily price ranges of the Hang Seng Index. The conditions for the strict and weak stationarity of the model as well as an expression for the autocorrelation function are obtained by writing the MCARR model as a first order autoregressive process with random coefficients. The chapter also introduces inverse gamma (IG) distribution to CARR models. The advantages of CARR-IG and MCARR-IG specifications over conventional CARR models are found in the empirical application both in- and out-of-sample. Chapter 4 discusses the simultaneous modeling of absolute returns and daily price ranges. In this part of the thesis a vector multiplicative error model (VMEM) with asymmetric Gumbel copula is found to provide substantial benefits over the existing VMEM models based on elliptical copulas. The proposed specification is able to capture the highly asymmetric dependence of the modeled variables thereby improving the performance of the model considerably. The economic significance of the results obtained is established when the information content of the volatility forecasts derived is examined.

Modeling ecological and evolutionary processes in spatially structured populations

Many species inhabit fragmented landscapes, resulting either from anthropogenic or from natural processes. The ecological and evolutionary dynamics of spatially structured populations are affected by a complex interplay between endogenous and exogenous factors. The metapopulation approach, simplifying the landscape to a discrete set of patches of breeding habitat surrounded by unsuitable matrix, has become a widely applied paradigm for the study of species inhabiting highly fragmented landscapes. In this thesis, I focus on the construction of biologically realistic models and their parameterization with empirical data, with the general objective of understanding how the interactions between individuals and their spatially structured environment affect ecological and evolutionary processes in fragmented landscapes. I study two hierarchically structured model systems, which are the Glanville fritillary butterfly in the Åland Islands, and a system of two interacting aphid species in the Tvärminne archipelago, both being located in South-Western Finland. The interesting and challenging feature of both study systems is that the population dynamics occur over multiple spatial scales that are linked by various processes. My main emphasis is in the development of mathematical and statistical methodologies. For the Glanville fritillary case study, I first build a Bayesian framework for the estimation of death rates and capture probabilities from mark-recapture data, with the novelty of accounting for variation among individuals in capture probabilities and survival. I then characterize the dispersal phase of the butterflies by deriving a mathematical approximation of a diffusion-based movement model applied to a network of patches. I use the movement model as a building block to construct an individual-based evolutionary model for the Glanville fritillary butterfly metapopulation. I parameterize the evolutionary model using a pattern-oriented approach, and use it to study how the landscape structure affects the evolution of dispersal. For the aphid case study, I develop a Bayesian model of hierarchical multi-scale metapopulation dynamics, where the observed extinction and colonization rates are decomposed into intrinsic rates operating specifically at each spatial scale. In summary, I show how analytical approaches, hierarchical Bayesian methods and individual-based simulations can be used individually or in combination to tackle complex problems from many different viewpoints. In particular, hierarchical Bayesian methods provide a useful tool for decomposing ecological complexity into more tractable components.