A U-statistic estimator for the variance of resampling-based error estimators

We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Therefore, several standard theorems on properties of U-statistics apply. In particular, it has minimal variance among all unbiased estimators and is asymptotically normally distributed. Moreover, there is an unbiased estimator for this minimal variance if the total sample size is at least the double learning set size plus two. In this case, we exhibit such an estimator which is another U-statistic. It enjoys, again, various optimality properties and yields an asymptotically exact hypothesis test of the equality of error rates when two learning algorithms are compared. Our statements apply to any deterministic learning algorithms under weak non-degeneracy assumptions. In an application to tuning parameter choice in lasso regression on a gene expression data set, the test does not reject the null hypothesis of equal rates between two different parameters

Nonasymptotic Convergence Rates for Cooperative Learning Over Time-Varying Directed Graphs

We study the problem of distributed hypothesis testing with a network of agents where some agents repeatedly gain access to information about the correct hypothesis. The group objective is to globally agree on a joint hypothesis that best describes the observed data at all the nodes. We assume that the agents can interact with their neighbors in an unknown sequence of time-varying directed graphs. Following the pioneering work of Jadbabaie, Molavi, Sandroni, and Tahbaz-Salehi, we propose local learning dynamics which combine Bayesian updates at each node with a local aggregation rule of private agent signals. We show that these learning dynamics drive all agents to the set of hypotheses which best explain the data collected at all nodes as long as the sequence of interconnection graphs is uniformly strongly connected. Our main result establishes a non-asymptotic, explicit, geometric convergence rate for the learning dynamic

PENGARUH PEMBELAJARAN PROJECT BASED LEARNING BERINTEGRASIKAN SCIENCE, TECHNOLOGY, ENGINEERING, AND MATHEMATICS (STEM) TERHADAP HASIL BELAJAR GEOGRAFI DI SMA NEGERI 1 GORONTALO

The influence of science, technology, engineering, and mathematics (STEM) Integrend Learnig Process on the Learning Outcomes of 1 th Grade Student (An Experimental Research Implementend in SMA 1 State Senior  High School if Gorontalo). This study aimed to determine the differences in learning outcomes of student with the implementation of the Ppa-STEM learning model whilw the control class implemented the learning cycle (5E) learning model on the topic of “population planning and Development Dynamis in Indonesia”. To achieve these objecives, this research employed experimental design with post-test Control Group Design. Data collection techniques involved learning result test, which was provided towards the sample of research. The sample of the study consisted of two classes; class XIb3 of social science as the control class employed the learning cycle (5E) model. During the hypothesis testing, the homogeneity and normality test of the data was conducted in order to conduct hypothesis testing by using parametric statistics. The data normality test employed a chi-square statistical test of the pair of null hypothesis Ho and its match Hi with α = 0,05 significal rate. The test result showed that χ2count less than χ2table for the experimental class with 3,449 less than 11,070 and the control class of 1,023 less then is 9,488. The result revealed that the two data classes can be normally distributed. Based on the results of normality test data, the average score pg students learning outcomes used the statistical test. The hypothesis test results obtained tcount greater than ttable which was 6,58 greater than 2,02. All in all, the results revealed that there were differences in the learning outcomes of students who used the two aforeentioned learning models

THE EFFECT OF PROCESS ORIENTED GUIDED INQUIRY LEARNING (POGIL) MODEL ON SCIENCE PROCESS SKILLS (SPS) AND STUDENTS' COGNITIVE ABILITIES ON THE CONCEPT OF REACTION RATE

This study aims to determine the effect of the Process Oriented Guided  Inquiry Learning (POGIL) model on Science Process Skills (SPS), cognitive abilities and the correlation between SPS and students' cognitive abilities on the reaction rate concept. The sample in this study were 35 students of class XI SMA Negeri Seribu Bukit 2016-2017 academic year. The data was collected through observation and test. 20 multiple choice questions (alpha:0.81) were used to collect data of student’s SPS. While students' cognitive abilities were obtained by pre-test and post-test using 20 multiple choice questions (alpha:0.84). The distributed normally and homogeneously. The hypothesis was tested by using Paired Sample t-Test at a significance level of 0.05. Based on the data analysis and hypothesis testing carried out, there was a significant difference in the effect of the POGIL model on Science Process Skills (SPS), cognitive abilities and significant interactions between SPS and students' cognitive abilities on the material reaction rate, indicated by the value of each probability or sig. 0,000, so it can be concluded that the results of testing the hypothesis reject Ho or accept Ha at the 5 percent alpha level

PENGARUH SIKAP BELAJAR SISWA TERHADAP HASIL BELAJAR PADA MATA PELAJARAN EKONOMI DI SMA NEGERI 72 JAKARTA (STUDI KASUS SISWA KELAS X IPS DAN BAHASA TAHUN AJARAN 2013-2014)

ABSTRACT NEISYA FATHIA ANNISA, Effect Of Student Learning Attitude Towards Learning Outsomes In Subject Economic In The State Senior High 72 Jakarta (Case Study Class X Social Science And Linguistic Academic Year 2013-2014) This study aimed to determine the effect of learning attitude towards learning outcomes based on data and facts are eloquent, true and trustworthy. This research was conducted for one month starting from the month of June 2014. The method used is a survey method with simple regression approach. The population of this research is all class X in SMAN 72 Jakarta, Academic Year 2013/2014, amounting to 241 students. The population of this study is affordable whole class X Social Science and the whole class X Language School Year 2013/2014, amounting to 132 Simple regression equation obtained was Y = 52,39 + 0.055X. Test requirements analysis to test the normality of the error estimates of regression Y on X shows that the error estimates of regression Y on X is normally distributed. In hypothesis testing, significance testing, and linearity expressed means and linear regression. The test results obtained by the regression coefficient of 10,61 and Farithmatic to F with dk numerator 1 and dk denominator 93 at level 5% error rate of 4.00 is obtained. because F table arithmatic > F , it can be concluded that the mean regression equation. Linearity test results obtained using ANOVA tables with dk numerator 27 and dk denominator 66 at 5% error level obtained F table values of 0.87 and 1,70 at F t . With the value of Fh < F the regression equation (y = 52,39 + 0.055 X) Calculation of linear coefficients of determination showed t 10,24% variation of the variable Y is determined by the variable X. The conclusion of this research is that there is a positive effect between Effect Of Student Learning Attitude Towards Learning Outsomes In Subject Economic In The State Senior High 72 Jakarta (Case Study Class X Social Science And Linguistic Academic Year 2013-2014) Keyword : Attitude Leraning, Learning Outcomes, Subject Economy

Distributed Hypothesis Testing, Attention Shifts and Transmitter Dynatmics During the Self-Organization of Brain Recognition Codes

BP (89-A-1204); Defense Advanced Research Projects Agency (90-0083); National Science Foundation (IRI-90-00530); Air Force Office of Scientific Research (90-0175, 90-0128); Army Research Office (DAAL-03-88-K0088

Integrating Symbolic and Neural Processing in a Self-Organizing Architechture for Pattern Recognition and Prediction

British Petroleum (89A-1204); Defense Advanced Research Projects Agency (N00014-92-J-4015); National Science Foundation (IRI-90-00530); Office of Naval Research (N00014-91-J-4100); Air Force Office of Scientific Research (F49620-92-J-0225

Hypothesis Testing in Feedforward Networks with Broadcast Failures

Consider a countably infinite set of nodes, which sequentially make decisions between two given hypotheses. Each node takes a measurement of the underlying truth, observes the decisions from some immediate predecessors, and makes a decision between the given hypotheses. We consider two classes of broadcast failures: 1) each node broadcasts a decision to the other nodes, subject to random erasure in the form of a binary erasure channel; 2) each node broadcasts a randomly flipped decision to the other nodes in the form of a binary symmetric channel. We are interested in whether there exists a decision strategy consisting of a sequence of likelihood ratio tests such that the node decisions converge in probability to the underlying truth. In both cases, we show that if each node only learns from a bounded number of immediate predecessors, then there does not exist a decision strategy such that the decisions converge in probability to the underlying truth. However, in case 1, we show that if each node learns from an unboundedly growing number of predecessors, then the decisions converge in probability to the underlying truth, even when the erasure probabilities converge to 1. We also derive the convergence rate of the error probability. In case 2, we show that if each node learns from all of its previous predecessors, then the decisions converge in probability to the underlying truth when the flipping probabilities of the binary symmetric channels are bounded away from 1/2. In the case where the flipping probabilities converge to 1/2, we derive a necessary condition on the convergence rate of the flipping probabilities such that the decisions still converge to the underlying truth. We also explicitly characterize the relationship between the convergence rate of the error probability and the convergence rate of the flipping probabilities