Structure learning of context-specific graphical models

Abstract The ultimate problem considered in this thesis is modeling a high-dimensional joint distribution over a set of discrete variables. For this purpose, we consider classes of context-specific graphical models and the main emphasis is on learning the structure of such models from data. Traditional graphical models compactly represent a joint distribution through a factorization justi ed by statements of conditional independence which are encoded by a graph structure. Context-speci c independence is a natural generalization of conditional independence that only holds in a certain context, speci ed by the conditioning variables. We introduce context-speci c generalizations of both Bayesian networks and Markov networks by including statements of context-specific independence which can be encoded as a part of the model structures. For the purpose of learning context-speci c model structures from data, we derive score functions, based on results from Bayesian statistics, by which the plausibility of a structure is assessed. To identify high-scoring structures, we construct stochastic and deterministic search algorithms designed to exploit the structural decomposition of our score functions. Numerical experiments on synthetic and real-world data show that the increased exibility of context-specific structures can more accurately emulate the dependence structure among the variables and thereby improve the predictive accuracy of the models.

Context-specific independence in graphical models

The theme of this thesis is context-speci c independence in graphical models. Considering a system of stochastic variables it is often the case that the variables are dependent of each other. This can, for instance, be seen by measuring the covariance between a pair of variables. Using graphical models, it is possible to visualize the dependence structure found in a set of stochastic variables. Using ordinary graphical models, such as Markov networks, Bayesian networks, and Gaussian graphical models, the type of dependencies that can be modeled is limited to marginal and conditional (in)dependencies. The models introduced in this thesis enable the graphical representation of context-speci c independencies, i.e. conditional independencies that hold only in a subset of the outcome space of the conditioning variables. In the articles included in this thesis, we introduce several types of graphical models that can represent context-speci c independencies. Models for both discrete variables and continuous variables are considered. A wide range of properties are examined for the introduced models, including identi ability, robustness, scoring, and optimization. In one article, a predictive classi er which utilizes context-speci c independence models is introduced. This classi er clearly demonstrates the potential bene ts of the introduced models. The purpose of the material included in the thesis prior to the articles is to provide the basic theory needed to understand the articles.

Time-varying Risk Premiums and Conditional Market Risk: Empirical Evidence from European Stock Markets

This study investigates the relationship between the time-varying risk premiums and conditional market risk in the stock markets of the ten member countries of Economy and Monetary Union. Second, it examines whether the conditional second moments change over time and are there asymmetric effects in the conditional covariance matrix. Third, it analyzes the possible effects of the chosen testing framework. Empirical analysis is conducted using asymmetric univariate and multivariate GARCH-in-mean models and assuming three different degrees of market integration. For a daily sample period from 1999 to 2007, the study shows that the time-varying market risk alone is not enough to explain the dynamics of risk premiums and indications are found that the market risk is detected only when its price is allowed to change over time. Also asymmetric effects in the conditional covariance matrix, which is found to be time-varying, are clearly present and should be recognized in empirical asset pricing analyses.

Word Equations and Related Topics. Independence, Decidability and Characterizations

The three main topics of this work are independent systems and chains of word equations, parametric solutions of word equations on three unknowns, and unique decipherability in the monoid of regular languages. The most important result about independent systems is a new method giving an upper bound for their sizes in the case of three unknowns. The bound depends on the length of the shortest equation. This result has generalizations for decreasing chains and for more than three unknowns. The method also leads to shorter proofs and generalizations of some old results. Hmelevksii’s theorem states that every word equation on three unknowns has a parametric solution. We give a significantly simplified proof for this theorem. As a new result we estimate the lengths of parametric solutions and get a bound for the length of the minimal nontrivial solution and for the complexity of deciding whether such a solution exists. The unique decipherability problem asks whether given elements of some monoid form a code, that is, whether they satisfy a nontrivial equation. We give characterizations for when a collection of unary regular languages is a code. We also prove that it is undecidable whether a collection of binary regular languages is a code.

Essays on auditor independence

Auditor independence is a cornerstone of the auditing profession and the basic principle that underpins the reputation of the auditing profession in the public eye. Indeed, it is the attribute most demanded from auditors by the public. Therefore, the sustainability of the auditing profession depends on how auditors can protect this principle. This dissertation consists of four interrelated essays concerned with auditor independence. Specifically, it examines situations that can threaten and impair auditor independence. In addition, this dissertation also examines several variables that may enhance and protect auditor independence. The first essay aims to examine the impact of social pressures occurring within audit firms on auditors’ judgment in the setting of a society with “high power distance” and “low individualism” cultural dimensions. The social pressures consisted of obedience pressure exerted by an auditor’s superior and conformity pressure exerted by an auditor’s colleague. Moreover, two moderating variables—a multi-dimensional professional commitment and locus of control—were included as moderator variables in the relationship between the social pressures faced by auditors and their judgment. The findings show that obedience and conformity pressures influence auditor judgment. Auditors who face the social pressures will make a judgment that may be even diametrically opposite to the independence principle. The findings also indicate that a multi-dimensional professional commitment and locus of control may potentially influence auditor judgment in a situation with social pressures. The second essay aims to investigate the association of advocacy and familiarity threats caused by auditor fee dependence and auditor tenure on auditor independence based on Finnish data, law, and auditing environment. This essay was motivated by the Green Paper on Audit Policy, published by the European Commission in 2010 that questions whether the maximum fee collected from a client should be regulated and whether consecutive assignments should be limited, among others. Contrary to popular belief, this essay does not find evidence that audit fees and long auditor tenure will jeopardise auditor independence. Therefore, the findings do not support policies to regulate auditor fees or limit auditor tenure in Finland. The third essay aims to examine the effect of client intimidation on auditor independence in an audit-client conflict situation. Intimidation threat is one of five independence threats that are explicitly referenced in the IFAC’s independence framework. Client intimidation was manifested in the client threatening to replace the auditor if the auditor did not adopt the client’s position. In addition, this essay examines the role of auditor’s perceived pressure and multi-dimensions of professional commitment as moderator variables. The findings suggest that auditors who experience client intimidation in an audit conflict situation are more likely to have their independence impaired than those who are in a similar situation but without client intimidation. Moreover, auditors who experience client intimidation perceive higher pressure than those who do not experience intimidation. Finally, auditors’ affective and continuance professional commitment dimensions moderate the relationship between auditors’ perceived pressures and auditor independence. The aim of the fourth essay is twofold. First, it aims to develop a scale for measuring auditors’ reputation awareness. Second, it aims to examine the correlation between the levels of auditor reputation awareness and auditor independence. A seven-item scale was developed as the reputation awareness scale. The findings indicate that the scale consists of one dimension. It also has a level of satisfactory reliability and a high level of validity. The findings show that there is a positive correlation between the level of auditors’ reputation awareness and auditor independence.

Time Varying Conditional Correlation Between Stock And Bond Returns: Evidence From CIVETS Nations

This thesis estimates long-run time variant conditional correlation between stock and bond returns of CIVETS (Colombia, Indonesia, Vietnam, Egypt, Turkey, and South Africa) nations. Further, aims to analyse the presence of asymmetric volatility effect in both asset returns, as well as, obverses increment or decrement in conditional correlation during pre-crisis and crisis period, which lead to make a reliable diversification decision. The Constant Conditional Correlation (CCC) GARCH model of Bollerslev (1990), the Dynamic Conditional Correlation (DCC) GARCH model (Engle 2002), and the Asymmetric Dynamic Conditional Correlation (ADCC) GARCH model of Cappiello, Engle, and Sheppard (2006) were implemented in the study. The analyses present strong evidence of time-varying conditional correlation in CIVETS markets, excluding Vietnam, during 2005-2013. In addition, negative innovation effects were found in both conditional variance and correlation of the asset returns. The results of this study recommend investors to include financial assets from these markets in portfolios, in order to obtain better stock-bond diversification benefits, especially during high volatility periods.

Russian and Eastern European Dynamic Conditional Correlations in light of the Russian crisis of 2014-2015

This thesis studies the impact of the latest Russian crisis on global markets, and especially Central and Eastern Europe. The results are compared to other shocks and crises over the last twenty years to see how significant they have been. The cointegration process of Central and Eastern European financial markets is also reviewed and updated. Using three separate conditional correlation GARCH models, the latest crisis is not found to have initiated similar surges in conditional correlations to previous crises over the last two decades. Market cointegration for Central and Eastern Europe is found to have stalled somewhat after initial correlation increases post EU accession.