scholarly journals Transductive Rademacher Complexity and its Applications

2009 ◽  
Vol 35 ◽  
pp. 193-234 ◽  
Author(s):  
R. El-Yaniv ◽  
D. Pechyony
Keyword(s):  
Error Bound ◽  
Error Bounds ◽  
Learning Algorithms ◽  
Transductive Learning ◽  
Rademacher Complexity ◽  
Rademacher Averages ◽  
Dependent Error ◽  
General Error

We develop a technique for deriving data-dependent error bounds for transductive learning algorithms based on transductive Rademacher complexity. Our technique is based on a novel general error bound for transduction in terms of transductive Rademacher complexity, together with a novel bounding technique for Rademacher averages for particular algorithms, in terms of their "unlabeled-labeled" representation. This technique is relevant to many advanced graph-based transductive algorithms and we demonstrate its effectiveness by deriving error bounds to three well known algorithms. Finally, we present a new PAC-Bayesian bound for mixtures of transductive algorithms based on our Rademacher bounds.

scholarly journals New error bounds for linear complementarity problems of Σ-SDD matrices and SB-matrices

2019 ◽  
Vol 17 (1) ◽  
pp. 1599-1614
Author(s):  
Zhiwu Hou ◽  
Xia Jing ◽  
Lei Gao
Keyword(s):  
Linear Algebra ◽  
Error Bound ◽  
Linear Complementarity Problem ◽  
Error Bounds ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Numerical Examples ◽  
Numer Algor ◽  
Better Than

Abstract A new error bound for the linear complementarity problem (LCP) of Σ-SDD matrices is given, which depends only on the entries of the involved matrices. Numerical examples are given to show that the new bound is better than that provided by García-Esnaola and Peña [Linear Algebra Appl., 2013, 438, 1339–1446] in some cases. Based on the obtained results, we also give an error bound for the LCP of SB-matrices. It is proved that the new bound is sharper than that provided by Dai et al. [Numer. Algor., 2012, 61, 121–139] under certain assumptions.

scholarly journals Bootstrap Domain-Specific Sentiment Classifiers from Unlabeled Corpora

2018 ◽  
Vol 6 ◽  
pp. 269-285 ◽  
Author(s):  
Andrius Mudinas ◽  
Dell Zhang ◽  
Mark Levene
Keyword(s):  
Supervised Learning ◽  
Learning Algorithms ◽  
General Purpose ◽  
Machine Learning Algorithms ◽  
Sentiment Classification ◽  
Two Phase ◽  
Transductive Learning ◽  
Domain Specific ◽  
Sentiment Lexicon ◽  
Supervised Learning Algorithms

There is often the need to perform sentiment classification in a particular domain where no labeled document is available. Although we could make use of a general-purpose off-the-shelf sentiment classifier or a pre-built one for a different domain, the effectiveness would be inferior. In this paper, we explore the possibility of building domain-specific sentiment classifiers with unlabeled documents only. Our investigation indicates that in the word embeddings learned from the unlabeled corpus of a given domain, the distributed word representations (vectors) for opposite sentiments form distinct clusters, though those clusters are not transferable across domains. Exploiting such a clustering structure, we are able to utilize machine learning algorithms to induce a quality domain-specific sentiment lexicon from just a few typical sentiment words (“seeds”). An important finding is that simple linear model based supervised learning algorithms (such as linear SVM) can actually work better than more sophisticated semi-supervised/transductive learning algorithms which represent the state-of-the-art technique for sentiment lexicon induction. The induced lexicon could be applied directly in a lexicon-based method for sentiment classification, but a higher performance could be achieved through a two-phase bootstrapping method which uses the induced lexicon to assign positive/negative sentiment scores to unlabeled documents first, a nd t hen u ses those documents found to have clear sentiment signals as pseudo-labeled examples to train a document sentiment classifier v ia supervised learning algorithms (such as LSTM). On several benchmark datasets for document sentiment classification, our end-to-end pipelined approach which is overall unsupervised (except for a tiny set of seed words) outperforms existing unsupervised approaches and achieves an accuracy comparable to that of fully supervised approaches.

scholarly journals Multi-Class Learning using Unlabeled Samples: Theory and Algorithm

2019 ◽  
Author(s):  
Jian Li ◽  
Yong Liu ◽  
Rong Yin ◽  
Weiping Wang
Keyword(s):  
Theoretical Analysis ◽  
Statistical Learning ◽  
Error Bound ◽  
State Of The Art ◽  
Experimental Results ◽  
Generalization Performance ◽  
Rademacher Complexity ◽  
Learning Framework ◽  
Multi Class Classification ◽  
Laplacian Regularization

In this paper, we investigate the generalization performance of multi-class classification, for which we obtain a shaper error bound by using the notion of local Rademacher complexity and additional unlabeled samples, substantially improving the state-of-the-art bounds in existing multi-class learning methods. The statistical learning motivates us to devise an efficient multi-class learning framework with the local Rademacher complexity and Laplacian regularization. Coinciding with the theoretical analysis, experimental results demonstrate that the stated approach achieves better performance.

scholarly journals Teaching Semi-Supervised Classifier via Generalized Distillation

2018 ◽  
Author(s):  
Chen Gong ◽  
Xiaojun Chang ◽  
Meng Fang ◽  
Jian Yang
Keyword(s):  
Supervised Learning ◽  
Error Bounds ◽  
State Of The Art ◽  
Training Data ◽  
Training Process ◽  
Rademacher Complexity ◽  
Optimization Framework ◽  
Specific Teaching ◽  
Teaching Function ◽  
Intelligent Teacher

Semi-Supervised Learning (SSL) is able to build reliable classifier with very scarce labeled examples by properly utilizing the abundant unlabeled examples. However, existing SSL algorithms often yield unsatisfactory performance due to the lack of supervision information. To address this issue, this paper formulates SSL as a Generalized Distillation (GD) problem, which treats existing SSL algorithm as a learner and introduces a teacher to guide the learner?s training process. Specifically, the intelligent teacher holds the privileged knowledge that ?explains? the training data but remains unknown to the learner, and the teacher should convey its rich knowledge to the imperfect learner through a specific teaching function. After that, the learner gains knowledge by ?imitating? the output of the teaching function under an optimization framework. Therefore, the learner in our algorithm learns from both the teacher and the training data, so its output can be substantially distilled and enhanced. By deriving the Rademacher complexity and error bounds of the proposed algorithm, the usefulness of the introduced teacher is theoretically demonstrated. The superiority of our algorithm to the related state-of-the-art methods has also been empirically demonstrated by the experiments on different datasets with various sources of privileged knowledge.

Error Bounds for Estimates of Entrained Ichthyoplankton

1983 ◽  
Vol 40 (1) ◽  
pp. 10-16 ◽  
Author(s):  
C. P. Madenjian ◽  
D. J. Jude
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Error Bound ◽  
Error Bounds ◽  
Correlation Time ◽  
Serial Correlation ◽  
Lake Michigan ◽  
Fish Larvae ◽  
Independent Component ◽  
Series Analysis

Entrainment of fish larvae and eggs was monitored at the J. H. Campbell Plant, eastern Lake Michigan, from 1977 to 1979. A procedure for calculating error bounds for estimated number of fish larvae (or eggs) entrained by the plant for each year of operation, assuming independence among observations, was outlined. A new method for calculating these bounds was devised by adjusting the variance for its non-independent component, using time series analysis. Serial correlation in the data was accounted for by modeling the sequence of entrainment data for a year as a time series. For many taxa of fish larvae the entrainment observations were determined to be independent and no adjustment was necessary. The width of the adjusted error-bound intervals ranged from 4.8 to 87.9% greater than unadjusted ones for those taxa for which adjustment was required, thus assuming independence among observations could result in serious underestimation of the error-bound interval.Key words: error bounds, variance, entrainment, Lake Michigan, serial correlation, time series analysis

scholarly journals A Note on Error Bounds for Approximating Transition Probabilities in Continuous-time Markov Chains

1988 ◽  
Vol 2 (4) ◽  
pp. 471-474 ◽  
Author(s):  
Nico M. van Dijk
Keyword(s):  
Markov Chains ◽  
Error Bound ◽  
Error Bounds ◽  
Continuous Time ◽  
Transition Probabilities ◽  
Practical Interest ◽  
Occupation Times ◽  
Continuous Time Markov Chains ◽  
Elegant Method ◽  
Comparison Relation

Recently, Ross [1] proposed an elegant method of approximating transition probabilities and mean occupation times in continuous-time Markov chains based upon recursively inspecting the process at exponential times. The method turned out to be amazingly efficient for the examples investigated. However, no formal rough error bound was provided. Any error bound even though robust is of practical interest in engineering (e.g., for determining truncation criteria or setting up an experiment). This note primarily aims to show that by a simple and standard comparison relation a rough error bound of the method is secured. Also, some alternative approximations are inspected.

Approximate Decoupling of the Equations of Motion of Linear Underdamped Systems

1988 ◽  
Vol 55 (3) ◽  
pp. 716-720 ◽  
Author(s):  
S. M. Shahruz ◽  
F. Ma
Keyword(s):  
Linear System ◽  
Error Bound ◽  
Error Bounds ◽  
Equations Of Motion ◽  
Diagonal Matrix ◽  
Common Procedure ◽  
Damping Matrix ◽  
Diagonally Dominant

One common procedure in the solution of a normalized damped linear system with small off-diagonal damping elements is to replace the normalized damping matrix by a selected diagonal matrix. The extent of approximation introduced by this method of decoupling the system is evaluated, and tight error bounds are derived. Moreover, if the normalized damping matrix is diagonally dominant, it is shown that decoupling the system by neglecting the off-diagonal elements indeed minimizes the error bound.

scholarly journals Quantile Regression Learning with Coefficient Dependent lq-Regularizer

2018 ◽  
Vol 173 ◽  
pp. 03033
Author(s):  
Pengju Sun ◽  
Meng Li ◽  
Hongwei Sun
Keyword(s):  
Quantile Regression ◽  
Error Bounds ◽  
Convergence Rates ◽  
Learning Algorithms ◽  
Concentration Inequality ◽  
Decomposition Techniques ◽  
Conditional Quantile ◽  
Pinball Loss ◽  
Regression Learning ◽  
Operator Decomposition

In this paper, We focus on conditional quantile regression learning algorithms based on the pinball loss and lq-regularizer with 1≤q≤2. Our main goal is to study the consistency of this kind of regularized quantile regression learning. With concentration inequality and operator decomposition techniques, we obtained satisfied error bounds and convergence rates.

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