اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدStaring at Economic Aggregators through Information Lenses
35
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
It is hard to exaggerate the role of economic aggregators -- functions that summarize numerous and / or heterogeneous data -- in economic models since the early XX$^{th}$ century. In many cases, as witnessed by the pioneering works of Cobb and Douglas, these functions were information quantities tailored to economic theories, i.e. they were built to fit economic phenomena. In this paper, we look at these functions from the complementary side: information. We use a recent toolbox built on top of a vast class of distortions coined by Bregman, whose application field rivals metrics in various subfields of mathematics. This toolbox makes it possible to find the quality of an aggregator (for consumptions, prices, labor, capital, wages, etc.), from the standpoint of the information it carries. We prove a rather striking result. From the informational standpoint, well-known economic aggregators do belong to the textit{optimal} set. As common economic assumptions enter the analysis, this large set shrinks, and it essentially ends up textit{exactly fitting} either CES, or Cobb-Douglas, or both. To summarize, in the relevant economic contexts, one could not have crafted better some aggregator from the information standpoint. We also discuss global economic behaviors of optimal information aggregators in general, and present a brief panorama of the links between economic and information aggregators. Keywords: Economic Aggregators, CES, Cobb-Douglas, Bregman divergences
قيم البحث
اقرأ أيضاً
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining `information. We discuss the extent to which Kolmogorovs and Shannons information t
heory have a common purpose, and where they are fundamentally different. We indicate how recent developments within the theory allow one to formally distinguish between `structural (meaningful) and `random information as measured by the Kolmogorov structure function, which leads to a mathematical formalization of Occams razor in inductive inference. We end by discussing some of the philosophical implications of the theory.
We prove that mutual information is actually negative copula entropy, based on which a method for mutual information estimation is proposed.
In this paper, we propose a new perspective for quantizing a signal and more specifically the channel state information (CSI). The proposed point of view is fully relevant for a receiver which has to send a quantized version of the channel state to t
he transmitter. Roughly, the key idea is that the receiver sends the right amount of information to the transmitter so that the latter be able to take its (resource allocation) decision. More formally, the decision task of the transmitter is to maximize an utility function u(x;g) with respect to x (e.g., a power allocation vector) given the knowledge of a quantized version of the function parameters g. We exhibit a special case of an energy-efficient power control (PC) problem for which the optimal task oriented CSI quantizer (TOCQ) can be found analytically. For more general utility functions, we propose to use neural networks (NN) based learning. Simulations show that the compression rate obtained by adapting the feedback information rate to the function to be optimized may be significantly increased.
Selecting a minimal feature set that is maximally informative about a target variable is a central task in machine learning and statistics. Information theory provides a powerful framework for formulating feature selection algorithms -- yet, a rigoro
us, information-theoretic definition of feature relevancy, which accounts for feature interactions such as redundant and synergistic contributions, is still missing. We argue that this lack is inherent to classical information theory which does not provide measures to decompose the information a set of variables provides about a target into unique, redundant, and synergistic contributions. Such a decomposition has been introduced only recently by the partial information decomposition (PID) framework. Using PID, we clarify why feature selection is a conceptually difficult problem when approached using information theory and provide a novel definition of feature relevancy and redundancy in PID terms. From this definition, we show that the conditional mutual information (CMI) maximizes relevancy while minimizing redundancy and propose an iterative, CMI-based algorithm for practical feature selection. We demonstrate the power of our CMI-based algorithm in comparison to the unconditional mutual information on benchmark examples and provide corresponding PID estimates to highlight how PID allows to quantify information contribution of features and their interactions in feature-selection problems.
It is commonly believed that the hidden layers of deep neural networks (DNNs) attempt to extract informative features for learning tasks. In this paper, we formalize this intuition by showing that the features extracted by DNN coincide with the resul
t of an optimization problem, which we call the `universal feature selection problem, in a local analysis regime. We interpret the weights training in DNN as the projection of feature functions between feature spaces, specified by the network structure. Our formulation has direct operational meaning in terms of the performance for inference tasks, and gives interpretations to the internal computation results of DNNs. Results of numerical experiments are provided to support the analysis.
الأسئلة المقترحة
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
