32,007 research outputs found
Bayesian inference in the time varying cointegration model
There are both theoretical and empirical reasons for believing that the parameters of macroeconomic models may vary over time. However, work with time-varying parameter models has largely involved Vector autoregressions (VARs), ignoring cointegration. This is despite the fact that cointegration plays an important role in informing macroeconomists on a range of issues. In this paper we develop time varying parameter models which permit coin- tegration. Time-varying parameter VARs (TVP-VARs) typically use state space representations to model the evolution of parameters. In this paper, we show that it is not sensible to use straightforward extensions of TVP-VARs when allowing for cointegration. Instead we develop a speci…cation which allows for the cointegrating space to evolve over time in a manner comparable to the random walk variation used with TVP-VARs. The properties of our approach are investigated before developing a method of posterior simulation. We use our methods in an empirical investigation involving a permanent/transitory variance decomposition for inflation
A mathematical theory of semantic development in deep neural networks
An extensive body of empirical research has revealed remarkable regularities
in the acquisition, organization, deployment, and neural representation of
human semantic knowledge, thereby raising a fundamental conceptual question:
what are the theoretical principles governing the ability of neural networks to
acquire, organize, and deploy abstract knowledge by integrating across many
individual experiences? We address this question by mathematically analyzing
the nonlinear dynamics of learning in deep linear networks. We find exact
solutions to this learning dynamics that yield a conceptual explanation for the
prevalence of many disparate phenomena in semantic cognition, including the
hierarchical differentiation of concepts through rapid developmental
transitions, the ubiquity of semantic illusions between such transitions, the
emergence of item typicality and category coherence as factors controlling the
speed of semantic processing, changing patterns of inductive projection over
development, and the conservation of semantic similarity in neural
representations across species. Thus, surprisingly, our simple neural model
qualitatively recapitulates many diverse regularities underlying semantic
development, while providing analytic insight into how the statistical
structure of an environment can interact with nonlinear deep learning dynamics
to give rise to these regularities
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