scholarly journals Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities

Econometrica ◽  
2019 ◽  
Vol 87 (3) ◽  
pp. 867-932 ◽  
Author(s):  
Elizabeth Baldwin ◽  
Paul Klemperer
Keyword(s):  
Coalition Formation ◽  
Competitive Equilibrium ◽  
Equivalence Theorem ◽  
Equilibrium Existence ◽  
Existence Of Equilibrium ◽  
New Methods ◽  
Geometric Objects ◽  
Bank Of England ◽  
Intersection Points

An Equivalence Theorem between geometric structures and utility functions allows new methods for understanding preferences. Our classification of valuations into “Demand Types” incorporates existing definitions (substitutes, complements, “strong substitutes,” etc.) and permits new ones. Our Unimodularity Theorem generalizes previous results about when competitive equilibrium exists for any set of agents whose valuations are all of a “demand type.” Contrary to popular belief, equilibrium is guaranteed for more classes of purely‐complements than of purely‐substitutes, preferences. Our Intersection Count Theorem checks equilibrium existence for combinations of agents with specific valuations by counting the intersection points of geometric objects. Applications include matching and coalition‐formation, and the “Product‐Mix Auction” introduced by the Bank of England in response to the financial crisis.

On an “Important Principle” of Arrow and Debreu

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Arnis Vilks
Keyword(s):  
Simple Model ◽  
Technological Progress ◽  
Competitive Equilibrium ◽  
Private Ownership ◽  
Existence Of Equilibrium ◽  
Important Principle

Abstract In their seminal 1954 paper on the existence of competitive equilibrium, Arrow and Debreu state what they call an “important principle”, namely that it is necessary for the existence of equilibrium that every consumer has some asset or can supply some labour service which has a positive price at equilibrium. It does not seem to have been noticed that this claim is incorrect. We provide a very simple model of a private ownership economy with three goods where a competitive equilibrium exists, but consumers who have nothing to sell but their labour end up with zero wealth in equilibrium. As zero wealth must be taken to mean non-survival, and the Arrow–Debreu model is frequently interpreted as assuming that all consumers can survive without trade, we also briefly discuss the issue of non-survival in equilibrium. We finally point out that our example illustrates the possibility that technological progress may result in a situation where the value of work becomes negligible.

Classification of Chaotic Behaviors in Jerky Dynamical Systems

2021 ◽  
Vol 30 (1) ◽  
pp. 93-110
Author(s):  
Tianyi Wang ◽  
Keyword(s):  
Machine Learning ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Learning Algorithm ◽  
Model Systems ◽  
Supervised Machine Learning ◽  
Learning Program ◽  
New Methods ◽  
Over Time

Differential equations are widely used to model systems that change over time, some of which exhibit chaotic behaviors. This paper proposes two new methods to classify these behaviors that are utilized by a supervised machine learning algorithm. Dissipative chaotic systems, in contrast to conservative chaotic systems, seem to follow a certain visual pattern. Also, the machine learning program written in the Wolfram Language is utilized to classify chaotic behavior with an accuracy around 99.1±1.1%.

Setting Attribute Weights for Nearest Neighbor Learning Algorithms Using C4.5

1997 ◽  
Vol 11 (03) ◽  
pp. 405-415 ◽  
Author(s):  
Charles X. Ling ◽  
John J. Parry ◽  
Handong Wang
Keyword(s):  
Machine Learning ◽  
Decision Trees ◽  
Distance Function ◽  
Nearest Neighbor ◽  
Learning Algorithms ◽  
Simple Approach ◽  
Nearest Neighbour ◽  
Attribute Weights ◽  
New Methods

Nearest Neighbour (NN) learning algorithms utilize a distance function to determine the classification of testing examples. The attribute weights in the distance function should be set appropriately. We study situations where a simple approach of setting attribute weights using decision trees does not work well, and design three improvements. We test these new methods thoroughly using artificially generated datasets and datasets from the machine learning repository.

Ensemble Methods for Improving Classification of Data Produced by Latent Dirichlet Allocation

2019 ◽  
Vol 0 (8/2018) ◽  
pp. 17-28
Author(s):  
Maciej Jankowski
Keyword(s):  
Text Analysis ◽  
Large Scale ◽  
Latent Dirichlet Allocation ◽  
Previous Analysis ◽  
Ensemble Methods ◽  
Topic Modelling ◽  
New Methods ◽  
Data Scientist ◽  
Dirichlet Allocation

Topic models are very popular methods of text analysis. The most popular algorithm for topic modelling is LDA (Latent Dirichlet Allocation). Recently, many new methods were proposed, that enable the usage of this model in large scale processing. One of the problem is, that a data scientist has to choose the number of topics manually. This step, requires some previous analysis. A few methods were proposed to automatize this step, but none of them works very well if LDA is used as a preprocessing for further classification. In this paper, we propose an ensemble approach which allows us to use more than one model at prediction phase, at the same time, reducing the need of finding a single best number of topics. We have also analyzed a few methods of estimating topic number.

scholarly journals Prediction of Offending: SARPO—The Czech Tool for Assessment of Offenders' Criminogenic Risk and Needs

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Vaclav Jiricka ◽  
Zuzana Podana ◽  
Michal Petras ◽  
Jindrich Hurka
Keyword(s):  
Complex Analysis ◽  
Informed Choice ◽  
Assessment Tools ◽  
The Past ◽  
New Methods ◽  
Limited Effectiveness ◽  
Risk Assessment Tools ◽  
Probation Service ◽  
Offending Behaviour

In the past three decades, developed prison and probation services have paid large attention to risk assessment tools predicting the probability of reoffending. This not only resulted in a more accurate classification of offenders, but also in a more informed choice of effective intervention helping to reduce relapse in offending behaviour. In terms of reducing the risk of reoffending intervention programmes considering the principle of criminogenic risks, needs, and responsivity proved successful, while imprisonment on its own, where intervention methods were not applied, showed only limited effectiveness. For historical reasons, the Czech Prison Service underwent a different development, although its objectives were similar. It was not until the beginning of a new millennium when the Czech prison system together with a newly created probation service decided to seek new methods of assessing offenders based on criminogenic risks. This paper presents development and results of the first Czech tool used for assessment of offenders’ risks and needs, called SARPO (from the Czech abbreviation of Complex Analysis of Offenders’ Risk and Needs).

Stationary solutions of non-autonomous Kolmogorov–Petrovsky–Piskunov equations

1999 ◽  
Vol 19 (3) ◽  
pp. 809-835 ◽  
Author(s):  
V. A. VOLPERT ◽  
YU. M. SUHOV
Keyword(s):  
Existence And Uniqueness ◽  
Space Variable ◽  
Geometric Analysis ◽  
Stationary Solutions ◽  
Classical Approach ◽  
Uniqueness Of Solutions ◽  
New Methods ◽  
Autonomous Equation ◽  
Autonomous Case

The paper is devoted to the following problem: \[ w'' (x) + c w'(x)+ F(w(x),x) = 0, \quad x\in{\mathbb R}^1,\quad w(\pm \infty) = w_{\pm}, \] where the non-linear term $F$ depends on the space variable $x$. A classification of non-linearities is given according to the behaviour of the function $F(w,x)$ in a neighbourhood of the points $w_+$ and $w_-$. The classical approach used in the Kolmogorov–Petrovsky–Piskunov paper [10] for an autonomous equation (where $F=F(u)$ does not explicitly depend on $x$), which is based on the geometric analysis on the $(w,w')$-plane, is extended and new methods are developed to analyse the existence and uniqueness of solutions in the non-autonomous case. In particular, we study the case where the function $F(w,x)$ does not have limits as $x \rightarrow \pm \infty$.

scholarly journals A standardized, extensible framework for optimizing classification improves marker-gene taxonomic assignments

2015 ◽  
Author(s):  
Nicholas A Bokulich ◽  
Jai Ram Rideout ◽  
Evguenia Kopylova ◽  
Evan Bolyen ◽  
Jessica Patnode ◽  
...  
Keyword(s):  
Marker Gene ◽  
Amplicon Sequencing ◽  
Evaluation Framework ◽  
Taxonomic Resolution ◽  
Marker Genes ◽  
Classification Methods ◽  
New Methods ◽  
Taxonomic Assignments ◽  
Different Levels

Background: Taxonomic classification of marker-gene (i.e., amplicon) sequences represents an important step for molecular identification of microorganisms. Results: We present three advances in our ability to assign and interpret taxonomic classifications of short marker gene sequences: two new methods for taxonomy assignment, which reduce runtime up to two-fold and achieve high precision genus-level assignments; an evaluation of classification methods that highlights differences in performance with different marker genes and at different levels of taxonomic resolution; and an extensible framework for evaluating and optimizing new classification methods, which we hope will serve as a model for standardized and reproducible bioinformatics methods evaluations. Conclusions: Our new methods are accessible in QIIME 1.9.0, and our evaluation framework will support ongoing optimization of classification methods to complement rapidly evolving short-amplicon sequencing and bioinformatics technologies. Static versions of all of the analysis notebooks generated with this framework, which contain all code and analysis results, can be viewed at http://bit.ly/srta-010.

scholarly journals TEXT CLASSIFICATION BASED ON FUZZY RADIAL BASIS FUNCTION

2019 ◽  
Vol 45 (1) ◽  
pp. 11-14
Author(s):  
Zuhair Ali
Keyword(s):  
Radial Basis Function ◽  
Language Processing ◽  
Text Classification ◽  
Basis Function ◽  
Automated Classification ◽  
New Methods ◽  
Radial Basis ◽  
Document Collection ◽  
Better Than

Automated classification of text into predefined categories has always been considered as a vital method in thenatural language processing field. In this paper new methods based on Radial Basis Function (RBF) and Fuzzy Radial BasisFunction (FRBF) are used to solve the problem of text classification, where a set of features extracted for each sentencein the document collection these set of features introduced to FRBF and RBF to classify documents. Reuters 21578 datasetutilized for the purpose of text classification. The results showed the effectiveness of FRBF is better than RBF.

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