16,079 research outputs found
Parameter identifiability of discrete Bayesian networks with hidden variables
Identifiability of parameters is an essential property for a statistical
model to be useful in most settings. However, establishing parameter
identifiability for Bayesian networks with hidden variables remains
challenging. In the context of finite state spaces, we give algebraic arguments
establishing identifiability of some special models on small DAGs. We also
establish that, for fixed state spaces, generic identifiability of parameters
depends only on the Markov equivalence class of the DAG. To illustrate the use
of these results, we investigate identifiability for all binary Bayesian
networks with up to five variables, one of which is hidden and parental to all
observable ones. Surprisingly, some of these models have parameterizations that
are generically 4-to-one, and not 2-to-one as label swapping of the hidden
states would suggest. This leads to interesting difficulties in interpreting
causal effects.Comment: 23 page
Vulnerability-attention analysis for space-related activities
Techniques for representing and analyzing trouble spots in structures and processes are discussed. Identification of vulnerable areas usually depends more on particular and often detailed knowledge than on algorithmic or mathematical procedures. In some cases, machine inference can facilitate the identification. The analysis scheme proposed first establishes the geometry of the process, then marks areas that are conditionally vulnerable. This provides a basis for advice on the kinds of human attention or machine sensing and control that can make the risks tolerable
Disintegration and Bayesian Inversion via String Diagrams
The notions of disintegration and Bayesian inversion are fundamental in
conditional probability theory. They produce channels, as conditional
probabilities, from a joint state, or from an already given channel (in
opposite direction). These notions exist in the literature, in concrete
situations, but are presented here in abstract graphical formulations. The
resulting abstract descriptions are used for proving basic results in
conditional probability theory. The existence of disintegration and Bayesian
inversion is discussed for discrete probability, and also for measure-theoretic
probability --- via standard Borel spaces and via likelihoods. Finally, the
usefulness of disintegration and Bayesian inversion is illustrated in several
examples.Comment: Accepted for publication in Mathematical Structures in Computer
Scienc
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Artificial Intelligence And Big Data Technologies To Close The Achievement Gap.
We observe achievement gaps even in rich western countries, such as the UK, which in principle have the resources as well as the social and technical infrastructure to provide a better deal for all learners. The reasons for such gaps are complex and include the social and material poverty of some learners with their resulting other deficits, as well as failure by government to allocate sufficient resources to remedy the situation. On the supply side of the equation, a single teacher or university lecturer, even helped by a classroom assistant or tutorial assistant, cannot give each learner the kind of one-to-one attention that would really help to boost both their motivation and their attainment in ways that might mitigate the achievement gap.
In this chapter Benedict du Boulay, Alexandra Poulovassilis, Wayne Holmes, and Manolis Mavrikis argue that we now have the technologies to assist both educators and learners, most commonly in science, technology, engineering and mathematics subjects (STEM), at least some of the time. We present case studies from the fields of Artificial Intelligence in Education (AIED) and Big Data. We look at how they can be used to provide personalised support for students and demonstrate that they are not designed to replace the teacher. In addition, we also describe tools for teachers to increase their awareness and, ultimately, free up time for them to provide nuanced, individualised support even in large cohorts
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