Probably approximately correct (PAC) learning analysis

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).

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A Formal Framework for Speedup Learning from Problems and Solutions

Journal of Artificial Intelligence Research ◽

10.1613/jair.154 ◽

1996 ◽

Vol 4 ◽

pp. 445-475 ◽

Cited By ~ 7

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.

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On Learning Perceptrons with Binary Weights

Neural Computation ◽

10.1162/neco.1993.5.5.767 ◽

1993 ◽

Vol 5 (5) ◽

pp. 767-782 ◽

Cited By ~ 5

Author(s):

Mostefa Golea ◽

Mario Marchand

Keyword(s):

Learning Curve ◽

Uniform Distribution ◽

Pac Learning ◽

Sample Complexity ◽

Average Case Analysis ◽

Average Case ◽

Hebb Rule ◽

Product Distributions ◽

Training Examples ◽

Learning Analysis

We present an algorithm that PAC learns any perceptron with binary weights and arbitrary threshold under the family of product distributions. The sample complexity of this algorithm is of O[(n/ε)4 ln(n/δ)] and its running time increases only linearly with the number of training examples. The algorithm does not try to find an hypothesis that agrees with all of the training examples; rather, it constructs a binary perceptron based on various probabilistic estimates obtained from the training examples. We show that, under the restricted case of the uniform distribution and zero threshold, the algorithm reduces to the well known clipped Hebb rule. We calculate exactly the average generalization rate (i.e., the learning curve) of the algorithm, under the uniform distribution, in the limit of an infinite number of dimensions. We find that the error rate decreases exponentially as a function of the number of training examples. Hence, the average case analysis gives a sample complexity of O[n ln(1/ε)], a large improvement over the PAC learning analysis. The analytical expression of the learning curve is in excellent agreement with the extensive numerical simulations. In addition, the algorithm is very robust with respect to classification noise.

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FUNCTION GRANULARITY ESTIMATION FOR MULTIMODAL OPTIMIZATION

International Journal of Artificial Intelligence Tools ◽

10.1142/s0218213005002065 ◽

2005 ◽

Vol 14 (01n02) ◽

pp. 199-213 ◽

Cited By ~ 1

Author(s):

JIAN ZHANG ◽

XIAOHUI YUAN ◽

BILL P. BUCKLES

Keyword(s):

Population Size ◽

Resource Sharing ◽

Fitness Landscape ◽

Function Optimization ◽

Pac Learning ◽

Multimodal Function Optimization ◽

Multimodal Function ◽

Optimal Population ◽

Probably Approximately Correct ◽

Fitness Distance Correlation

In this article, we study the subspace function granularity and present a method to estimate the sharing distance and the optimal population size. To achieve multimodal function optimization, niching techniques diversify the population of Evolutionary Algorithms (EA) and encourage heterogeneous convergence to multiple optima. The key to a successful diversification is effective resource sharing. Without knowing the fitness landscape, resource sharing is usually determined by uninformative assumptions on the number of peaks. Using the Probably Approximately Correct (PAC) learning theory and the ∊-cover concept, a PAC neighborhood for a set of samples is derived. Within this neighborhood, we sample the fitness landscape and compute the subspace Fitness Distance Correlation (FDC) coefficients. Using the estimated granularity feature of the fitness landscape, the sharing distance and the population size are determined. Experiments demonstrate that by using the estimated population size and sharing distance an Evolutionary Algorithm successfully identifies multiple optima.

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4 Pattern Recognition for Healing Burns to Compute Evidence: Space Syntax and Machine Learning Analysis of Burns Center Karachi

Sir Syed Research Journal of Engineering & Technology ◽

10.33317/ssurj.v1i1.64 ◽

2013 ◽

Vol 1 (1) ◽

pp. 13

Author(s):

Javaria Manzoor Shaikh ◽

JaeSeung Park

Keyword(s):

Pattern Recognition ◽

Prediction Models ◽

Uv Light ◽

Healing Process ◽

Space Syntax ◽

Depth Map ◽

Routine Tasks ◽

Hyper Plane ◽

First Time ◽

Learning Analysis

Usually elongated hospitalization is experienced byBurn patients, and the precise forecast of the placement of patientaccording to the healing acceleration has significant consequenceon healthcare supply administration. Substantial amount ofevidence suggest that sun light is essential to burns healing andcould be exceptionally beneficial for burned patients andworkforce in healthcare building. Satisfactory UV sunlight isfundamental for a calculated amount of burn to heal; this delicaterather complex matrix is achieved by applying patternclassification for the first time on the space syntax map of the floorplan and Browder chart of the burned patient. On the basis of thedata determined from this specific healthcare learning technique,nurse can decide the location of the patient on the floor plan, hencepatient safety first is the priority in the routine tasks by staff inhealthcare settings. Whereas insufficient UV light and vitamin Dcan retard healing process, hence this experiment focuses onmachine learning design in which pattern recognition andtechnology supports patient safety as our primary goal. In thisexperiment we lowered the adverse events from 2012- 2013, andnearly missed errors and prevented medical deaths up to 50%lower, as compared to the data of 2005- 2012 before this techniquewas incorporated.In this research paper, three distinctive phases of clinicalsituations are considered—primarily: admission, secondly: acute,and tertiary: post-treatment according to the burn pattern andhealing rate—and be validated by capable AI- origin forecastingtechniques to hypothesis placement prediction models for eachclinical stage with varying percentage of burn i.e. superficialwound, partial thickness or full thickness deep burn. Conclusivelywe proved that the depth of burn is directly proportionate to thedepth of patient’s placement in terms of window distance. Ourfindings support the hypothesis that the windowed wall is mosthealing wall, here fundamental suggestion is support vectormachines: which is most advantageous hyper plane for linearlydivisible patterns for the burns depth as well as the depth map isused.

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