A Comparison of Machine-Learning Methods to Select Socioeconomic Indicators in Cultural Landscapes

Cultural landscapes are regarded to be complex socioecological systems that originated as a result of the interaction between humanity and nature across time. Cultural landscapes present complex-system properties, including nonlinear dynamics among their components. There is a close relationship between socioeconomy and landscape in cultural landscapes, so that changes in the socioeconomic dynamic have an effect on the structure and functionality of the landscape. Several numerical analyses have been carried out to study this relationship, with linear regression models being widely used. However, cultural landscapes comprise a considerable amount of elements and processes, whose interactions might not be properly captured by a linear model. In recent years, machine-learning techniques have increasingly been applied to the field of ecology to solve regression tasks. These techniques provide sound methods and algorithms for dealing with complex systems under uncertainty. The term ‘machine learning’ includes a wide variety of methods to learn models from data. In this paper, we study the relationship between socioeconomy and cultural landscape (in Andalusia, Spain) at two different spatial scales aiming at comparing different regression models from a predictive-accuracy point of view, including model trees and neural or Bayesian networks

Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks

We discuss the computational complexity of approximating maximum a posteriori inference in sum-product networks. We first show NP-hardness in trees of height two by a reduction from maximum independent set; this implies non-approximability within a sublinear factor. We show that this is a tight bound, as we can find an approximation within a linear factor in networks of height two. We then show that, in trees of height three, it is NP-hard to approximate the problem within a factor $2^{f(n)}$ for any sublinear function $f$ of the size of the input $n$. Again, this bound is tight, as we prove that the usual max-product algorithm finds (in any network) approximations within factor $2^{c \cdot n}$ for some constant $c < 1$. Last, we present a simple algorithm, and show that it provably produces solutions at least as good as, and potentially much better than, the max-product algorithm. We empirically analyze the proposed algorithm against max-product using synthetic and realistic networks.Comment: 18 page

Equi-energy sampler with applications in statistical inference and statistical mechanics

We introduce a new sampling algorithm, the equi-energy sampler, for efficient statistical sampling and estimation. Complementary to the widely used temperature-domain methods, the equi-energy sampler, utilizing the temperature--energy duality, targets the energy directly. The focus on the energy function not only facilitates efficient sampling, but also provides a powerful means for statistical estimation, for example, the calculation of the density of states and microcanonical averages in statistical mechanics. The equi-energy sampler is applied to a variety of problems, including exponential regression in statistics, motif sampling in computational biology and protein folding in biophysics.Comment: This paper discussed in: [math.ST/0611217], [math.ST/0611219], [math.ST/0611221], [math.ST/0611222]. Rejoinder in [math.ST/0611224]. Published at http://dx.doi.org/10.1214/009053606000000515 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Monotone concave operators: An application to the existence and uniqueness of solutions to the Bellman equation

We propose a new approach to the issue of existence and uniqueness of solutions to the Bellman equation, exploiting an emerging class of methods, called monotone map methods, pioneered in the work of Krasnosel’skii (1964) and Krasnosel’skii-Zabreiko (1984). The approach is technically simple and intuitive. It is derived from geometric ideas related to the study of fixed points for monotone concave operators defined on partially order spaces.Dynamic Programming; Bellman Equation; Unbounded Returns

An Experiment on Forward versus Backward Induction: How Fairness and Levels of Reasoning Matter

We report the experimental results on a game with an outside option where induction contradicts with background induction based on a focal, risk dominant equilibrium. The latter procedure yields the equilibrium selected by Harsanyi and Selton's (1888) theory, which is hence here in contradiction with strategic stability (Kohlberg-Mertens (1985)). We find the Harsanyi-Selton solution to be in much better agreement with our data. Since fairness and bounded rationality seem to matter we discuss whether recent behavioral theories, in particular fairness theories and learning, might explain our findings. The fairness theories by Fehr and Schmidt (1999), Bolton and Ockenfels (2000), when calibrated using experimental data on dictator- and ultimatum games, indeed predict that forward induction should play no role for our experiment and that the outside option should be chosen by all sufficiently selfish players. However, there is a multiplicity of "fairness equilibra", some of which seem to be rejected because they require too many levels of reasoning"experiments, equilibrium selection, forward induction, fairness, levels of reasoning.

Parameter Learning of Logic Programs for Symbolic-Statistical Modeling

We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. definite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distribution semantics, possible world semantics with a probability distribution which is unconditionally applicable to arbitrary logic programs including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM algorithm, the graphical EM algorithm, that runs for a class of parameterized logic programs representing sequential decision processes where each decision is exclusive and independent. It runs on a new data structure called support graphs describing the logical relationship between observations and their explanations, and learns parameters by computing inside and outside probability generalized for logic programs. The complexity analysis shows that when combined with OLDT search for all explanations for observations, the graphical EM algorithm, despite its generality, has the same time complexity as existing EM algorithms, i.e. the Baum-Welch algorithm for HMMs, the Inside-Outside algorithm for PCFGs, and the one for singly connected Bayesian networks that have been developed independently in each research field. Learning experiments with PCFGs using two corpora of moderate size indicate that the graphical EM algorithm can significantly outperform the Inside-Outside algorithm