885 research outputs found
Structural Agnostic Modeling: Adversarial Learning of Causal Graphs
A new causal discovery method, Structural Agnostic Modeling (SAM), is
presented in this paper. Leveraging both conditional independencies and
distributional asymmetries in the data, SAM aims at recovering full causal
models from continuous observational data along a multivariate non-parametric
setting. The approach is based on a game between players estimating each
variable distribution conditionally to the others as a neural net, and an
adversary aimed at discriminating the overall joint conditional distribution,
and that of the original data. An original learning criterion combining
distribution estimation, sparsity and acyclicity constraints is used to enforce
the end-to-end optimization of the graph structure and parameters through
stochastic gradient descent. Besides the theoretical analysis of the approach
in the large sample limit, SAM is extensively experimentally validated on
synthetic and real data
Feature Dynamic Bayesian Networks
Feature Markov Decision Processes (PhiMDPs) are well-suited for learning
agents in general environments. Nevertheless, unstructured (Phi)MDPs are
limited to relatively simple environments. Structured MDPs like Dynamic
Bayesian Networks (DBNs) are used for large-scale real-world problems. In this
article I extend PhiMDP to PhiDBN. The primary contribution is to derive a cost
criterion that allows to automatically extract the most relevant features from
the environment, leading to the "best" DBN representation. I discuss all
building blocks required for a complete general learning algorithm.Comment: 7 page
Minimum Description Length Induction, Bayesianism, and Kolmogorov Complexity
The relationship between the Bayesian approach and the minimum description
length approach is established. We sharpen and clarify the general modeling
principles MDL and MML, abstracted as the ideal MDL principle and defined from
Bayes's rule by means of Kolmogorov complexity. The basic condition under which
the ideal principle should be applied is encapsulated as the Fundamental
Inequality, which in broad terms states that the principle is valid when the
data are random, relative to every contemplated hypothesis and also these
hypotheses are random relative to the (universal) prior. Basically, the ideal
principle states that the prior probability associated with the hypothesis
should be given by the algorithmic universal probability, and the sum of the
log universal probability of the model plus the log of the probability of the
data given the model should be minimized. If we restrict the model class to the
finite sets then application of the ideal principle turns into Kolmogorov's
minimal sufficient statistic. In general we show that data compression is
almost always the best strategy, both in hypothesis identification and
prediction.Comment: 35 pages, Latex. Submitted IEEE Trans. Inform. Theor
- …