Estimating Maximally Probable Constrained Relations by Mathematical Programming

Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of estimating an equivalence relation on a set) and ranking (the problem of estimating a linear order on a set). We contribute a family of probability measures on the set of all relations between two finite, non-empty sets, which offers a joint abstraction of multi-label classification, correlation clustering and ranking by linear ordering. Estimating (learning) a maximally probable measure, given (a training set of) related and unrelated pairs, is a convex optimization problem. Estimating (inferring) a maximally probable relation, given a measure, is a 01-linear program. It is solved in linear time for maps. It is NP-hard for equivalence relations and linear orders. Practical solutions for all three cases are shown in experiments with real data. Finally, estimating a maximally probable measure and relation jointly is posed as a mixed-integer nonlinear program. This formulation suggests a mathematical programming approach to semi-supervised learning.Comment: 16 page

Estimating macrobenthic secondary production from body weight and biomass: a field test in a non-boreal intertidal habitat

Production (P) and biomass (B) data of different species from 3 stations in the intertidal zone of the Ria Formosa (southern Portugal, 37-degrees-N) were analysed. They were compared with equations from the literature to estimate P/BBAR ratios from body weight. A clear distinction must be made between (1) an intraspecific and (2) an interspecific comparison. (1) Results from 3 species supported a body weight exponent of -0.25 for the P/BBAR ratio, as is to be expected from a linear relationship between growth and respiration. (2) In an interspecific comparison, the weight exponent depends on the contribution of age or growth rate to the presence of large specimens in a sample. It is concluded that production in the specific habitat examined cannot be calculated properly from body weight and biomass by 1 simple equation which mixes interspecific and intraspecific effects, rather that both aspects should be separated into 2 different calculation steps.e Ger- man-Portuguese research project 'Die Biologie der Ria For- mosa', funded by the Bundesministerium fur Forschung und Technologie, Germany (Grant no. 03F0562Ainfo:eu-repo/semantics/publishedVersio

Estimating Euler equations

In this paper we consider conditions under which the estimation of a log-linearized Euler equation for consumption yields consistent estimates of preference parameters. When utility is isoelastic and a sample covering a long time period is available, consistent estimates are obtained from the loglinearized Euler equation when the innovations to the conditional variance of consumption growth are uncorrelated with the instruments typically used in estimation. We perform a Montecarlo experiment, consisting in solving and simulating a simple life cycle model under uncertainty, and show that in most situations, the estimates obtained from the log-linearized equation are not systematically biased. This is true even when we introduce heteroscedasticity in the process generating income. The only exception is when discount rates are very high (e.g. 47% per year). This problem arises because consumers are nearly always close to the maximum borrowing limit: the estimation bias is unrelated to the linearization and estimates using nonlinear GMM are as bad. Across all our situations, estimation using a log-linearized Euler equation does better than nonlinear GMM despite the absence of measurement error. Finally, we plot life cycle profiles for the variance of consumption growth, which, except when the discount factor is very high, is remarkably flat. This implies that claims that demographic variables in log-linearized Euler equations capture changes in the variance of consumption growth are unwarranted

Estimating Vulnerability

Many existing measures of vulnerability lack a theoretical basis. In this paper we propose to measure vulnerability rigorously as the welfare of a household which solves an intertemporal optimisation model under risk.In such models, in essence a stochastic version of the Ramsey model, an important part of chronic poverty may be caused by the ex ante response of households to risks. Our simulation results indicate that whether or not a household is to be classified as vulnerable depends strongly on the time horizon considered. We use the model to assess the accuracy of existing regression-based vulnerability measures. We find that these methods can be vastly improved by including asset measures in the regression.Vulnerability, household models.

Estimation of pulse heights and arrival times

The problem is studied of estimating the arrival times and heights of pulses of known shape observed with white additive noise. The main difficulty is estimating the number of pulses. When a maximum likelihood formulation is employed for the estimation problem, difficulties similar to the problem of estimating the order of an unknown system arise. The problem may be overcome using Rissanen's shortest data description approach. An estimation algorithm is described, and its consistency is proved. The results are illustrated by a simulation study using an example from seismic data processing also studied by Mendel

Spatial variability of groundwater recharge - I. Is it really variable?

The spatial variability of recharge is an important consideration in estimating recharge especially as all methods of estimating it are 'point' estimates and in most places recharge varies in space. This paper along with the accompanying paper attempts to find a suitable answer to the question of taking this variability into account in estimating groundwater recharge. This paper attempts to determine if recharge is actually varying in space and that this is 'true' variability and that it is not an artefact of the method used for estimating recharge. It also pulls together information on spatial variability of recharge reported by various workers in the literature, in order to determine if recharge is truly variable in space