Isabelle for Philosophers

This is an introduction to the Isabelle proof assistant aimed at philosophers and their students

Selecting a robust decision making method to evaluate employee performance

This paper investigates how to select a robust decision making method to evaluate employee performance. Two multiple criteria decision making (MCDM) methods are considered for the evaluation of US coast guard officers. Sensitivity analysis is conducted to understand the nature of uncertainty in evaluation criteria and employee performance. Outcomes from this analysis provide an understanding of the most critical factors governing the evaluation. MCDM methods dealing with discrete sets of alternatives are considered. The stability of two MCDM methods' outcomes are compared and the method with the most stable outcome is recommended. The minimum percentage change in criteria weights and performance scores required to alter the outcome of the evaluation is calculated. An MCDM method is recommended based on a best compromise in minimum percentage change required in inputs to alter the outcome of a method

High--Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality

High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the "curse of dimensionality" states: many problems become exponentially difficult in high dimensions. Recently, the other side of the coin, the "blessing of dimensionality", has attracted much attention. It turns out that generic high-dimensional datasets exhibit fairly simple geometric properties. Thus, there is a fundamental tradeoff between complexity and simplicity in high dimensional spaces. Here we present a brief explanatory review of recent ideas, results and hypotheses about the blessing of dimensionality and related simplifying effects relevant to machine learning and neuroscience.Comment: 18 pages, 5 figure

On the solution uniqueness in portfolio optimization and risk analysis

We consider the issue of solution uniqueness of the mean-deviation portfolio optimization problem and its inverse for asset returns distributed over a finite number of scenarios. Due to the asymmetry of returns, the risk is assessed by a general deviation measure introduced by [Rockafellar et al., Mathematical Programming, Ser. B, 108 (2006), pp. 515–540] instead of the standard deviation as in the classical Markowitz optimization problem. We demonstrate that, in general, one cannot expect the uniqueness of Pareto-optimal profit sharing in cooperative investment and the uniqueness of solutions in the mean-deviation Black-Litterman asset allocation model. For a large class of deviation measures, we provide a resolution of the above non-uniqueness issues based on the principle of law-invariance. We provide several examples illustrating the non-uniqueness and the law-invariant solution