Determinacy and Learnability of Monetary Policy Rules in Small Open Economies

This paper evaluates under which conditions different Taylor-type rules lead to determinacy and expectational stability (E-stability) of rational expectations equilibrium in a simple New Keynesian small open economy model, developed by Gali and Monacelli (2005). In particular, we extend the Bullard and Mitra (2002) results of determinacy and E-stability in a closed economy to this small open economy framework. Our results highlight an important link between the Taylor principle and both determinacy and learnability of equilibrium in small open economies. More importantly, the degree of openness coupled with the nature of the policy rule adopted by the monetary authorities might change this link in important ways. A key finding is that, contrary to Bullard and Mitra, expectations-based rules that involve the CPI and/or the nominal exchange rate limit the region of E-stability and the Taylor Principle does not guarantee E-stability. We also show that some forms of managed exchange rate rules can help to alleviate problems of both indeterminacy and expectational instability, yet these rules might not be desirable since they promote greater volatility in the economy.

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

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

Towards unsupervised ontology learning from data

Data-driven elicitation of ontologies from structured data is a well-recognized knowledge acquisition bottleneck. The development of efficient techniques for (semi-)automating this task is therefore practically vital - yet, hindered by the lack of robust theoretical foundations. In this paper, we study the problem of learning Description Logic TBoxes from interpretations, which naturally translates to the task of ontology learning from data.In the presented framework, the learner is provided with a set of positive interpretations (i.e., logical models) of the TBox adopted by the teacher. The goal is to correctly identify the TBox given this input. We characterize the key constraints on the models that warrant finite learnability of TBoxes expressed in selected fragments of the Description Logic ε λ and define corresponding learning algorithms.This work was funded in part by the National Research Foundation under Grant no. 85482

Formal Modeling of Connectionism using Concurrency Theory, an Approach Based on Automata and Model Checking

This paper illustrates a framework for applying formal methods techniques, which are symbolic in nature, to specifying and verifying neural networks, which are sub-symbolic in nature. The paper describes a communicating automata [Bowman & Gomez, 2006] model of neural networks. We also implement the model using timed automata [Alur & Dill, 1994] and then undertake a verification of these models using the model checker Uppaal [Pettersson, 2000] in order to evaluate the performance of learning algorithms. This paper also presents discussion of a number of broad issues concerning cognitive neuroscience and the debate as to whether symbolic processing or connectionism is a suitable representation of cognitive systems. Additionally, the issue of integrating symbolic techniques, such as formal methods, with complex neural networks is discussed. We then argue that symbolic verifications may give theoretically well-founded ways to evaluate and justify neural learning systems in the field of both theoretical research and real world applications

Learning, monetary policy and housing prices

This paper evaluates different types of simple monetary policy rules according to the determinacy and learnability of rational expectations equilibrium criteria within a dynamic stochastic general equilibrium framework. Incorporating housing prices and collateralized borrowing into the standard model allow us to answer important policy questions. One objective is to investigate whether responding to housing prices affects determinacy and learnability of rational expectations equilibrium. For this purpose, we work with a New Keynesian model in which housing plays an accelerator role in business cycles as a collateralized asset. The results show that for current data rule, responding to asset prices does not improve learnable outcomes but for a monetary policy with lagged data and forward-looking rules we see improved learnable outcome if current housing prices are available to monetary authority. Moreover, we examine the effects of interest rate inertia and price stickiness on E-stability of REE.monetary policy rules, determinacy, learning, housing prices