Uncertainty in Economic Growth and Inequality

A step to consilience, starting with a deconstruction of the causality of uncertainty that is embedded in the fundamentals of growth and inequality, following a construction of aggregation laws that disclose the invariance principle across heterogeneous individuals, ending with a reconstruction of metric models that yields deeper structural connections via U.S. GDP and income data

Reduction of Markov Chains using a Value-of-Information-Based Approach

In this paper, we propose an approach to obtain reduced-order models of Markov chains. Our approach is composed of two information-theoretic processes. The first is a means of comparing pairs of stationary chains on different state spaces, which is done via the negative Kullback-Leibler divergence defined on a model joint space. Model reduction is achieved by solving a value-of-information criterion with respect to this divergence. Optimizing the criterion leads to a probabilistic partitioning of the states in the high-order Markov chain. A single free parameter that emerges through the optimization process dictates both the partition uncertainty and the number of state groups. We provide a data-driven means of choosing the `optimal' value of this free parameter, which sidesteps needing to a priori know the number of state groups in an arbitrary chain.Comment: Submitted to Entrop

Long Memory in Time Series of Economic Growth and Convergence

not availableeconomics of technology ;

Convex Optimization for Binary Classifier Aggregation in Multiclass Problems

Multiclass problems are often decomposed into multiple binary problems that are solved by individual binary classifiers whose results are integrated into a final answer. Various methods, including all-pairs (APs), one-versus-all (OVA), and error correcting output code (ECOC), have been studied, to decompose multiclass problems into binary problems. However, little study has been made to optimally aggregate binary problems to determine a final answer to the multiclass problem. In this paper we present a convex optimization method for an optimal aggregation of binary classifiers to estimate class membership probabilities in multiclass problems. We model the class membership probability as a softmax function which takes a conic combination of discrepancies induced by individual binary classifiers, as an input. With this model, we formulate the regularized maximum likelihood estimation as a convex optimization problem, which is solved by the primal-dual interior point method. Connections of our method to large margin classifiers are presented, showing that the large margin formulation can be considered as a limiting case of our convex formulation. Numerical experiments on synthetic and real-world data sets demonstrate that our method outperforms existing aggregation methods as well as direct methods, in terms of the classification accuracy and the quality of class membership probability estimates.Comment: Appeared in Proceedings of the 2014 SIAM International Conference on Data Mining (SDM 2014

Epidemics of rules, information aggregation failure and market crashes

This short paper argues that rationally motivated coordination between agents is an important ingredient to understand the current economic crisis. We argue that changes in parameters that model the structure of a macro-economy or financial markets are not exogenous but arise as agents adopt rules that appear to be the norm around them. For example, if a rule is adopted by the majority of ones' neighbors it will become acceptable or, alternatively, if agents learn that changing their rule leads to greater gains, they will modified their rules. However, as rules develop and spread they may have consequences at the aggregate level which are not anticipated by individuals. These rules may be adopted by implicit consensus as they turn out to be profitable for individuals, but they may also weaken the constraints imposed by regulators. Indeed, the emergence of new rules or the modification of old ones may render the whole system more fragile, which may then cease to function. To illustrate this we develop a simple model, motivated by the 2007-2008 crisis in credit derivatives markets, to show how coordination on simple and apparently profitable rules may cause a market to collapse.Coordination; economic crisis; economic rules; information aggregation

Protein folding disorders: Toward a basic biological paradigm

Mechanistic 'physics' models of protein folding fail to account for the observed spectrum of protein folding and aggregation disorders, suggesting that a more appropriately biological paradigm will be needed for understanding the etiology, prevention, and treatment of these diseases

Base-stock policies for lost-sales models: Aggregation and asymptotics

This paper considers the optimization of the base-stock level for the classical periodic review lost-sales inventory system. The optimal policy for this system is not fully understood and computationally expensive to obtain. Base-stock policies for this system are asymptotically optimal as lost-sales costs approach infinity, easy to implement and prevalent in practice. Unfortunately, the state space needed to evaluate a base-stock policy exactly grows exponentially in both the lead time and the base-stock level. We show that the dynamics of this system can be aggregated into a one-dimensional state space description that grows linearly in the base-stock level only by taking a non-traditional view of the dynamics. We provide asymptotics for the transition probabilities within this single dimensional state space and show that these asymptotics have good convergence properties that are independent of the lead time under mild conditions on the demand distribution. Furthermore, we show that these asymptotics satisfy a certain ow conservation property. These results lead to a new and computationally efficient heuristic to set base-stock levels in lost-sales systems. In a numerical study we demonstrate that this approach performs better than existing heuristics with an average gap with the best base-stock policy of 0.01% across a large test-bed