scholarly journals A Formal Framework for Speedup Learning from Problems and Solutions

1996 ◽  
Vol 4 ◽  
pp. 445-475 ◽  
Author(s):  
P. Tadepalli ◽  
B. K. Natarajan
Keyword(s):  
Problem Solving ◽  
Sufficient Conditions ◽  
Theoretical Work ◽  
Pac Learning ◽  
Speedup Learning ◽  
Conditions For Learning ◽  
Control Rules ◽  
Formal Framework ◽  
Problems And Solutions ◽  
Probably Approximately Correct

Speedup learning seeks to improve the computational efficiency of problem solving with experience. In this paper, we develop a formal framework for learning efficient problem solving from random problems and their solutions. We apply this framework to two different representations of learned knowledge, namely control rules and macro-operators, and prove theorems that identify sufficient conditions for learning in each representation. Our proofs are constructive in that they are accompanied with learning algorithms. Our framework captures both empirical and explanation-based speedup learning in a unified fashion. We illustrate our framework with implementations in two domains: symbolic integration and Eight Puzzle. This work integrates many strands of experimental and theoretical work in machine learning, including empirical learning of control rules, macro-operator learning, Explanation-Based Learning (EBL), and Probably Approximately Correct (PAC) Learning.

SOME SUFFICIENT CONDITIONS OF LEARNABILITY IN THE LIMIT FROM POSITIVE DATA

2000 ◽  
Vol 11 (03) ◽  
pp. 515-524
Author(s):  
TAKESI OKADOME
Keyword(s):  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Conditions For Learning ◽  
Positive Data ◽  
Necessary And Sufficient ◽  
Learning In The Limit

The paper deals with learning in the limit from positive data. After an introduction and overview of earlier results, we strengthen a result of Sato and Umayahara (1991) by establishing a necessary and sufficient condition for the satisfaction of Angluin's (1980) finite tell-tale condition. Our other two results show that two notions introduced here, the finite net property and the weak finite net property, lead to sufficient conditions for learning in the limit from positive data. Examples not solvable by earlier methods are also given.

scholarly journals A Formal Account of Structuring Motor Actions With Sensory Prediction for a Naive Agent

2020 ◽  
Vol 7 ◽  
Author(s):  
Jean-Merwan Godon ◽  
Sylvain Argentieri ◽  
Bruno Gas
Keyword(s):  
Sufficient Conditions ◽  
Combinatorial Structure ◽  
Prediction Function ◽  
Formal Framework ◽  
Sensory Predictions ◽  
Spatial Displacements ◽  
Motor Actions ◽  
Sensory Prediction ◽  
Sensorimotor Contingency

For naive robots to become truly autonomous, they need a means of developing their perceptive capabilities instead of relying on hand crafted models. The sensorimotor contingency theory asserts that such a way resides in learning invariants of the sensorimotor flow. We propose a formal framework inspired by this theory for the description of sensorimotor experiences of a naive agent, extending previous related works. We then use said formalism to conduct a theoretical study where we isolate sufficient conditions for the determination of a sensory prediction function. Furthermore, we also show that algebraic structure found in this prediction can be taken as a proxy for structure on the motor displacements, allowing for the discovery of the combinatorial structure of said displacements. Both these claims are further illustrated in simulations where a toy naive agent determines the sensory predictions of its spatial displacements from its uninterpreted sensory flow, which it then uses to infer the combinatorics of said displacements.

Law in action or living law? Back to the beginning in sociology of law

Legal Studies ◽  
1984 ◽  
Vol 4 (2) ◽  
pp. 157-174 ◽  
Author(s):  
David Nelken
Keyword(s):  
Problem Solving ◽  
Recent Survey ◽  
Sociology Of Law ◽  
Conceptual Frameworks ◽  
Problems And Solutions ◽  
The Law ◽  
Sociological Approaches

Sociology of law often seems to be marked by a form of intellectual apartheid. Whilst social theorists refine their conceptual frameworks, those with more practical concerns robustly set out to investigate the ‘law in action’. Mixing of the two approaches is thought likely to impede their necessary separate development. One recent survey of the field concluded that:‘The trend is likely to be a continuing divergence between its theoretical and practical branches: the theoretical consisting mainly of re-analyses of old sociological approaches to law, and the practical continuing with its problem-solving approach without confronting the theoretical problems implicit in what it accepts as problems and solutions’.

The VC Dimension and Pseudodimension of Two-Layer Neural Networks with Discrete Inputs

1996 ◽  
Vol 8 (3) ◽  
pp. 625-628 ◽  
Author(s):  
Peter L. Bartlett ◽  
Robert C. Williamson
Keyword(s):  
Neural Networks ◽  
Basis Function ◽  
Upper Bounds ◽  
Pac Learning ◽  
Learning Performance ◽  
Sigmoid Function ◽  
Vc Dimension ◽  
Learning Framework ◽  
Probably Approximately Correct ◽  
Training Examples

We give upper bounds on the Vapnik-Chervonenkis dimension and pseudodimension of two-layer neural networks that use the standard sigmoid function or radial basis function and have inputs from {−D, …,D}n. In Valiant's probably approximately correct (pac) learning framework for pattern classification, and in Haussler's generalization of this framework to nonlinear regression, the results imply that the number of training examples necessary for satisfactory learning performance grows no more rapidly than W log (WD), where W is the number of weights. The previous best bound for these networks was O(W4).

scholarly journals On parameter estimation in the bass model by nonlinear least squares fitting the adoption curve

2013 ◽  
Vol 23 (1) ◽  
pp. 145-155 ◽  
Author(s):  
Darija Marković ◽  
Dragan Jukić
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Sufficient Conditions ◽  
Marketing Research ◽  
Nonlinear Least Squares ◽  
Theoretical Work ◽  
Bass Model ◽  
Least Squares Fitting ◽  
Least Squares Estimate

The Bass model is one of the most well-known and widely used first-purchase diffusion models in marketing research. Estimation of its parameters has been approached in the literature by various techniques. In this paper, we consider the parameter estimation approach for the Bass model based on nonlinear weighted least squares fitting of its derivative known as the adoption curve. We show that it is possible that the least squares estimate does not exist. As a main result, two theorems on the existence of the least squares estimate are obtained, as well as their generalization in the ls norm (1 ≤ s < ∞). One of them gives necessary and sufficient conditions which guarantee the existence of the least squares estimate. Several illustrative numerical examples are given to support the theoretical work.

scholarly journals Profiling and predicting the problem-solving patterns in China’s research systems: A methodology of intelligent bibliometrics and empirical insights

2020 ◽  
pp. 1-24
Author(s):  
Yi Zhang ◽  
Mengjia Wu ◽  
Zhengyin Hu ◽  
Robert Ward ◽  
Xue Zhang ◽  
...  
Keyword(s):  
Problem Solving ◽  
Driving Forces ◽  
High Quality Research ◽  
Evolutionary Mechanisms ◽  
Existing Problems ◽  
Research Systems ◽  
Network Analytics ◽  
The Future ◽  
Problems And Solutions ◽  
Research Problems

Uncovering the driving forces, strategic landscapes, and evolutionary mechanisms of China’s research systems is attracting rising interest around the globe. One topic of interest is to understand the problem-solving patterns in China’s research systems now and in the future. Targeting a set of high-quality research articles published by Chinese researchers between 2009 and 2018, and indexed in the Essential Science Indicators database, we developed an intelligent bibliometrics-based methodology for identifying the problem-solving patterns from scientific documents. Specifically, science overlay maps incorporating link prediction were used to profile China’s disciplinary interactions and predict potential cross-disciplinary innovation at a macro level. We proposed a function incorporating word embedding techniques to represent subjects, actions, and objects (SAO) retrieved from combined titles and abstracts into vectors and constructed a tri-layer SAO network to visualize SAOs and their semantic relationships. Then, at a micro level, we developed network analytics for identifying problems and solutions from the SAO network, and recommending potential solutions for existing problems. Empirical insights derived from this study provide clues to understand China’s research strengths and the science policies underlying them, along with the key research problems and solutions that Chinese researchers are focusing on now and might pursue in the future.

scholarly journals Deskripsi Kemampuan Pemecahan Masalah Trigonometri Ditinjau dari Tipe Kepribadian dan Tingkat Kecemasan Belajar Siswa Kelas X SMA Negeri 6 Makassar

2018 ◽  
Vol 6 (2) ◽  
pp. 158
Author(s):  
Kasriana Kasriana ◽  
Rasid Ode
Keyword(s):  
High School Students ◽  
Problem Solving ◽  
Sufficient Conditions ◽  
Relevant Information ◽  
Necessary Condition ◽  
Planning Problem ◽  
High Anxiety ◽  
School Students ◽  
Anxiety Levels ◽  
To Receive

Abstrak Penelitian ini bertujuan untuk mendeskripsikan siswa SMA dalam memecahkan masalah berdasarkan tipe kepribadian dan tingkat kecemasan belajar. Subjek penelitian ini adalah siswa kelas X SMA Negeri 6 Makassar dengan cara stratified sampling. Hasil penelitian menunjukan bahwa:(1) dalam memahami masalah, siswa tipe idealist tingkat kecemasan tinggi tidak menuliskan syarat cukup dan syarat perlu; (2) dalam membuat rencana pemecahan masalah, siswa mampu dalam menentukan informasi yang relevan untuk menyelesaikan soal; (3) dalam melaksanakan rencana pemecahan masalah, siswa mengerjakan soal sesuai dengan langkah pemecahan masalah. (1) dalam memahami masalah, Subjek idealist dengan tingkat kecemasan rendah mampu menuliskan apa yang diketahui dan apa yang ditanyakan; (2) dalam membuat rencana pemecahan masalah, siswa mampu mengaitkan antara hal yang diketahui dan hal yang ditanyakan; (3) dalam melaksanakan rencana pemecahan masalah, siswa menggunakan langkah-langkah yang telah disusun. (1) dalam memahami masalah, siswa tipe rational dengan tingkat kecemasan tinggi tidak menuliskan syarat cukup dan syarat perlu; (2) dalam membuat rencana pemecahan masalah, siswa mampu menerima informasi yang digunakan untuk menentukan rumus. (3) dalam melaksanakan rencana pemecahan masalah, siswa mampu menyelesaikan soal sesuai strategi yang telah dirancang. (1) dalam memahami masalah, siswa tipe rational dengan tingkat kecemasan rendah tidak menuliskan syarat cukup dan syarat perlu; (2) dalam membuat rencana pemecahan masalah, siswa mampu mengaitkan informasi yang ada pada soal; (3) dalam melaksanakan rencana pemecahan masalah, siswa mampu menggunakan langkah-langkah secara benar. Kata kunci: Pemecahan masalah, tipe kepribadian, kecemasan belajar Abstract This study aimed to describe the high school students in solving problems based on personality types and levels of anxiety learn. The subjects were students of class X SMA 6 Makassar with stratified sampling.The results showed that: (1) in understanding the problem, studentstype of idealist high anxiety levels did not write sufficient conditions and a necessary condition; (2) in planning problem solving, students are able to determine the relevant information to solve problems; (3) in carrying out the plan of solving the problem, the students do the problems in accordance with the troubleshooting steps. (1) in understanding the problem, subject idealist with low anxiety level is able to write what is known and what is being asked; (2) in planning problem solving, students are able to find connections between things that are known and things that were asked; (3) in carrying out the plan of solving the problem, the students use the steps that have been prepared. (1) in understanding the problem, students rational types with high anxiety levels did not write sufficient conditions and a necessary condition; (2) in planning problem solving, students are able to receive the information used to determine the formula. (3) in carrying out the plan of solving the problem, students are able to solve problems that have been designed in accordance strategy. (1) in understanding the problem, students rational types with low anxiety levels did not write sufficient conditions and a necessary condition; (2) in planning problem solving, students are able to associate the information on the matter; (3) in carrying out the plan of solving the problem, students are able to use the steps correctly

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