Bayesian Optimization for Probabilistic Programs

We present the first general purpose framework for marginal maximum a posteriori estimation of probabilistic program variables. By using a series of code transformations, the evidence of any probabilistic program, and therefore of any graphical model, can be optimized with respect to an arbitrary subset of its sampled variables. To carry out this optimization, we develop the first Bayesian optimization package to directly exploit the source code of its target, leading to innovations in problem-independent hyperpriors, unbounded optimization, and implicit constraint satisfaction; delivering significant performance improvements over prominent existing packages. We present applications of our method to a number of tasks including engineering design and parameter optimization

An Entropy Search Portfolio for Bayesian Optimization

Bayesian optimization is a sample-efficient method for black-box global optimization. How- ever, the performance of a Bayesian optimization method very much depends on its exploration strategy, i.e. the choice of acquisition function, and it is not clear a priori which choice will result in superior performance. While portfolio methods provide an effective, principled way of combining a collection of acquisition functions, they are often based on measures of past performance which can be misleading. To address this issue, we introduce the Entropy Search Portfolio (ESP): a novel approach to portfolio construction which is motivated by information theoretic considerations. We show that ESP outperforms existing portfolio methods on several real and synthetic problems, including geostatistical datasets and simulated control tasks. We not only show that ESP is able to offer performance as good as the best, but unknown, acquisition function, but surprisingly it often gives better performance. Finally, over a wide range of conditions we find that ESP is robust to the inclusion of poor acquisition functions.Comment: 10 pages, 5 figure

The Price-Level Computation Method

It has been submitted that, for the very large number of different traditional type formulae to determine price indices associated with a pair of periods, which are joined with the longstanding question of which one to choose, they should all be abandoned. For the method proposed instead, price levels associated with periods are first all computed together, subject to a consistency of the data, and then price indices that are as taken together true are determined from their ratios. An approximation method can apply in the case of inconsistency. Here is an account of the mathematics of the methodinflation, index-number problem, non-parametric, price index, price level, revealed preference

Optimal exact designs of experiments via Mixed Integer Nonlinear Programming

Optimal exact designs are problematic to find and study because there is no unified theory for determining them and studyingtheir properties. Each has its own challenges and when a method exists to confirm the design optimality, it is invariablyapplicable to the particular problem only.We propose a systematic approach to construct optimal exact designs by incorporatingthe Cholesky decomposition of the Fisher Information Matrix in a Mixed Integer Nonlinear Programming formulation. Asexamples, we apply the methodology to find D- and A-optimal exact designs for linear and nonlinear models using global orlocal optimizers. Our examples include design problems with constraints on the locations or the number of replicates at theoptimal design points

The Computation of Optimum Linear Taxation

The equitable sharing of the benefits arising from planned development is a subject of lively contemporary debate. One of the tasks being carried out by the System and Decision Sciences Area of the International Institute for Applied Systems Analysis (IIASA) concerns the treatment of planning and redustribution problems in ways that can provide some guidance to decision makers in the formulation of economic policy. This report examines the first part of a study undertaken to assess the redistributive leverage provided by different instruments of planning. It is devoted specifically to the analysis and computation of optimal redistributive policies in small, general equilibrium models of economic planning

Remote estimation of surface moisture over a watershed

The author has identified the following significant results. Contoured analyses of moisture availability, moisture flux, sensible heat flux, thermal inertia, and day and nighttime temperatures over a Missouri watershed for a date in June and in September show that forests and creeks exhibit the highest values of moisture availability, whereas farmlands and villages are relatively dry. The distribution of moisture availability over agricultural districts differs significantly between the two cases. This difference is attributed to a change in the surface's vegetative canopy between June and September, with higher moisture availabilities found in the latter case. Horizontal variations of moisture, however, do indicate some relationship between moisture availability and both local rainfall accumulations and the nature of the terrain

Economic analyses for the evaluation of is projects

Information system projects usually have numerous uncertainties and several conditions of risk that make their economic evaluation a challenging task. Each year, several information system projects are cancelled before completion as a result of budget overruns at a cost of several billions of dollars to industry. Although engineering economic analysis offers tools and techniques for evaluating risky projects, the tools are not enough to place information system projects on a safe budget/selection track. There is a need for an integrative economic analysis model that will account for the uncertainties in estimating project costs benefits and useful lives of uncertain and risky projects. The fuzzy set theory has the capability of representing vague data and allows mathematical operators and programming to be applied to the fuzzy domain. The theory is primarily concerned with quantifying the vagueness in human thoughts and perceptions. In this article, the economic evaluation of information system projects using fuzzy present value and fuzzy B/C ratio is analyzed. A numerical illustration is included to demonstrate the effectiveness of the proposed methods

Optimal Portfolio Allocation under a Probabilistic Risk Constraint and the Incentives for Financial Innovation

We derive, in a complete markets environment, an investor's optimal portfolio allocation subject to both a budget constraint and a probabilistic risk constraint. We demonstrate that the set of feasible portfolios need not be connected or convex, while the number of local optima increases exponentially with the number of securities implying that finding the optimal portfolio is computationally complex (NP hard). The resulting optimal portfolio allocation may not be monotonic in the state-price density. A novel type of financial innovation, which splits states of nature, is shown to weakly enhance welfare, restore monotonicity in the state-price density, and may reduce complexity

The Kalai-Smorodinski solution for many-objective Bayesian optimization

An ongoing aim of research in multiobjective Bayesian optimization is to extend its applicability to a large number of objectives. While coping with a limited budget of evaluations, recovering the set of optimal compromise solutions generally requires numerous observations and is less interpretable since this set tends to grow larger with the number of objectives. We thus propose to focus on a specific solution originating from game theory, the Kalai-Smorodinsky solution, which possesses attractive properties. In particular, it ensures equal marginal gains over all objectives. We further make it insensitive to a monotonic transformation of the objectives by considering the objectives in the copula space. A novel tailored algorithm is proposed to search for the solution, in the form of a Bayesian optimization algorithm: sequential sampling decisions are made based on acquisition functions that derive from an instrumental Gaussian process prior. Our approach is tested on four problems with respectively four, six, eight, and nine objectives. The method is available in the Rpackage GPGame available on CRAN at https://cran.r-project.org/package=GPGame