Combining experiments to discover linear cyclic models with latent variables

Volume: Vol 9 : AISTATS 2010 Host publication title: Proceedings of the 13th International Conference on Artificial Intelligence and StatisticsPeer reviewe

Bivariate least squares linear regression: towards a unified analytic formalism

Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error models, the dependent variable relates to the independent variable according to the usual additive model. Linear models of regression lines are considered in the general case of correlated errors in X and in Y for heteroscedastic data. The special case of (C) generalized orthogonal regression is considered in detail together with well known subcases. In the limit of homoscedastic data, the results determined for functional models are compared with their counterparts related to extreme structural models. While regression line slope and intercept estimators for functional and structural models necessarily coincide, the contrary holds for related variance estimators even if the residuals obey a Gaussian distribution, with a single exception. An example of astronomical application is considered, concerning the [O/H]-[Fe/H] empirical relations deduced from five samples related to different stars and/or different methods of oxygen abundance determination. For selected samples and assigned methods, different regression models yield consistent results within the errors for both heteroscedastic and homoscedastic data. Conversely, samples related to different methods produce discrepant results, due to the presence of (still undetected) systematic errors, which implies no definitive statement can be made at present. A comparison is also made between different expressions of regression line slope and intercept variance estimators, where fractional discrepancies are found to be not exceeding a few percent, which grows up to about 20% in presence of large dispersion data.Comment: 56 pages, 2 tables, and 2 figures. New Astronomy, accepte

On the Number of Experiments Sufficient and in the Worst Case Necessary to Identify All Causal Relations Among N Variables

We show that if any number of variables are allowed to be simultaneously and independently randomized in any one experiment, log2(N) + 1 experiments are sufficient and in the worst case necessary to determine the causal relations among N >= 2 variables when no latent variables, no sample selection bias and no feedback cycles are present. For all K, 0 < K < 1/(2N) we provide an upper bound on the number experiments required to determine causal structure when each experiment simultaneously randomizes K variables. For large N, these bounds are significantly lower than the N - 1 bound required when each experiment randomizes at most one variable. For kmax < N/2, we show that (N/kmax-1)+N/(2kmax)log2(kmax) experiments aresufficient and in the worst case necessary. We over a conjecture as to the minimal number of experiments that are in the worst case sufficient to identify all causal relations among N observed variables that are a subset of the vertices of a DAG.Comment: Appears in Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence (UAI2005

Juego y deporte: deslindes, matices y mezcolanzas

El tema de la charla de hoy es la diferencia entre juego y deporte. Hay muchos autores que diferencian entre el juego y el deporte como diciendo que el deporte es un juego más reglado, más precisamente reglado con una complejidad más grande de reglas con respecto al juego. No creo, no estoy de acuerdo con esto, ni creo que esa sea la diferencia fundamental entre ambos. Creo que no hay juegos sin reglas, que la regla es tan privativa del deporte como del juego. La diferencia estaría en lo siguiente: el deporte es una manifestación lúdica tardía en el ser humano.Facultad de Humanidades y Ciencias de la Educació