Estimating the Accuracy of Spectral Learning for HMMs

Hidden Markov models (HMMs) are usually learned using the expectation maximisation algorithm which is, unfortunately, subject to local optima. Spectral learning for HMMs provides a unique, optimal solution subject to availability of a sufficient amount of data. However, with access to limited data, there is no means of estimating the accuracy of the solution of a given model. In this paper, a new spectral evaluation method has been proposed which can be used to assess whether the algorithm is converging to a stable solution on a given dataset. The proposed method is designed for real-life datasets where the true model is not available. A number of empirical experiments on synthetic as well as real datasets indicate that our criterion is an accurate proxy to measure quality of models learned using spectral learning

Planning with Information-Processing Constraints and Model Uncertainty in Markov Decision Processes

Information-theoretic principles for learning and acting have been proposed to solve particular classes of Markov Decision Problems. Mathematically, such approaches are governed by a variational free energy principle and allow solving MDP planning problems with information-processing constraints expressed in terms of a Kullback-Leibler divergence with respect to a reference distribution. Here we consider a generalization of such MDP planners by taking model uncertainty into account. As model uncertainty can also be formalized as an information-processing constraint, we can derive a unified solution from a single generalized variational principle. We provide a generalized value iteration scheme together with a convergence proof. As limit cases, this generalized scheme includes standard value iteration with a known model, Bayesian MDP planning, and robust planning. We demonstrate the benefits of this approach in a grid world simulation.Comment: 16 pages, 3 figure

Instabilities and robust control in natural resource management

Most renewable natural resources exhibit marked demographic and environmental stochasticities, which are exarcebated in management decisions by the uncertainty regarding the choice of an appropriate model to describe system dynamics. Moreover, demand and supply analysis often indicates the presence of instabilities and multiple equilibria, which may lead to management problems that are intensified by uncertainty on the evolution of the resource stock. In this paper the fishery management problem is used as an example to explore the potential of robust optimal control, where the objective is to choose a harvesting rule that will work under a range of admissible specifications for the stock-recruitment equation. The paper derives robust harvesting rules leading to a unique equilibrium, which could be helpful in the design of policy instruments such as robust quota systems.info:eu-repo/semantics/publishedVersio

Empirical likelihood estimation of the spatial quantile regression

The spatial quantile regression model is a useful and flexible model for analysis of empirical problems with spatial dimension. This paper introduces an alternative estimator for this model. The properties of the proposed estimator are discussed in a comparative perspective with regard to the other available estimators. Simulation evidence on the small sample properties of the proposed estimator is provided. The proposed estimator is feasible and preferable when the model contains multiple spatial weighting matrices. Furthermore, a version of the proposed estimator based on the exponentially tilted empirical likelihood could be beneficial if model misspecification is suspect

Investor heterogeneity and the cross-section of U.K. investment trust performance

We use the upper and lower bounds derived by Ferson and Lin (2010) to examine the impact of investor heterogeneity on the performance of U.K. investment trusts relative to alternative linear factor models. We find using the upper bounds that investor heterogeneity has an important impact for nearly all investment trusts. The upper bounds are large in economic terms and significantly different from zero. We find no evidence of any trusts where all investors agree on the sign of performance beyond what we expect by chance. Using the lower bound, we find that trusts with a larger disagreement about trust performance have a weaker relation between the trust premium and past Net Asset Value (NAV) performance

Land of Addicts? An Empirical Investigation of Habit-Based Asset Pricing Models

A popular explanation of aggregate stock market behavior suggests that assets are priced as if there were a representative investor whose utility is a power function of the difference between aggregate consumption and a “habit” level, where the habit is some function of lagged and (possibly) contemporaneous consumption. But theory does not provide precise guidelines about the parametric functional relationship between the habit and aggregate consumption. This makes for- mal estimation and testing challenging; at the same time, it raises an empirical question about the functional form of the habit that best explains asset pricing data. This paper studies the ability of a general class of habit-based asset pricing models to match the conditional moment restrictions implied by asset pricing theory. Our approach is to treat the functional form of the habit as unknown, and to estimate it along with the rest of the model’s finite dimensional parameters. This semiparametric approach allows us to empirically evaluate a number of interesting hypotheses about the specification of habit-based asset pricing models. Using stationary quarterly data on consumption growth, assets returns and instruments, our empirical results indicate that the estimated habit function is nonlinear, the habit formation is internal, and the estimated time-preference parameter and the power utility parameter are sensible. In addition, our estimated habit function generates a positive stochastic discount factor (SDF) proxy and performs well in explaining cross-sectional stock return data. We find that an internal habit SDF proxy can explain a cross-section of size and book-market sorted portfolio equity returns better than (i) the Fama and French (1993) three-factor model, (ii) the Lettau and Ludvigson (2001b) scaled consumption CAPM model, (iii) an external habit SDF proxy, (iv) the classic CAPM, and (v) the classic consumption CAPM

Composite Fermion Metals from Dyon Black Holes and S-Duality

We propose that string theory in the background of dyon black holes in four-dimensional anti-de Sitter spacetime is holographic dual to conformally invariant composite Dirac fermion metal. By utilizing S-duality map, we show that thermodynamic and transport properties of the black hole match with those of composite fermion metal, exhibiting Fermi liquid-like. Built upon Dirac-Schwinger-Zwanziger quantization condition, we argue that turning on magnetic charges to electric black hole along the orbit of Gamma(2) subgroup of SL(2,Z) is equivalent to attaching even unit of statistical flux quanta to constituent fermions. Being at metallic point, the statistical magnetic flux is interlocked to the background magnetic field. We find supporting evidences for proposed holographic duality from study of internal energy of black hole and probe bulk fermion motion in black hole background. They show good agreement with ground-state energy of composite fermion metal in Thomas-Fermi approximation and cyclotron motion of a constituent or composite fermion excitation near Fermi-point.Comment: 30 pages, v2. 1 figure added, minor typos corrected; v3. revised version to be published in JHE

Risk, Unexpected Uncertainty, and Estimation Uncertainty: Bayesian Learning in Unstable Settings

Recently, evidence has emerged that humans approach learning using Bayesian updating rather than (model-free) reinforcement algorithms in a six-arm restless bandit problem. Here, we investigate what this implies for human appreciation of uncertainty. In our task, a Bayesian learner distinguishes three equally salient levels of uncertainty. First, the Bayesian perceives irreducible uncertainty or risk: even knowing the payoff probabilities of a given arm, the outcome remains uncertain. Second, there is (parameter) estimation uncertainty or ambiguity: payoff probabilities are unknown and need to be estimated. Third, the outcome probabilities of the arms change: the sudden jumps are referred to as unexpected uncertainty. We document how the three levels of uncertainty evolved during the course of our experiment and how it affected the learning rate. We then zoom in on estimation uncertainty, which has been suggested to be a driving force in exploration, in spite of evidence of widespread aversion to ambiguity. Our data corroborate the latter. We discuss neural evidence that foreshadowed the ability of humans to distinguish between the three levels of uncertainty. Finally, we investigate the boundaries of human capacity to implement Bayesian learning. We repeat the experiment with different instructions, reflecting varying levels of structural uncertainty. Under this fourth notion of uncertainty, choices were no better explained by Bayesian updating than by (model-free) reinforcement learning. Exit questionnaires revealed that participants remained unaware of the presence of unexpected uncertainty and failed to acquire the right model with which to implement Bayesian updating

Inherent Plasticity of Brown Adipogenesis in White Fat of Mice Allows for Recovery from Effects of Post-Natal Malnutrition

Interscapular brown adipose tissue (iBAT) is formed during fetal development and stable for the life span of the mouse. In addition, brown adipocytes also appear in white fat depots (wBAT) between 10 and 21 days of age in mice maintained at a room temperature of 23°C. However, this expression is transient. By 60 days of age the brown adipocytes have disappeared, but they can re-emerge if the adult mouse is exposed to the cold (5°C) or treated with β3-adrenergic agonists. Since the number of brown adipocytes that can be induced in white fat influences the capacity of the mouse to resist the obese state, we determined the effects of the nutritional conditions on post-natal development (birth to 21 days) of wBAT and its long-term effects on diet-induced obesity (DIO). Under-nutrition caused essentially complete suppression of wBAT in inguinal fat at 21 days of age, as indicated by expression of Ucp1 and genes of mitochondrial structure and function based upon microarray and qRT-PCR analysis, whereas over-nutrition had no discernible effects on wBAT induction. Surprisingly, the suppression of wBAT at 21 days of age did not affect DIO in adult mice maintained at 23°C, nor did it affect the reduction in obesity or cold tolerance when DIO mice were exposed to the cold at 5°C for one week. Gene expression analysis indicated that mice raised under conditions that suppressed wBAT at 21 days of age were able to normally induce wBAT as adults. Therefore, neither severe hypoleptinemia nor hypoinsulinemia during suckling permanently impaired brown adipogenesis in white fat. In addition, energy balance studies of DIO mice exposed to cold indicates that mice with reduced adipose stores preferentially increased food intake, whereas those with larger adipose tissue depots preferred to utilize energy from their adipose stores

Can sacrificial feeding areas protect aquatic plants from herbivore grazing? Using behavioural ecology to inform wildlife management

Effective wildlife management is needed for conservation, economic and human well-being objectives. However, traditional population control methods are frequently ineffective, unpopular with stakeholders, may affect non-target species, and can be both expensive and impractical to implement. New methods which address these issues and offer effective wildlife management are required. We used an individual-based model to predict the efficacy of a sacrificial feeding area in preventing grazing damage by mute swans (Cygnus olor) to adjacent river vegetation of high conservation and economic value. The accuracy of model predictions was assessed by a comparison with observed field data, whilst prediction robustness was evaluated using a sensitivity analysis. We used repeated simulations to evaluate how the efficacy of the sacrificial feeding area was regulated by (i) food quantity, (ii) food quality, and (iii) the functional response of the forager. Our model gave accurate predictions of aquatic plant biomass, carrying capacity, swan mortality, swan foraging effort, and river use. Our model predicted that increased sacrificial feeding area food quantity and quality would prevent the depletion of aquatic plant biomass by swans. When the functional response for vegetation in the sacrificial feeding area was increased, the food quantity and quality in the sacrificial feeding area required to protect adjacent aquatic plants were reduced. Our study demonstrates how the insights of behavioural ecology can be used to inform wildlife management. The principles that underpin our model predictions are likely to be valid across a range of different resource-consumer interactions, emphasising the generality of our approach to the evaluation of strategies for resolving wildlife management problems