Projective, Sparse, and Learnable Latent Position Network Models

When modeling network data using a latent position model, it is typical to assume that the nodes' positions are independently and identically distributed. However, this assumption implies the average node degree grows linearly with the number of nodes, which is inappropriate when the graph is thought to be sparse. We propose an alternative assumption---that the latent positions are generated according to a Poisson point process---and show that it is compatible with various levels of sparsity. Unlike other notions of sparse latent position models in the literature, our framework also defines a projective sequence of probability models, thus ensuring consistency of statistical inference across networks of different sizes. We establish conditions for consistent estimation of the latent positions, and compare our results to existing frameworks for modeling sparse networks.Comment: 51 pages, 2 figure

On learnability of E–stable equilibria

While under recursive least squares learning the dynamics of the economy converges to rational expectations equilibria (REE) which are E–stable, some recent examples propose that E–stability is not a sufficient condition for learnability. In this paper, we provide some further evidence on the conditions under which E–stability of a particular equilibrium might fail to imply its stochastic gradient (SG) or generalized SG learnability. We also claim that the requirement on the speed of convergence of the learning process imposed by [4] also implies that E–stable equilibria are likely to be GSG learnable. We show this in a simple â€New Keneysian†model of optimal monetary policy design in which the stability of REE under SG learning. In this case, the paper gives the conditions which are necessary for reversal of learnabilityAdaptive learning, E–stability, stochastic gradient, learnability

Predictive PAC Learning and Process Decompositions

We informally call a stochastic process learnable if it admits a generalization error approaching zero in probability for any concept class with finite VC-dimension (IID processes are the simplest example). A mixture of learnable processes need not be learnable itself, and certainly its generalization error need not decay at the same rate. In this paper, we argue that it is natural in predictive PAC to condition not on the past observations but on the mixture component of the sample path. This definition not only matches what a realistic learner might demand, but also allows us to sidestep several otherwise grave problems in learning from dependent data. In particular, we give a novel PAC generalization bound for mixtures of learnable processes with a generalization error that is not worse than that of each mixture component. We also provide a characterization of mixtures of absolutely regular ($\beta$-mixing) processes, of independent probability-theoretic interest.Comment: 9 pages, accepted in NIPS 201

Monetary Policy, Determinacy, and Learnability in the Open Economy

We study how determinacy and learnability of global rational expectations equilibrium may be affected by monetary policy in a simple, two country, New Keynesian framework. The two blocks may be viewed as the U.S. and Europe, or as regions within the euro zone. We seek to understand how monetary policy choices may interact across borders to help or hinder the creation of a unique rational expectations equilibrium worldwide which can be learned by market participants. We study cases in which optimal policies are being pursued country by country as well as some forms of cooperation. We find that open economy considerations may alter conditions for determinacy and learnability relative to closed economy analyses, and that new concerns can arise in the analysis of classic topics such as the desirability of exchange rate targeting and monetary policy cooperation.

Monetary Policy, Determinancy and Learnability in the Open Economy

We study how determinacy and learnability of global rational expectations equilibrium may be affected by monetary policy in a simple, two country, New Keynesian framework.The two blocks may be viewed as the U.S. and Europe, or as regions within the euro zone.We seek to understand how monetary policy choices may interact across borders to help or hinder the creation of a unique rational expectations equilibrium worldwide which can be learned by market participants. We study cases in which optimal policies are being pursued country by country as well as some forms of cooperation.We find that open economy considerations may alter conditions for determinacy and learnability relative to closed economy analyses, and that new concerns can arise in the analysis of classic topics such as the desirability of exchange rate targeting and monetary policy cooperation. Keywords: Indeterminacy, learning, monetary policy rules, new open economy macroeconomics, exchange rate regimes, second generation policy coordination.learning;monetairy policy;open economy;macroeconomics;exchange rate;indeterminacy;second generation policy coordination

Monetary policy, determinacy, and learnability in the open economy

We study how determinacy and learnability of global rational expectations equilibrium may be affected by monetary policy in a simple, two country, New Keynesian framework. The two blocks may be viewed as the U.S. and Europe, or as regions within the euro zone. We seek to understand how monetary policy choices may interact across borders to help or hinder the creation of a unique rational expectations equilibrium worldwide which can be learned by market participants. We study cases in which optimal policies are being pursued country by country as well as some forms of cooperation. We find that open economy considerations may alter conditions for determinacy and learnability relative to closed economy analyses, and that new concerns can arise in the analysis of classic topics such as the desirability of exchange rate targeting and monetary policy cooperation. JEL Classification: E52, F33indeterminacy, international policy coordination, monetary policy rules, new open economy macroeconomics